DOCUMENT RESUME

ED 083 932 HE 004 802

AUTHOR Tallman, B. M.; Newton, R. D.TITLE A Student Flow Model for Projection of Enrollment in

a Multi-Campus University.INSTITUTION Pennsylvania State Univ., University Park. Office of

Budcot and Planning.PUB DATE 24 Jul 73NOTE 1C p.

EDRS PRICE MF-$0.65 HC-$6.58DESCRIPTORS Campuses; College Students; *Enrollment Projections;

*Enrollment Trends; *Higher Education; *Models;Simulation; State Universities; *StudentEnrollment

ABSTRACTT: is report is concerned with the development of a

model for projecting the enrollments of The Pennsylvania StateUniversity by simulating the flow of students through the campusesand colleges of which the institution is composed. Because itconcerns a twenty-two campus system of a single university, it notonly constitutes an institutional application but also represents aprototype of a state-system of higher education. Markovian inconcept, the model is based upon the premise that at a point in timea given group of students, possessing a set ofinstitutionally-assigned characteristics distinguishing them asunique from all others, has an associated set of probabilities, whichdescribe their distribution at the next point in time among similarsets of unique categorizations. When suitably classified enrollmentsat one point in time are provided as input to such a model andmultiplied by appropriate sets of probability distributions, theoutput constitutes a projection of enrollments at the next point intime. (Author)

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A STUDENT FLOW MODEL

FOR PROJECTION OF ENROLLMENT

IN A MULTI-CAMPUS UNIVERSITY

B. M. Tallman and R. D. Newton

July 24, 1973

Operations ResearchOffice of Budget and Planning

The Pennsylvania State UniversityUniversity Park, Pennsylvania 16802

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

SUMMARY

II: INTRODUCTION

CONCEPTUALIZATION

PAGE

iv

Markov Process III- 1

Mode) Formulation III- 2

Transition Matrix III- 3

Projection Model III- 9

Mathematical Relationship III-11

IV: DEVELOPMENT IV- 1

Criteria for Structure IV- 1

Categorization of Students IV- 3

Location IV- 4

Academic Level IV- 5

Fields of Specialization IV- 5

Data Requirements IV-13

Associate and Baccalaureate Transition Matrices IV-14

Empirical Relationship for Adjunct Enrollment IV-17

Regression Equations for Graduate Enrollment IV-20

Organization Matrix IV-20

V: PROJECTION MODEL V- 1

ComponentsInput

OperationOutput

Detailed OutputSummary Output

Evaluation

V- 1

V- 2

V- 3V- 5V- 5

V- 6V-12

VI: SYSTEM APPLICATION VI- 1

Components

COEF-1 ModuleITER-1 ModuleDISAG-1 Module

Cost of Operation

i i

VI- 2VI- 2VI- 2

VI- 4VI- 4

TABLE OF CONTENTS (cowihued)PAGE

VII: FUTURE EFFORTS VII- I

Projection of Transition RatesInter-Campus Student FlowGraduate and Adjunct Enrollment MethodologyOrganization Matrix

REFERENCES

APPENDIX A: COEF-1 ModuleAPPENDIX B: ITER-1 ModuleAPPENDIX C: DISAG-1 Module

Ref- 1

A- 1

B- 1

C- 1

LIST OF TABLESTABLE PAGE

III-1 Illustrative Example of Distribution of Enrollment inOrigin State Among Terminal States

III-2 Illustrative Example of Transition Rates BetweenOrigin and Terminal States

III-3 Illustrative Example of Projection Model

IV-1 Campuses

IV-2 Hierarchy of Academic Levels

IV-3 Hierarchy of Fields of Specialization

IV-4 Fields in SMART Record Used to Categorize Studentsat Each Fall Term

V-1 Detail of Projected Fall Term 1975 Resident EducationEnrollment - University Park Campus

V-2 Summary of Projected Fall Term 1975 Resident EducationEnrollment The Pennsylvania State University

V-3 Comparison of Actual and Projected Fall Term 1972Enrollment By Campus

V-4 Comparison of Actual and Projected Fall Term 1972 Enroll-ment By Administrative Division

V-5 Comparison of Actual and Projected Fall Term 1972 Enroll-ment By Degree-Level Within Administrative Division

VI-1 Operating Characteristics

iv

III- 8

IV-18

V-17

VI- 5

FIGURE

III-1

LIST OF FIGURESPAGE

Illustrative Example of the Flow of Students From OneOrigin State to All Possible Terminal States III- 5

111-2 Illustrative Example of the Flow of Students From AllOrigin States to All Possible Terminal States III- 7

IV -.I Interrelationships Among Transition Matrix Vectors IV-16

V-1 Schematic Diagram of Steps in Enrollment ProjectionProcess V- 4

VI-1 Flow Diagram of Module Interrelationships VI- 3

A-1 Macro Flow Chart for COEF-1 Module A- 3

B-1 Macro Flow Chart for ITER-1 Module B- 14

C-1 Macro Flow Chart for DISAG-1 Module C- 4

v

I: SUMMARY

The patterns of movement of students in a multi-campus institution of

higher education have a significant impact upon the magnitude and major pro-

gram composition of the enrollment at any one location. Inasmuch as the

size and make-up of the student body are determinants of the demand for in-

structional services, it is of major importance that the institution be able

to measure and predict these patterns of flow and to reflect them in their

projections of enrollment.

This report is concerned with the development of a model designated

as SFM-1 for projecting the enrollments of The Pennsylvania State Uni-

versity by simulating the flow of students through the campuses and colleges

of which the institution is composed. Conceptually, it is based upon the

premise that at a point in time a given group of students, possessing a set

of institutionally-assigned characteristics distinguishing them as unique

from all others, has an associated set of probabilities, which describe their

distribution at the next point in time among similar sets of unique categoriza-

tions. When suitably classified enrollments at one point in time are provided

as input to such a model and multiplied by appropriate sets of probability

distributions, the output constitutes a projection of enrollments at the next

point in time.

Models of this type are categorized as Markovian in formulation. Although

conceptually accepted by the higher educational community as an improved method-

ology for projecting enrollments, applications are few in number and even fewer

in those cases involving not only movement within a given location but among

1-2

different locations as well. The model described in this report bears a

resemblance to two previously formulated models of state-systems of higher

education encompassing the aspect of inter-campus flow, but it differs from

both in that it provides a much ' her level of disaggregation making it

suitable for both system-wide as well as campus management. oecause it con-

cerns a twenty-two campus system of a single university, it not only constitutes

an institutional application but also represents a prototype of a state-system

of higher education.

The work was conducted principally between December 1971 and August 1972.

It has resulted in a system, utilizing the existing records of the University

and the facilities of the Computation Center, which is capable, given a fore-

cast of admissions, of generating a ten-year projection of Fall term enrollment

by campus, degree-level, student-level, college, and department at a computa-

tional cost of $35 with an annual updating expense of $110. The projections

one year into the future are accurate within 0.5% when measured on a system-

wide basis and within 4% when the sum of differences without regard for sign

between the actual and projected enrollments by campus are expressed as a

percent of total enrollment.

In practice the Student Flow Model may serve several purposes. First,

in conjunction with the Admissions Model it provides an efficient way to

project future enrollments. Secondly, the output from the model when employ-

ed as input to the Instructional Activity Model generates projections of the

demand for instructional activity. And lastly, the model may ultimately

serve as an essential part of a total simulation model of the University.

II: INTRODUCTION

The ways in which students move through and from a system of higher

education - progressing in academic level, changing their fields of

specialization, transferring to new locations, withdrawing, and graduat-

ing are major determinants of both the magnitude and composition of the

demand imposed upon the institution for instructional services. Within

a college or university, the demand for instructional services can be

related to the enrollment of students at various academic levels in dif-

ferent curricula. Consequently, projections of enrollment similarly

disaggregated are requisite for providing adequate lead time to assure

the allocation of resources in an efficient and effective manner.

Although an institution and indeed the educational community at

large may influence the patterns of student movement, it does not con-

trol them. Once admitted, the initiative passes to the student and it is

the institution which must respond to the varying patterns of movement

during the period of attendance. Consequently, it is of major importance

that the institution be-able to measure and predict these patterns well

in advance of their occurrence and to reflect then in their projections

of enrollment.

For this reason considerable interest in recent years has been shown

in the use of what is characterized as the Markov process for describing

the flow of students through an educational system. The Markov process

is based upon the premise that at a point in time a given group of in-

dividuals possessing a set of characteristics categorizing them as unique

11-2

from all other groups - such as sophomore engineering students - has

an associated set of transition probabilities, which in turn describes

the status of the group at the next point in time - such as 80P: will

be junior engineering students, 5% :viii have transferred to another cur-

riculum, 5% will have withdrawn, etc. Using historical data, it is

possible to construct sets of transition probabilities, measuring the

distribution of students in each origin state among all possible ...erminal

states and to use these values as a vehicle for projecting enrollments

from one point in time to the next.

Although conceptually accepted, there have been relatively few ap-

plications using a Markovian approach for projecting enrollments. With

the exception of one by Gani (3) in :963 concerning the projections of

enrollment in the Australian system of higher education, all were reported

around the turn between the last and current decades. Models for simulat-

ing aggregate enrollments at each major level of national systems of

education were devised by Thonstad (15) and Zabrowski (16). Additionally,

the technique was adopted to describe student-flows within the framework

of resource simulation models for institutions of higher education by

Koenig et al. (5) and Firmin (2) and to evaluate admission and enrollment

options by Smith (12), Marshall (8), and Oliver et al. (TO).

Of particular note, because they reflect the movement of students not

only within an institution but also among different locations, are two other

applications. The first is the HEED model, designed and implemented by the

Office of Program Planning and Fiscal Management (4) in the State of Wash-

ington to simulate the flows of undergraduate students by various academic

levels within a state-wide system of higher education. The other, similar

in concept but providing an additional dimension to the categorization of

students, namely that of broadly defined disciplines of study, is a model

I1-3

developed and pilot-tested by Baisuck et al. (1) of the Rensselaer Research

Corporation for the New York State iducation Departr-wnt. but apparently not

implemented For routine application by its sponscrs.

Of more recent origin, NCHEMS, recognizing the inherent importance of

enrollment projections upon resource management. initiated a program to

develop an institutional student-flw model (7). Availability of this model

is currently anticipated by the beginning of 1974.

At The Pennsylvania State University, a model was developed in 1968 by

Newton (9) employing a Markovian concept of student-flow for projecting

system-wide enrollments by academic level and college, but its utility was

limited by inadequate specification of inter-campus flows. Later research

conducted by Richard (11) provided evidence that different sources of in-

coming students need not be categorized separately for establishing their

subsequent patterns of behavior. Both of these investigations provided

insight for defining the design specifications of the model described in

this report.

The model described in this report is concerned with projecting thc.

enrollments in an institution of higher education by simulating the flow

of students within and from the institution. Explicit in its use is the

availability for input of a forecast of admissions into the institution.

It is principally Markovian in concept, although it has been necessary to

rely on other techniques at least on a transitory basis in order to cir-

cumvent certain informational limitations. As such it is not methodologically

unique. What is unique about the model, which has been designated as SFM -1,

is that it depicts student-flow within as well as among the twenty-two campuses

of The Pennsylvania State University. Consequently, it bears a resemblance

to both the HEEP and Rensselaer models, but differs from both in that it is

more highly disaggregated, making it suitable for institutional as well as

campus management. Be,..ause it concerns a twenty-lwo campus system of a

single university, it also represents a prototype application of a state-

system of higher education.

Successful pursuit of efforts of this type bre dependent upon the

contributing roles played by a number of individuals and this project is

not an exception. Several of these are of particular note. .Even within

an educational institution, acceptance of the need to break new ground

can be a frustrating experience and for their support in nothing more

tangible than a conceptualized goal we are indebted to both C. G. Norris

and P. M. Etters. For their patient counsel and response to a myriad of

questions in the process of design, recognition is due W. R. Haffner and

A. W. Tyson. Lastly and of major significance is the contribution of C.

A. Lindsay made years before work even began on the model; had he not

taken the initiative in the middle 1960's in the development of what still

must be regarded as a remarkable concept for maintenance of chronological

records of student progression, the essential data for construction of the

Student Flow Model would have been lacking.

III: CONCEPTUALIZATION

In the previous chapter, it was stated

that in a muLti-campu4 nstitution 06 UgheA educati.on,

the pattenivs 06 ;student movement among academic Cevets,

4iacts 04 6peulaUzation, and campuzu have a 6ign,(16icant

impact upon the magnitude and ajot-ptogtam composition

the enAotement at any one Location.

In this chapter it will be shown how these flows of students may be

conceptualized in a form analogous to what is characterized as a Markov pro-

cess, which in turn may be used as the basis for development of a model for

projecting enrollments in an institution of higher education.

MARKOV PROCESS

A Markov process is a discrete time system characterized by a set of

probabilities, one for each of the transitions from each origin state to

each of the possible terminal states at the next juncture in time. Between

two states, the transition probabilities or rates are assumed to be depen-

dent'only upon the origin state. If these rates, as measured from historical

observations, are constant over time, they may be employed as the basis for

projecting the flow from an origin state to each of the possible states at

the next point in time.

The flow of students within and from an educational institution is analo-

gous to a Markovian process. At any point in time, such as the start of a

term, semester, or academic year, students may be categorized into states or

common groups in accord with some measure of their academic level first year,

III-2

second year, etc. and associate degree, baccalaureate degree, etc. within

their fields of specialization liberal arts, law, engineering, etc.

within the institution. For a multi-campus institution, an additional

element representing location is added to the dimensional characteristics

of each category. For each group of students having a unique combination of

these characteristics, there exists a set of probabilities which describe

their distribution among all possible states at the next point in time. The

utility of a Markov-type model for projecting student-flows lies in the fact

that when enrollments, suitably categorized into common states at one point

in time, are multiplied by the appropriate transition rates the result is a

projection of the enrollments similarly categorized for the next point in

time.

MODEL FORMULATION

In order to formulate a student-flow model in a form analogous to a Markov-

type process, it is necessary to have available chronological records of

students containing at calendar-identifiable points in time each student's

academic level, field oc study and, for a multi-campus institution, location.

From such a record it is possible to determine

1: at some historical point in time, such as the start of

the Fall term, the enrollment of students suitably

categorized in accord with unique combinations of aca-

demic level, field of study, and location;

2: For the students categorized into each of these origin

states, the enrollments at the next point in time, such

as the following Fall term, in each suitably categorized

terminal state; and

3: by dividing the enrollment in each terminal state by that

appropriate to its origin state, to develop a set of tran-

sition rates.

III-3

The model operates on the assumption that the future enrollment is

derived through the probabilities of students moving between two defined

points in time from one state to other states. These probabilities are

expressed by means of the transition rates. Once a student enters the

system, there is a limited number of optional paths in which he can move

from year to year. Once he is admitted to the institutional system, the

individual either moves from state to state until he graduates or with-

draws.

Transition Matrix

For illustrative purposes, a hypothetical example has been devised to

show how data of the type described may be developed and used to compile the

probability rates comprising a transition matrix. In order to simplify the

discussion, the example is limited in scope to a single-campus institution.

Let us assume that a hypothetical institution has students enrolled in two

different fields of specialization Letters and Applied Sciences and at

two student-levels first and second year within an associate degree-

level program. Under such a structure, all returning and new students must

be categorized within one of the following four origin states:

Letters 1st year

Letters - 2nd year

Applied Sciences 1st year

Applied Sciences 2nd year

One year later, all of these students must be categorized within one of the

following six terminal states:

Letters 1st year

Letters 2nd year

Applied Sciences ist year

Applied Sciences 2nd year

Graduated

Withdrawn

Let us furthermore assume that, from an appropriate record source, we

can determine that it a point in time, such as the Fall term of 1970, there

were 100 students enrolled as first-year students in Letters. One year

later, in the Fall of 1971, these same students were distributed as follows:

10 in first-year Letters, 60 in second-year Letters, 10 in first-year Applied

Sciences, and 5 in second-year Applied Sciences. In addition, 15 had with-

drawn from attendance in the institution. The flow of students between the

one origin state and all possible terminal states during these two points

in time may be symbolically described as shown in Figure III-1. In order

to determine the transition rates between the origin and terminal states,

the enrollment in each terminal state is divided by the enrollment in their

common origin state. For the case under consideration, the computed rates

Letween each pair of states is shown on the arrows depicting the flow of

students in Figure III-I. As will be noted, these fractions account for

the entire flow from the crigin state to all possible terminal states be-

tween the two points in time. As a consequence, the summation of the rates

from any one origin state must be equal to 1.0.

FIGURE 111-1

ILLUSTRATIVE EXAMPLE OF THE FLOW OF STUDENTS

FROM ONE ORIGIN STATE TO ALL POSSIBLE TERMINAL STATES

ORIGINSTATE

TERMINALSTATES

III-6

In a similar manner, the various flows of students in the hypothetical

institution between each of the origin states and each of the possible ter-

minal states at their respective sequential points in time may be depicted

as shown in Figure III-2. The distribution of the enrollment in each origin

state among all possible terminal states for the illustrative example is shown

in Table III-1 and the appropriately calculated transition rates are listed

in Table III-2.

FIGURE III-2

ILLUSTRATIVE EXAMPLE OF THE FLOW OF STUDENTS FROM ALL ORIGIN

STATES TO ALL POSSIBLE TERMINAL STATES

ORIGINSTATES

Letters1st Year

App.Sci.

1st Year

TERMINALSTATES

Letters1st Year

Letters2nd Year

App.Sci.

1st Year

Letters2nd Year

App.Sci.2nd Year

Graduate

App.Sci.

2nd Year ithdraw

TABLE III-1

ILLUSTRATIVE EXAMPLE OF DISTRIBUTION OF ENROLLMENT IN ORIGIN STATE AMONG TERMINAL STATES

Origin

Enrollment At Terminal State

State

Enrollment

Letters-I

Letters-2

App. Sci.-1

App. Sci.-1

Grad.

Withdraw

Letters-1

100

10

60

lo

515

Letters-2

55

3.47

5

App. Sci.-1

50

I4

525

15

App. Sci.-2

35

525

5

Origin

State

TABLE III-2

ILLUSTRATIVE EXAMPLE OF TRANSITION RATES BETWEEN ORIGIN AND TERMINAL STATES

Transition Rates To

Letters-1

Letters-2

App. Sci.-1

App. Sci.-2

Grad.

Withdraw.

Letters-1

.100

.600

.100

.050

.150

Letters-2

.055

.855

.090

App. Sci.-1

.020

.080

.100

.500

.300

App. Sci.-2

.143

.714

.143

111-9

Projection Model

Provided that the rates comprising the transition matrix are stable over

time, it may be employed together with the enrollment of returning students

and a given forecast of new admissions at one point in time to generate pro-

jections of the enrollment of returning students at the next point in time.

This is done by multiplying the sum of enrollment of returning students and

of new admissions for each year by the appropriate rates in the transition

matrix and then aggregating the products over common states to derive the

enrollment of returning students for the following period of time. The

process is then repeated in an iterative mode until projections are develop-

ed for the entire projected time-frame.

To illustrate in tabular form how the process proceeds in an iterative

fashion, assume for the hypothetical institution an input of returning stu-

dents for time-period 1 and forecasts of new admissions for time-periods 1,

2, and 3 and the applicability of the transition matrix shown in Table 111-2.

The steps involved in developing enrollment projections for three time-periods

are depicted in Table 111-3.

The number of possible student-flows has been limited in this example

in order to illustrate diagramatically as well as computationally the steps

involved in the projection process. However, conceptually the steps des-

cribed in the example are equally applicable to any student-flow problem

regardless of the number of dimensions academic levels, fields of specializa-

tion, and locations used to describe origin and terminal states.

(INPUT)

(OUTPUT)

-1

rEnrollment at TiMe=1

New

Return

Total

Letters-1

110

+10

=120

x

Letters-2

5+

75

=80

x

Ap.Sci.-1

60

+20

=80

x

Ap.Sci.-2

2+

58

=60

x

Enrollment at Time=2

New

Return AC Total

Letters-1

120

+14

=134

Letters-2

10

78

=88

Ap.Sci.-1

80

25

=105

Ap.Sci.-2

10

+54

=64

Enrollment at Time=3

New

Return Alic Total

Letters-1

125

+15

=130

Letters-2

5+

89

=94

Ap.Sci.-1

100

29

=129

Ap.Sci.-2

10

68

=78

TABLE III-3

ILLUSTRATIVE EXAMPLE OF PROJECTION MOOEL

(TRANSITION MATRIX)

Transition Rates

Letters-1

Letters-2

.100

.600

.020

.080

Ap.Sci.-1

Ap.Sci.-2

.100

.050

.055

.100

.500

.143

Transition Rates

Grad.

Withdraw

.150

.855

.090

.300

.714

.143

Letters-1

Letters-2

.100

.600

.020

.080

Ap.Sci.-1

Ap.Sci.-2

.100

.050

.055

.100

.500

.143

Grad.

Withdraw

.150

.855

.090

.300

.714

.143

Returning Enrollment for Time=2

Letters-1

Letters-2

Ap.Sci.-1

Ap.Sci.-1

Grad.

Withdraw

=12

72

12

618

=5

68

7

=2

68

4o24

943

8

14

78

25

54

111

57

Returning Enrollment for Time=3

Letters-1

Letters-2

Ap.Sci.-1

Ap.Sci-1

Grad.

Withdraw

1381

13

720

575

8

28

11

52

32

946

9

15

89

29

68

121

69

MATHEMATICAL RELATIONSHIP

Mathematically the enrollment at some point in time may be projected

from a prior point in time by means of the following relationship:

mE. = E E. + N. for j = 1, 2 m

o

j,t +l .

=1j(i),t j,t+1 (1)

where: Ej,t+1 = student enrollment in year t+1 in terminal state j,

where j defines a unique set of characteristics common

to all students in that terminal state.

Ej(i),t = student enrollment in year t in origin state i who move

to terminal state j in year t+1, where i and j define

sets of characteristics common to all students in each

of the respective states.

Nj,t+, = new students entering the system in year t+1 in state j.

Since Ej represents measures of the flows between origin state i and

terminal state j of students already in attendance, transition rates express-

ing the distribution of students in state i among state j may be computed

from historical data as follows:

fij = E.(i),t for j= 1, 2 m (2)

Ei,t-1

where:j

f.o

= transition rate of students between origin state i and ter-

minal state j.

Therefore, Equation 1 may be expressed as follows:

mE. = E f.. E. + N. for j= 1, 2 ... mj,t+1 i=1 tj 1,t j,t +l (3)

IV-I

IV: DEVELOPMENT

In the previous chapters, it was shown

1: that in a multi-campws iutitution o6 highert

education, the patteA4 o6 student movement

among academic &vets, o6 zpeciatiza-

tion, and camptau have a 4igni6icant impact

upon the mcgnitude and majors-p4ogliam compo4i-

tion oi6 ennottment at any one Location, and

2: that thue patteku o6 movement may be ductibed

by ze,ts o6 tnamition 4atez exp4e44ing the puba-

bititiez o6 4tudent6 6ottowing vaitiou's pathis

between ,succe,66ive pointA in time.

This chapter is concerned with establishment of a suitable base of

historical data from which the transition matrices as well as ancillary

relationships may be developed for incorporation with a model for pro-

jecting student-flow for a large multi-campus institution, namely The

Pennsylvania State University.

CRITERIA FOR STRUCTURE

Inasmuch as the composition of the output from a model is dependent

upon both the structure of the model and the data used to develop it, a

delineation of required output constitutes the initial step in design.

This is necessary to assure the utility of a model as a vehicle for sup-

plying both explicit and perceived informational needs.

IV-2

At The Pennsylvania State Univer..iiy. admi.o.inn. are planned by mean

of an iterative process, involving the generation of enrollment projections

for a series of options concerning the magnitude and composition of ad-

missions with subsequent selection for implementation of the one option

which produces an enrollment projection reflectirg the greatest consistency

with that representing both policy and resource constraints. This pro-

jection of enrollment is then employed as the basic input to the procedures

employed for developing the University's internal budget and for preparation

of documents in support of the appropriation request to the Commonwealth.

Although the contents of the projection output required for these three

interrelated processes differ from one another, any model from which they

are derived must possess a commonality of base to provide assurance of

consistency.

For the iterative process involved in planning admissions and enroll-

ments, the enrollment projections must be displayed in a disaggregated form

by campus and by degree-level in the initial phase of testing various optional

levels of admission. Once the resulting enrollments are in general alignment

with policy and resource constraints, further disaggregation by degree-level

and in the case of the University Park Campus by college or category of en-

rollment is usually required.

For application to the internal budgetary process, projections of enroll-

ment are used both as a direct as well as an indirect - input with the latter

involving subsequent use ;n a.riving instructional activity consumption and

production from the instructional Activity Model. As a direct input, the

levels of disaggregation required of enrollment projections in the final

stage of the admission and enrollment planning process satisfy the require-

ments of budgetary responsibility, which currently rests at the so-called

administrative-division level. However, for analytical purposes, the enroll-

IV-3

ments are further subdivided by department for the University Park and

Capitol Campuses as well as the Hershey Medical Center and by college for

the balance of the campuses in the system.

At the present time, in support of the University's appropriation re-

quest to the Commonwealth both PPBS and formula submissions are required.

Currently enrollment projections on a head-count basis are not required for

these submissions. They do, however, represent an indirect input since they

are employed in the Instructional Activity Model to derive instructional

activity consumption and production values, which are inherent parts of both

sets of documents, and to derive projections of degrees-awarded by HEGIS

discipline-division in the case of the PPBS process.

For the three interrelated processes, there is consistency in the con-

tent required of enrollment projections with respect to campus, degree-level,

and student-level. Although somewhat of a dichotomy does exist concerning

the level of aggregation required for specifying fields of specialization,

the need to delineate these fields at the departmental level for certain

campuses of the University and at the HEGIS discipline-division level for

the PPBS submission makes it necessary to produce enrollment projections

for all campuses at the departmental level of specialization.

CATEGORIZATION OF STUDENTS

In accord with the broad criteria adopted for assessing the utility

of enrollment projections in relation to both internal and external needs,

students are categorized in accord with attributes identifying physical.

location, academic level, and field of specialization. Physical location

is denoted by campus, academic level by degree-level and within same where

appropriate, by student-level, and field of specialization by college or

category of enrollment and, within same where appropriate, by departmental

responsibility for major programs of study. All measurements of the number

IV-4

of students within each category arc in terms of head-count enrollments

applicable to the Fall term of each academic year.

Location

Twenty-five geographical identities are currently employed to classify

the locations of attendance for the resident education function of the Uni-

versity. These encompass the twenty-two campuses and centers of the University

as well as three other geographical identities which are essentially extensions

of programs administered by organizational units at the University Park Campus.

For this reason the latter three involving the nursing program conducted

at selected hospitals, graduate students registered for off-campus research,

and students enrolled in the study-abroad program are included for pur-

poses of classifying enrollments as part of University Park Campus. Shown

below are the twenty-two locations adopted for use in categorizing students.

TABLE IV-1

CAMPUSES

Allentown CenterAltoona CampusBeaver CampusBehrend CampusBerks CampusCapitol CampusDelaware County CampusDuBois CampusFayette CampusHazleton CampusHershey Medical CenterKing of Prussia Graduate CenterMcKeesport CampusMont Alto CampusNew Kensington CampusOgontz CampusSchuylkill CampusShenango Valley CampusUniversity Park CampusWilkes-Barre CampusWorthington-Scranton CampusYork Campus

IV-5

Academic Level

Within the hierarchy conceived and used to describe the academic levels

of students, students may be categorized from the standpoint of degree-

level associate, baccalaureate, etc. and within certain of these by

student-level first year, second year, etc. The relationships between

these measures of academic level are shown in Table IV-2.

TABLE IV-2

HIERARCHY OF ACADEMIC LEVELS

DEGREE-LEVEL STUDENT -LEVEL

Associate 1

2

Baccalaureate 1

2

3

4 & 5

Graduate 1

2 or more

Adjunct Not Applicable

For the application under review, students are classified by degree-

level and within same by student-level with one exception. The specific

exception concerns suppression of student-level within the graduate degree-

level, an expedient necessitated by current data limitations.

Fields of Specialization

Within the hierarchy used to describe fields of specialization, most

students may be categorized in accord with the specific major program of

study in which they are enrolled, the department having responsibility for

the curriculum, content of the program, or the college in which the depart-

ment is situated for organizational and fiscal purposes. For application

to the Student Flow Model, student categorization by field of specialization

111-6

is limited to the aggregations of majors at the college and departmental

organization levels. Although subdivision by major program was conceived

as a desirable goal, it was considered to be infeasible to derive reliable

projections of enrollment by major at each student-level. It was necessary

to impose this limitation because of the very small numbers of students

enrolled in most majors and frequently exhibiting random patterns over

time at many of the campuses of which the University system is composed.

In addition to the eleven colleges offering degree programs at one or

more degree-levels, there are four administrative categories in which a

student may be classifies' for purposes of enrollment. These categories

of enrollment are Division of Counseling, Capitol Campus, Inter-College,

and Non-Degree. For undergraduate study, a student's program is ad-

ministered by the Division of Counseling if he has not selected a major

for study. At the Capitol Campus, the responsibility for undergraduate

majors rests with the faculty at that location and the same is true for

the preponderance of graduate programs. Students in interdisciplinary

programs are classified within the Inter-College category for purposes of

enrollment. A student will be assigned non-degree status for purposes of

enrollment categorization if he has been admitted to the Graduate School

but has not selected a field of study or if he has simply adjunct status.

Within each of the eleven colleges as well as the Capitol Campus and

Inter-College categories, a further subdivision of major program assign-

ment may be made to departmental units.

Shown in Table IV-3 are the colleges or categories of enrollment

and, where applicable within same, the departments adopted for classify-

ing students in accord with their fields of specialization, together with

the appropriate five-digit budget code used internally by the University

IV-7

for resource assignment. In addition is shown for each department the

HEGIS discipline-division code applicable to the preponderance of major

programs within its area of responsibility.

TABLE IV-3

HIERARCHY OF FIELDS OF SPECIALIZATION'

College of Category of Enrollment

DEPARTMENT OF ENROLLMENT

HEGIS CODE

Name

Budget

Bacc.

Assoc.

College of Agriculture

Agricultural Economics

204-08

01

54

Agricultural Education

204-10

08

55

Agricultural Engineering

204-12

09

53

Entomology

204-13

04

54

Agronomy

204-15

01

54

Plant Pathology

204-16

04

54

Animal Science

204-17

01

54

Dairy Science

204-37

01

54

Forestry

204-53

01

54

Horticulture

204-66

01

54

Poultry Science

204-77

01

54

Veterinary Science

204-88

04

54

Inter-Department

204-00

01

54

College of Arts and Architecture

General Education

205-07

10

50

Architecture

205-11

02

53

Art History

205-14

10

50

Landscape Architecture

205-33

02

53

Music

205-38

10

50

Art

205-44

10

50

Theatre

205-48

10

50

Inter-Department

205-00

10

50

College of Business Administration

Accounting

206-11

05

50

Business Logistics

206-15

05

50

Finance

206-19

05

50

Insurance and Real Estate

206-24

05

50

Management Science

206-35

05

50

Marketing

206-36

05

50

Inter-Department

206-00

05

50

Status at end of 1971-72 Academic Year.

TABLE IV-3 (continued)

HEGIS CODE

HIERARCHY OF FIELDS OF SPECIALIZATION

DEPARTMENT OF ENROLLMENT

College or Category of Enrollment

Name

Budget

Bacc.

Assoc.

College of Earth and Min. Sciences

Geography

224-12

22

55

Meteorology

224-18

19

53

Geosciences

224-19

19

53

Mineral Economics

224-24

19

53

Mineral Engineering

224-25

09

53

Materials Science and Constitution

224-36&20

09

53

Inter-Department

224-00

19

53

College of Education

Academic Curriculum and Field Exp.

212-06&32

08

55

Art Education

212-08

08

55

Counselor Education

212-09

08

55

Educational Psychology

212-10

08

55

Educational Policy

212-12

08

55

Vocational Education

212-14

08

55

Home Economics Education

212-21

08

55

Music Education

212-24

08

55

Special Education

212-31

08

55

Inter-Department

212-00

08

55

College of Engineering

Aerospace Engineering

205-14

09

53

Architectural Engineering

205-17

09

53

Chemical Engineering

215-19.

09

53

Civil Engineering

215-21

09

53

Electrical Engineering

215-31

09

53

Acoustics

215-33

09

53

Engineering Mechanics

215-37

09

53

Engineering Science

215-38

09

53

Industrial Engineering

215-44

09

53

Mechanical Engineering

215-51

09

53

General Engineering

215-55

09

53

Nuclear Engineering

215-56

09

53

Inter-Department

215-00

09

53

TABLE IV -3 (continued)

HIERARCHY OF FIELDS OF SPECIALIZATION

DEPARTMENT OF ENROLLMENT

HEGIS CODE

College or Category of Enrollment

Name

Budget

Bacc.

Assoc.

College of Health, Physical

Education and Recreation

Instruction

227-11

08

55

College of Human Development

Individual and Family Studies

218-11

13

50

Biological Health

218-12

12

52

Biological. Health, Nursing

218-13

12

52

Community Development

218-14

21

55

Man-Environment Relations

218-15

13

50

Inter-Department

218-00

21

55

College of Liberal Arts

General Education

221-07

15

50

Anthropology

221-12

22

55

Classics

221-15

11

50

Economics

221-18

22

55

English

221-20

15

50

French

221-28

11

50

German

221-31

11

50

History

221-34

22

55

Journalism

221-41

06

50

Labor Studies

221-43

05

50

Linguistics

221-46

15

50

Philosophy

221-51

15

50

Political Science and

Public Administration

221-54&37

22

55

Psychology

221-55

20

55

Religious Studies

221-56

15

50

Slavic

221-59

11

50

Sociology

221-64

22

55

Spanish, Italian, Portugese

221-65

11

50

Speech

221-67

15

50

Inter-Department

221-05

49

50

College or Category of Enrollment

TABLE IV-3 (continued)

HEGIS CODE

HIERARCHY OF FIELDS OF SPECIALIZATION

DEPARTMENT OF ENROLLMENT

Name

Budget

Bacc.

Assoc.

College of Medicine

Anatomy

217-12

04

54

Anesthesiology

217-14

12

52

Comprehensive Medicine

217-15

12

52

Behavioral Science

217-18

12

52

Biological Chemistry

217-22

12

52

Family Medicine

217-25

12

52

Medicine

217-41

12

52

Obstetrics

217-47

12

52

Pathology

217-49

04

54

Pediatrics

217-51

12

52

Pharmacology

217-52

12

52

Psychiatry

217-59

12

52

Radiology

217-62

12

52

Surgery

217-67

12

52

College of Science

General Education

228-07

04

54

Astronomy

228-09

19

53

Biochemistry

228-12

04

54

Biology

228-15

04

54

Chemistry

228-21

19

53

Computer Science

228-28

07

51

Mathematics

228-44

07

51

Microbiology

228-46

04

54

Physics

228-54

19

53

Statistics

228-74

17

53

Division of Counseling

capitol Campus

Humanities, Social Sciences, and

Education

260-10

22

55

Engineering Technology

260-20

09

53

Business Administration

260-30

05

50

Mathematics

260-90

07

51

TABLE IV-3 (continued)

HIERARCHY OF FIELDS OF SPECIALIZATION

College or Category of Enrollment

DEPARTMENT OF ENROLLMENT

HEGIS CODE

Name

Budget

Bacc.

Assoc.

Inter-College

Environmental Pollution Control

231-20

49

50

Regional Planning and Admin.

231-22

49

50

Other Graduate Inter-College

232-01

49

50

Undergraduate Inter-College

231-09

49

50

Non-Degree

IV-13

DATA REQUIREMENTS

In Chapter II, it was stated, that although the Student Flow Model

described in this report was Markovian in concept, it was necessary to

rely on other methodology to circumvent current data limitations.

For projecting ooth associate and baccalaureate degree-level enroll-

ments, which collectively comprise over 80% of the University's resident

education enrollment, the flows of students are developed in accord with

a Markov-type process, as described conceptually in Chapter III. In this

step students were categorized in origin and terminal states in accord

with their campus, degree-level, student-level, and college or category

of enrollment. Although the basic record, from which the data on student

flow were extracted, would have permitted identification of major programs

of study, which in turn could have been aggregated to the departmental

level, this option was not exercised because of the very small enrollments

observed in many of the major programs of study in the various campuses

of the University.

In the current absence of machine-addressable longitudinal records

on both adjunct and graduate degree-level students, it is not possible to

utilize a Markov process as a basis for projecting enrollments of these

two classes of students. For adjunct enrollments it is necessary to employ

an empirical relationship between the number of adjunct students at a campus

and the enrollment of baccalaureate and associate degree-level students.

Graduate enrollment projections are developed from linear regression equa-

tions by college or category of enrollment at each campus.

Further disaggregation of the enrollment projections for all degree-

levels of students by field of specialization from the college to the

departmental level is achieved by use of a so-called Organization Matrix,

which subdivides the college enrollments on the basis of prior history.

IV-l4

In summation the data requirements may be classified in accord with

their application in development of the components of the model as follows:

I: Transition matrices for use in the Markov process

describing the flow of associate and baccalaureate

students.

2: An empirically observed relationship between adjunct

students and undergraduate enrollments.

3: Sets of linear regression equations applicable to

graduate enrollments.

4: An Organization Matrix for disaggregation of enroll-

ments to the departmental level.

Associate and Baccalaureate Transition Matrices

For projecting both associate and baccalaureate degree-level enroll-

ments, four types of transition matrices are developed for use in "moving"

students from each origin state in a Fall term to all possible terminal

states in the next Fall term. These are as follows: Campus, Progression,

Inter-Campus, and Switch Degree.

The Campus Matrix is the basic vehicle by which students are "moved"

from one year to the next within a campus. For each campus at which

associate degree-level programs are offered, there are two such matrices,.

one for each student-level; for campuses offering baccalaureate study there

are four, one for each student-level. Each matrix consists of a series of

vectors one for each college of enrollment in an origin state each of

which in turn is comprised of a set of fractions representing the distribu-

tion to all terminal states. Within each of these college vectors, the

terminal states consist of the colleges of enrollment and additionally

the proportions graduating, withdrawing, switching to the other under-

graduate degree-level, and transferring to another campus.

IV-15

In series with each Campus Matrix is a Progression Matrix, by which

students are retained at the same student-level or advanced to the next

student-level. Each of the vectors, of which the matrix is composed,

consists of the two fractions representing the shares advancing and being

retained.

Two other types of matrices are used to "move" students among campuses.

The first is an Inter-Campus Matrix which, when used in conjunction with

the flow of students through the so-called "transfer-cell" in a vector of

a Campus Matrix, distributes students of the same degree-level among the

campuses. The second is a Switch Degree Matrix which, when used in con-

junction with the flow of students through the so-called "switch-degree"

cell in a vector of a Campus Matrix, not only distributes students among

the campuses but also changes the degree-level of their program of study.

Shown in Figure IV-1 are examples of vectors drawn from the four

types of transition matrices and their relationship to one another in the

student flow process from an origin to a terminal state.

FIGURE IV-1

INTERRELATIONSHIPS AMONG TRANSITION MATRIX VECTORS

ORIGIN STATE

Enrollment -for one campusfor one degree-levelfor nne student-levelfor une college

AGR 0

ALA .000

BA .662

EO .000

ENG .024

HPE .000HO .000

LA .000

EMS .000

SCI .021

00C .026

IC .000

GRAO .000

WO .16

SO .024

TRAN .071

tv-16

CAMPUS

VECTOR RET .029

AOV .071

PROGRESSIONVECTOR AA .000

AN .000BO .167

BS .000BR .083 TERMINAL STATECL .000

IvOE

OS

.000

.167

Enrollment -by campus

AA .000 FE .333 by degree-level

AN .000 HN .000 by student-level

BO .000 MA .083 by college

BS .000 MK .000

BR .000 NK .000

CL .000 02 .000

OE .000 SL .000

OS .000 SN .083

FE .000 SV .000

HN .000 UP .000

MA .000 WS .083

MK .000 YK .000

NK .250 ...02 .000

SLSN

.000

.000

SWITCH OEGREEVECTOR

SV .000

UP .750

W8 .000

YK .000

INTER-CAMPUS

VECTOR

IV-17

These matrices are developed from what is referred to as the Student

Master Research Tape - or SMART - which is a series of longitudinal records

over time of each undergraduate student indicating his term by term status

with respect to degree-level, student-level, major program of study, campus,

and attendance status from the time of admission to graduation or alterna-

tively a maximum of twenty elapsed terms. (6) For the purpose of this

application, only certain of the fields of each term-record on each student

are employed. In Table IV-4 are the appropriate fields within each record

on SMART utilized for developing the transition matrices.

For use with the Student Flow Model, the transition matrices are develop-

ed annually from data applicable to the changes occurring between the most

recent sequential pair of Fall-terms. These values are assumed to be ap-

plicable over the entire projected time-frame. The validity of this

assumption, however, was subject to evaluation prior to its adoption by

generating the matrices for each sequential pair of Fall-terms over the past

seven years and examining the patterns of behavior of corresponding values

over time. The analysis revealed that the transition probabilities for

corresponding categories remained relatively stable when the values were

either relatively large in magnitude (i.e. between 0.5 and 1.0 as contrasted

to less than 0.1) or were computed from relatively large populations of students.

Since both of these conditions contribute to the ability of the model to

generate reasonably accurate projections of enrollment, it was concluded

that the transition rates were sufficiently stable over time to assume

their applicability in the future for purposes of enrollment projection.

Empirical Relationship for Adjunct Enrollment

The projected enrollment of adjunct students is computed by means of

an empirical relationship, which on the basis of historical data was found

to be applicable at all but four campuses. Basically, the relationship is

TABLE IV-4

FIELDS IN SMART RECORD USED TO CATEGORIZE STUDENTS AT EACH FALL TERM

STUDENT CATEGORY

Campus

Degree-Level

NAME OF FIELD

Campus

Degree

CODE IN FIELD

2 character Campus Code

2 for associate

2 for baccalaureate

Student-Level

Term Standing

1-3 for first year

4-6 for second year

7-9 for third year

10 and over for fourth and fifth year

College or Category of Enrollment

College/Major

3 character Major Code

Switch Degree

Legend

8 for associate to baccalaureate

9 for baccalaureate to associate

Withdrawn

Legend

4, 5, or 6

1V-19

based on the observation that, as the enrollment of students at the

associate and baccalaureate degree-levels at a campus increases, the

expression of adjunct enrollment as an equivalent fraction of the as-

sociate and baccalaureate enrollment decreases. Utilizing the fractions

calculated from historical data and the projected enrollments of associate

and baccalaureate degree-level students, adjunct enrollment at a campus

is computed using the following relationship:

ED,ct

= (EA,ct

EB,ct

) (fa

)

where: ED,ct

= adjunct enrollment at campus c in year t

EA,ct

= associate enrollment at campus c in year t

EB,ct

= baccalaureate enrollment at campus c in year t

fa

= adjunct enrollment as a fraction of associate

and baccalaureate enrollment.

The values of fa

for the Altoona and Ogontz Campuses is 0.15 and for

the Fayette and New Kensington Campuses is 0.40. For the balance of

the campuses in the system, the value of fa is related to the combined as-

sociate and baccalaureate degree-level enrollment at

Associate and Baccalaureate Enrollment

the campus as follows:

fa

< 100 .4o

101- 300 .20

301- 500 .10

501- 700 .06

701-1000 .04

1001-2000 .03

>2001 .01

Although the relationship is incorporated within the program logic,

it must be reviewed periodically for applicability.

IV-20

Regression Equations for Graduate Enrollment

Graduate degree-level enrollments are developed from linear regression

equations, which are incorporated within the model and are updated annually

to reflect new data. The equations represent the graduate degree-level

enrollments by college or category of enrollment for each campus of the

University over time. The summation of the extrapolated values for any

one campus at any point in time is subject to normalization relative to

maximum and/or minimum levels of graduate degree-level enrollments permitted

at the particular campus. These maximums and minimums are supplied as in-

put to the model.

Organization Matrix

The Organization Matrices are employed to disaggregate enrollments

in various fields of specialization from the college to the departmental

level. Each matrix consists of a series of vectors - one for each college

or category of enrollment at each student-level within degree-level for each

campus each of which in turn is comprised of a. set of fractions represent-

ing the distribution of a given college's enrollment among the departments

of which it is composed. The Organizational Matrices are updated annually

from the data issued in the Final Distribution of Enrollment Report for the

Fall term.

V-1

V: PROJECTION MODEL

In the previous chapters, it was shown

1: that in a mutti-campuis imtitution o4 highen

education, the pattekivs o4 6tudent movement

among academic tevetz, 4ie2ds c)4 oeciatiza-

tion, and campuza have a 6igni4icant impact

upon the magnitude and majok-ptognam compos i-

tion c)4 the eniLottment at any one tocation,

2: that -these pattenn.s o4 movement may be dacAibed

by uses o4 tAan6i.tion naves expta6ing the

pkobabititia o4 4tudet's 4o22owing vahiou/S

path4 between 6ucca6ive point's in time, and

3: how a 6uitab2e ba4e o4 hatmicat data .may be

compited and used 40A devetopment o4 the6e

matAica.

This chapter is concerned with the use of the components described in

the preyious chapter as an integrated model, which, given the current enroll-

ment and a forecast of new admissions, may be employed to generate projections

of enrollment.

COMPONENTS

The projection model consists of the following major components:

1: A series of transition matrices Campus, Progression,

Inter-Campus, and Switch-Degree - consisting of vectors

of the fractional distribution of undergraduate enrollment

at one origin state campus, degree-level, student-

level, and college or category of enrollment in

the Fall term of one year among all possible terminal

states in the subsequent Fall term.

2: A curvilinear relationship between the number of

associate and baccalaureate degree-level students

at a campus and the equivalent fraction of these

students representing adjunct enrollment.

3: A series of regression equations representing the

enrollment of graduate students over time in each

college or category of enrollment at each campus.

4: A series of Organizational Matrices one for each

student-level within each degree-level at each campus

consisting of vectors of the fractional distribution

of the enrollment in each college or category of

enrollment among the departments responsible for the

major programs of study.

INPUT

V-2

The inputs to the projection model are as follows:

1: Actual Fall term enrollment for the most recent historical

year subdivided by campus, degree-level, student-level

where appropriate, and college or category of enrollment,

as developed from the Final Distribution of Enrollment

Report issued by the Records Office of the Division of

Admissions, Records, and Schedulinc

2: Projections of freshmen admissions for each calendar

year, but expressed in terms of those registered in the

Fall term of the particular year, for as many years as

V-3

desired by campus, degree-level, and college or category

of enrollment, as generated by the Admissions Model (14).

3: Projections of both advanced-standing and adjunct-to-

degree undergraduate admissions as well as undergraduate

readmissions for each calendar year for as many years

as desired by campus, degree-level, student-level, and

college or category of enrollment, as generated by the

Admissions Model (14).

4: Parameters establishing the maximum and minimum levels

of graduate enrollment by campus for each year in the pro-

jected time-frame.

OPERATION

Procedurally the following steps, as schematically depicted in Figure

V-1, are involved in the projection process of the model:

1: The actual associate and baccalaureate degree-level enroll-

ment by campus, student-level, and college of enrollment

for the most recent Fall term is iterated through the Campus,

Progression, Inter-Campus, and Switch-Degree Matrices to

derive the enrollment of returning students in the Fall term

of the first year in the projected time-frame. To these

values are added the forecast of new admissions and of re-

admissions to generate the projected undergraduate degree-level

enrollments for the first year.

2: The projected enrollments for the first year in the time-

frame are then iterated through the matrices to derive

returning students for the second year. To these are added

the forecasts of new admissions and readmissions to generate

projected undergraduate degree-level enrollments for the

second year.

Admissions

Returning Students

FIGURE V-1

SCHEMATIC DIAGRAM OF STEPS IN ENROLLMENT PROJECTION PROCESS

Origin

If/I

citudent

iStudent

EjLevel -1

I1

1Level-2

Associate Level Enrollment By

Campus, Student-Level, & Collegd.

(ASSOCIATE TRANSITION MATRICES)

Returning Students

Admissions

ro

.EStudent

f

E.,Level -1

,

Student

1'Student

Level-2

1(Level -3

I

Student

(Level -3

1BaccalaureatelLevel Enrollment

by Campus, Student-Level, & College

(BACCALAUREATE TRANSITION MATRICES)

Maximum and Minimum Graduate

Enrollment by Campus

Years

(GRADUATE REGRESSION EQUATIONS)

(1) rn

*I)o

__-J

Dept. &IStudent-Level

(ASSOC. ORGANIZATION MATRIX)

//

L.__

. _

(BACC. ORGAINIZATION MATRIX)

Adjunct Enrollment

By Campus

P

(ADJUNCT RELATIONSHIP)

Graduate Level

,By Campus, Student-Level & Con. (GRAD. ORGANIZATION MATRIX)

Enrollment by

Campus,

Degree-Level,

Student-Level,

College, &

Department

11- 5

3: The process is then repeated until undergraduate degree-

level enrollment projections have been developed for

each year in the projected time-frame.

4: For each year in the projected time-frame, adjunct enroll-

ments are computed for each campus using the empirical

relationship provided within the model.

5: For each year in the projected time-frame, graduate en-

rollments by campus and college or category of enrollment

are projected using the regression equations provided within

the model and the input parameters relating to the minimum

and maximum enrollments by campus.

6: The projections of enrollment by college or category of

enrollment for each year in the projected time-frame are

then disaggregated to the departmental level.

OUTPUT

Output from the projection model is of two types. Common to both is a

subdivision of Fall term enrollment for each year in the projected time-frame

by degree-level and within same by student-level wherever appropriate.

Detailed Output

The first of the two types is characterized as detailed output of Fall

term enrollment and contains for each campus an analysis by college or cate-

gory of enrollment as well as department wherever appropriate. In order to

provide further identification of each departmental entity, the internal

five-digit budget and two-digit HEGIS discipline-division codes are also

shown. A sample of this output for one campus and one year is shown in

Table V-1.

V-6

Summary Output

The second type is characterized as summary output. Here the detail

by college and department is suppressed to provide on a single page the

Fall term enrollment by campus for the enti-e University system. A sample

of this output for one year is shown in Table V-2.

.AP

.L.C

I,LT

I!-, r

TABLE V-1:

DETAIL OF PROJECTED FALL TERM 1975

RESIDENT EDUCATION ENROLLMENT - UNIVERSITY PARK CAMPUS

TCTAL

lehl___

Till

-AL:

AS

ST

1

0

AS

ST

1/

7R

AC

C1

142

BA

CC

2

1.36

BA

CC

3

As/

BACC 4

4Q3

GR

AD

AC

J

14k

Ar.QTr. Frn

714-

0301

*0

170

1323

3262

147

Pr.

e11

rniir

204-

10O

F0

C0

3755

5224

168

Ar,

pIr.

Fki

r.20

4-12

CS

0r

0r

1412

033

FNTrmr1"GY

204-11

04

00

00

00

2424

inpr,mnvy

714-

1501

CC

024

2320

3810

5P

LAN

T D

AT

I20

4-1'

_,C

4C

00

00

031

31A

A' i

mA

1S

r i

214-

1701

00

094

105

6438

291

FA

TP

Y S

IT2C

4-'3

701

00

00

0n

1010

F0D

Fci

-Dy

204-

53C

l*0

nn

6011

411

759

35C

proTIC

204-

6601

01

024

3228

1710

1P

LTP

Y s

r T

204-

77C

I0

00

00

03

3V

ET

Sr!

204-

89C

40

00

00

010

10IN

TIP

OF

PT

204-

0 )

01*

C0

307

9791

7728

585

ApT

s_L

AR

EH

'DT AL :

AS

Sr

D

1A

sSr

4

8ACC.

12g

1R

AC

C

Z1

2B

AC

C

Z/2

3B

AC

C

1113_

4m

lAn

_Z42

AC

JT

CT

AL

131:II__

e p rw

705-

1102

00

053

5017

817

298

AP

TII

IST

735-

16IC

00

08

207

8711

7LA

M A

Dr

1320

5-33

070

n0

2747

360

110

v l i

s i

r20

5-18

I C0

00

2422

110

57A

PT

705-

441

C0

DC

I67

7380

4026

0T

HF

AT

DF

205-

491C

0C

064

6747

2720

51N

TF

R D

EP

T70

5-00

100

022

924

04

8233

9

AS

ST

1A

SS

('2

RA

CC

1B

AC

C2

BA

CC

3B

AC

C4

GP

AD

AC

JT

CT

AL

suai

NE

ss A

ru

TU

T91

..:D

0Z

6R443

221

221

331

344_

ArrntINT IN r,

206-

1105

00

04

297

379

067

9'US Lnr.

706-

15C

.0

00

030

740

104

rmaN

cE20

6-19

050

00

040

830

123

1S F

.0

296-

240.

03

J0

3064

094

Por

;T S

r 1

216-

3505

00

14

8912

90

222

NA

DK

ET

IHr,

206-

36C

50

cn

469

11R

021

1T

NT

FP

-nF

DT

706-

0005

00

269

435

436

5537

715

71

Assr 1

TABLE V-1 (continued)

184r.0

7RAU,

3RACC

4GRAD

ACJ

TCTAL

ASSC

2RACC

ErucATIoN

TOTAL:

00

7qt

42i

102

222

1029

332i___

Ar roof)

F.

FF7xo n2-06320F

00

0204

688

645

224

1761

APT Fr

712-08

OF

03

043

74

65

61

240

In PSYr

21?-11

OP

00

01

00

41

41

FD 001 ICY

712-12

C.

C0

065

138

101

194

498

vrr Fr

212-14

CA

00

025

42

28

61

156

HrmF f:Cr 10

212-21

CF

C0

00

00

41

41

muSIC FD

212-24

CF

00

025

32

37

31

125

sorr Fn

212-36

CE

aI

099

74

46

173

392

INTER -DEPT

212-01

Cr'

C0

296

40

11

00

347

rcoN CD

217-09

CP

C0

01

00

194

194

EN.C2INFPI"J

InIAL:

ASSN

0

1ASSC 2

0

3ACC

1

5IQ

RACC 2

4f24

RACC 3

tg/

BACC 4

Grad

GRAD

ACJ

A15

TCTAL

2Z21___

,IrRn plc,

2i9-14

os

C0

14

21

20

17

92

ARCH FNG

215-17

OS

0C

079

42

53

12

186

AGPIC FNG

OS

00

014

14

20

12

60

rHpm FmG

215-19

CS

Cr)

037

77

47

46

207

r1VIL FNG

215-21

CC

03

074

139

131

83

429

FL Fri-

EN

r;215-31

CS

09

093

131

140

59

472

r_tvr mECH

215-37

OS

C0

019

28

33

33

113

FNG SCI

215-1R

CS

00

05

21

20

046

IND FNG

215-44

CS

00

014

42

66

41

163

mFCH FNG

215-51

OS

C0

056

105

113

46

320

CFM FNG

215-55

CS

00

00

00

88

Nun_ FNG

215 -56

cc

C0

019

21

20

37

97

ImTFP-DEPT

215 -00

09

C0

550

4?

70

0599

mEALn- F. Pr

TOTAL!

HPF INSTP4,

227-11

CE*

ASSC 1

ASST 2

0

BACC

1RACC 2

RACC 3

BACC 4

GRAD

ACJ

TCTAL

0laa

70k

Z/c

223

'55

1033

0100

206

275

291

155

1C33

TABLE V-1 (continued)

ASSC

1ASSC

?RACC

1RACC

7RACC

3RACE

4GRA')

ACJ

TCTAL

HumAN QPv

TnIAL°

DQ

212

_IDL

I0I9

254

112

3192___

INr r.

FAm sTun

718-11

11

00

014B

319

244

95

806

P1rL HLTH

218-17

12*

C0

049

75

3R

27

189

PlrA "ORS

211-13

17

C0

n141

117

85

0343

(-rim+.

nFNI

21P-14

21

CC

0194

351

376

0925

YGN-FNVT0

211-15

17*

00

085

702

197

48

532

1mTFR-DFPT

218-00

21

CC

110

85

00

0195

AcSC

1ASS':

7RACC

IRACC

2RACC

1RACC

4GRAD

ACJ

TCTAL

LIEE0AL APTS

MAL:

22

1214

022

11.04

_I5112_

1115A_

4125___

avrIA,Tr,

et_PsSICS

221-12

??1-19

22 11

C 00 C

0 0

11 1

44 A

34 1

53

11

142 15

Ft0MPHICS

221-14

22

00

02

26

34

74

136

FNCLISH

221-24

IF

00

023

133

146

127

429

PO Fmr IA

721-71

11

0C

09

41

16

53

141

CFP1AAN

221-31

11

0C

02

17

15

32

66

HTSTnQY

221-34

22

00

09

84

91

74

257

JCIPMA1 TSm

221-41

OE

(1

C0

25

171

116

53

365

LAR0n STUD

221-43

C5

00

02

26

25

053

LImGOTSTICS

221-46

15

C0

00

10

10

21

41

OHTL1SOPHY

221-51

15

C0

06

32

2T

53

118

Pm_ cc

F.Pus an

221-543722

00

027

288

217

148

680

PSYCHrl OGY

221 -55

2C

00

042

210

185

116

553

prLIG srun

221-56

15

00

07

15

it

21

49

SLAVIC

721-59

11

0C

04

53

11

23

SrCT01n0Y

221-64

22

00

075

172

144

53

394

cr.

IT

r.^OR

221-66

11

0C

072

29

17

42

110

clIFFrm

221-67

15

00

05

60

74

95

234

IMTF14-0FoT

221-05

49

00

1014

7R4

A3R

214

21

2371

AS5C

1ASSC

2RACC

1RACC

2RACC

IRACC

4GRAD

ACJ

TCTAL

usie L u_S

PUPA.:

0Q

132

/U.

12k

lfill_

_iiii

1063___

r,F(GRAPHY

274 -12

22

00

03

46

54

67

vFTF0R0L9GY

224-1R

IS

C0

02R

41

30

58

157

CFrSCIENCES

224-19

IS

00

031

49

37

148

264

"AIM FCC

224-24

If

00

06

22

18

36

82

v1M ENO

724-25

OS

00

047

17

40

58

182

U&T SCT

r.

CoNIST

224-32009*

00

018

43

29

94

184

TmTFP-DFDT

224-01

IS

00

13R

10

00

0148

SEIF"'CF

/OM:

Assr

9

1

TABLE V-1

(continued)

RACC

1

ula

RACC

/51

2RACC

11E2-

3(MCC

21Z-

4GQAO

_522

ADJ

TCTAL

4495-- -

ASST

Q

2

UN FMK:

778 -07

04*

00

865

?63

273

220

27

1648

AST0,1%0mY

228-09

1S

00

n15

12

920

56

810cHEm

228-12

04

n0

045

48

46

68

207

plc' ncY

228-15

04

C0

0210

309

266

41

826

CurRisTey

27A-21

19

00

030

71

46

143

290

row, SrI

228-2R

C7

00

n90

166

129

123

5C7

m.1..4

22A-44

C7

00

021

131

64

102

320

mTron

228-46

C4*

00

053

154

110

27

344

0HYSICs

229-54

15

00

023

24

28

102

177

STATISTICS

778-74

17

00

00

00

27

27

ASSC

ASST

2sac('

1RACC

2RACC

()ACC

4GRAD

ACj

TCTAL

DADA-CA -

THAL:

0a

15c

761

213

15

Q610

ASS!"

1ASST

'RACC

1RACC

2RAC!:

3RACC

4GRAD

ACJ

TCTAL

lAifEzIELL.:Gr

/nTAL'

92

aQ

QQ

152

152

FRA, rrL UNIT

231-20

4S

0()

30

00

12

12

orn pt.

F.

Any

231-22

49*

0C

00

00

32

32

nHy r.E.,, sn

..-:

222-01

C4*

CJ

00

00

88

88

Arrusirtrs

231-xx

oc

n0

00

00

20

20

ASSC 1

ACV- '

BAC(

18ACC 2

RACC 1

RACC 4

GRAD

ACJ

TCTAL

0.1.017.CF.Cprr

IQTAL:

00

Q4

0_2

4/2

4/2--_

ASSC 1

ASST 2

RACC

1RACC ?

RACC 1

BACC 4

GRAD

ACJ

TCTAL

UN1YA "Pg

C94PUS_ICIALS:

011

472/

cwt.}

2125_

/023

5544

'LL

3C36i--

TABLE V-2:

SUMMARY OF PROJECTED FALL TERM 1975 RESIDENT EDUCATION ENROLLMENT - THE PENNSYLVANIA STATE UNIVERSITY

ASSO 1

ASSO 2

BACC 1

BACC 2

BACC 3

BACC 4

GRAD

ADJ

TOTAL

ALIQOAA_

CAmPli_LUIALII

ZAl

_115

_All

A29

70

02221111___

ALLEUIDAu_

LABEUS_IGIALSI__

_a___

2__

__hi

__1/

12

038

134

BFHRFNO

CAMPUS T0TAIS:

122

615

834

500

52'Ja

90

48

1746

LIEBB.1___

LAUPUi TOTAL51

188

__HA__

348

147

_i

a0

30

m__

BEAYER__

LAUEUS_IDIALSI__

22

_HD__

-522_311___

63

039

1031

LAEII

CAMPUS TOTAIS;

_a _________a___

01

_11/5

goa

667

31

2782

UELAAAHE

LAmPus_iorAil.

LL

_12_

582

362

10

20

33

1153

OUBOIS

CAMPUS MIA'S:

114

__HA

_191

fi

____Q

na

47

518

EAYLUE-------"tiella-Lf1TAI S:

137

148

326

179

41

0318

1115

HALLfTON

CAMPUS TOTS

aa

35

449

_127

30

79

770

MnNT_ALI12__

LAMPUS_IOIALS1

_1112

_HA__

221

_lAZ

_l______

00

28

738

tiaiEtHEafil-LAHZ115 ail rAl a:

77

-al__

667

378

10

40

35

1222

NFW KFNIINGTON

claula TOTAiS:

165

-HA__

_aaa

208

-/-_-_

1D___128

1150

OGONTZ

CAMPUS Torposl

Lia

561

0713__

1634

SLWILHILL

LASRUS_I2I4Li2

ill

_____1H__

an

_19A

__1__

Z____

Q_____

36

638

SLEANTD1

LABEUS_MIALSi

1211

____H/__

_111

_Z21

_A

02____

ZE____

_141__

sHumico

LAMEUH_IDIALia_

78

35

116_I

00

47

522

LaiIIA_EARt

LABEUS ILLIALil

a_

__II__

izu

1221

AlZH

/D23

52A4

31111

38366

kilL

li.E

i_ilA

itilE

__LAHEUS_IOIALH1

____112

_55_-

67

__Zil

_____D

_a_

046

277

IDE&

LA8211S IOIALSI__

21

Al_

312

liA

_A___

10

1H

.4212

_BEHHHEY

LAMELM_IOIALSI__

_a

LI--

0_a

a2

Ali_

Q__

_Ali__

&LtJJi Of EUSSIA EAME115_IDIALS.:

_a

___D__

_2

a___2__

___D__

255

11__

255__

ECM STATF UNIMLBSIII QBANQ MEALS'

2482

11111

11435

2222

__9A3A__

7967

.629D

1991

50368

V-12

EVALUATION

Evaluation of the performance of a predictive model usually involves

providing actual historical data as input and comparing the output

with the appropriate historical records. By utilizing such an approach

any variations between the output from the model and historical data may

be attributed to the characteristics of the model itself. However, for

evaluation of the model described in this report, a departure from this

type of procedure has been adopted which actually provides a somewhat more

stringent basis for measurement of validity. Rather than using actual ad-

missions data as input, the output from the Admissions Model (14) was

employed. Thus the evaluation is in reality an evaluation of both the Ad-

missions and Student Flow Models on a combined basis. In brief this approach

was adopted because of the existence of certain empirical relationships,

interfacing between the two models, which essentially translate student

admissions throughout a given calendar year into student registrations

in the Fall term of the same year with an ensuing question arising as to

the proper assignment of these relationships to one of the two models for

purposes of evaluation. Adoption of the combined approach eliminates the

need for what would otherwise be an arbitrary assignment.

For this reason the evaluation was conducted by comparing the actual

1972 enrollments with those projected by the Student Flow Model, which in

turn was provided with input from the Admissions Model containing the

targets and parameters which had been established in January 1972 for

guidance of the admissions process for that calendar year. From a system-

wide standpoint, the total projection of enrollment differed only by 0.5%

from the actual.

However, this value is of limited significance for internal management

application, since it is achieved in part as a result of compensating errors

V-13

in over- and under-projecting the individual sectors of which the University's

total enrollment in resident education is composed. Furthermore, since en-

rollments are ultimately determinants of the demand for instructional services

and it is usually infeasible from an operational view to consider the inter-

change among campuses of resources for the instructional function, the forecast

errors of the campus enrollments are of importance. The differences between

the projected and actual enrollments for each campus are shown in Table V-3.

The summation of these differences, without regard for sign, expressed as

a percentage of the actual enrollment for the total system amounts to 4.0%.

This means that this fraction of the projected enrollment was distributed

among campuses in a manner differing from that which actually occurred.

For evaluation purposes, two other bases may also be of possible interest.

In the report on the Instructional Activity Model (13), it was stated that the

interchange of resources for providing instructional activity was operational-

ly infeasible not only among the campuses but also, in the case of the University's

largest campus at University Park, among colleges. However, errors in the com-

position of the enrollment at any one location are somewhat mitigated in their

impact upon the composition of demand for instructional activity because students

register for courses not only within their own college but in others as well.

Nevertheless, for evaluation purposes there is interest in the forecast errors

among the individual colleges at the University Park Campus and the balance of

the campuses as unitary organizations since collectively these units, which

internally are categorized as administrative divisions, constitute the level

of budgetary responsibility in the University. As shown in Table V-4, the

summation of the differences, without regard for sign, between the actual and

projected enrollments for these units amounts to 7.90 of the actual enroll-

ment for the total system, which implies that this fraction of the enrollment

was distributed by the model among administrative divisions in a manner dif-

fering from that which actually transpired.

TABLE V-3

COMPARISON OF ACTUAL AND PROJECTED FALL-TERM 1972 ENROLLMENT

BY CAMPUS

ENROLLMENT

ACTUAL PROJECTED DIFFERENCE

1,700 1,581 -119212 145 67

1,573 1,626 + 53714 685 29

936 1,023 + 872,190 2,495 +3051,021 871 -150

497 471 26

1,062 960 -102

773 849 + 76749 703 46

1,053 1,041 12

1,026 1,020 6

1,757 1,642 -115

660 727 + 67649 722 + 73550 499 51

396 293 -103564 534 30

301 353 + 52245 341 + 96

28,635 28,921 +266

TOTAL 47,263 47,502 +239 (0.5%)

ABSOLUTE SUM 47,263 1,931 (4.0%)

TABLE V-4

COMPARISON OF ACTUAL AND PROJECTED FALL-TERM 1972 ENROLLMENT

BY ADMINISTRATIVE DIVISION

ENROLLMENT

ACTUAL PROJECTED DIFFERENCE

1,700 1,581 -119212 145 67

1,573 1,626 + 53714 685 29

936 1,023 + 872,190 2,495 +3051,021 871 -150

497 471 26

1,062 960 -102

773 849 + 76749 703 46

1,053 1,041 21

1,026 1,020 6

1,757 1,642 -115660 727 + 67649 722 + 73550 499 51

396 293 -103564 534 30

301 353 + 52245 341 + 96

1,617 1,395 -2221,311 1,260 51

2,737 2,710 27

4,255 4,576 +3212,781 2,730 51

992 841 -151

3,045 2,808 -2375,698 6,218 +5201,013 1,001 12

3,693 3,779 + 86

573 672 + 99212 56 -156708 875 +167

TOTAL 47,263 47,502 +239 (0.5%)

ABSOLUTE SUM 47,263 3,765 (7.9%)

V-16

The last basis for evaluation purposes concerns the convention which

seems to prevail for displaying the enrollment projections resulting from

the admissions and enrollment planning process, described briefly in Chapter

IV. For this purpose, the projections are subdivided not only by administra-

tive division but also by degree-level. In this case, as shown in Table V-5,

the summation of the differences, without regard for sign, between actual

and projected enrollments by degree-level for each administrative division

amounts to 10.0% of the actual enrollment for the total system, which implies

that this fraction of the enrollment was distributed among degree-levels and

administrative divisions in a manner differing from that actually occurring.

In closing, it should be noted that the forecast errors, described

above, are limited to a one-year projection into the future. At the present

time it is obviously not possible to provide an evaluation beyond this time-

frame.

TABLE V-5

COMPARISON OF ACTUAL AND PROJECTED FALL-TERM 1972 ENROLLMENT

BY DEGREE-LEVEL WITHIN ADMINISTRATIVE DIVISION

ENROLLMENT

DIFFERENCE

ENROLLMENT

DIFFERENCE

ENROLLMENT

DIFFERENCE

ACTUAL

PROJECTED

ACTUAL

PROJECTED

ACTUAL

PROJECTED

443

356

- 87

823

704

-119

299

355

+ 56

56

7o

+ 14

266

241

- 25

893

937

+ 44

184

203

+ 19

474

469

-5

448

431

-17

281

229

- 52

604

669

+ 65

126

139

+ 13

17o

210

+ 40

436

413

- 23

169

160

-9

131

134

+3

870

857

-13

938

1,027

+ 89

195

188

-7

539

493

- 46

408

459

+ 51

262

217

- 45

1,390

1,261

-129

717

739

+ 22

142

148

+6

505

548

+ 43

209

56

-153

285

251

- 34

406

452

+ 46

449

412

- 37

153

154

+1

318

322

+4

198

206

+8

24o

236

-4

96

3o

- 66

60

24

- 36

159

167

+8

369

343

- 26

121

44

- 77

108

138

+ 3o

1,226

1,047

-179

48

38

- 10

179

230

+ 51

1,120

1,031

- 89

53

39

-14

113

32

+ is

2,437

2,355

- 82

39

55

+ 16

226

215

,-

11

3,362

3,639

+277

67

33

- 34

146

143

-3

2,330

2,299

35

42

+7

36 1

26 0

-10

-1

864

2,875

702

2,643

+1?411

326

27

274

32

- 52

+5

30

-3

4,760

5,191

28

39

+ 11

20

-2

605

542

- 63

30

30

0

15

+4

2,975

3,040

+ 65

247

291

+ 44

10

-1

573

672

+ 99

208

214

+6

30

-3

61

106

+ 45

47

41

-6

1,059

1,019

- 40

502

603

+101

64

4o

- 24

96

51

- 45

10

-1

119

45

- 74

1,027

1,273

+ 66

301

353

+ 52

74

48

- 26

385

418

+ 33

244

341

+ 97

49

48

-1

713

774

+ 61

355

322

- 33

10

-1

1,649

1,837

+188

191

229

+ 38

259

463

+204

TOTAL

47,263

47,502

+239

(0.5%)

ABSOLUTE SUM

47,263

4,728

(10.00

VI-1

VI: SYSTEM APPLICATION

In the previous chapters, it was shown

1: that in a mutts-campm institution 06 Ughet

education, the pattekm of student movement

among academic teveEs, 6ietd4 06 zpecciatiza-

tion, and campuses have a igni6icant impact

upon the magnitude and majm-p/Log/Lam compoition

o6 the enkottment at any one tocation,

2: that .these patteAws o6 mooement may be desctibed

by ,se,tis o6 tkamition ka&s expkez6ing the

pkobabilitim o6 ztudentis 6otSowing va/tious

patho between zuccm,sive ;:)ointis time,

3: how a 6uitabte base o6 hi!.taticat data may be

compited and used don. development of these.

t' ant mat/Lica, and

4: how them matkica togethut with ancUlaky

ketatonishipz may be used as a pkojecton

modes, which, given the cukkent enkatment

and .a 60/Lecast 06 new admbsionz, may be em-

ployed to generate pkojectom o6 enkotement.

This chapter is concerned with a description of the system developed

to carry out the steps outlined in Chapters IV and V for routine application

within The Pennsylvania State University for generation of projections of

enrollment for the Fall term. The interrelationships among the components

VI-2

are delineated and the function, procedural steps, and operational cost of

each programmed module are outlined in brief. Details concerning the pro-

gram logic and application are shown in the Appendices.

COMPONENTS

The system comprising the Student Flow Model consists of three modules.

These are programmed in Fortran IV for operation on the IBM System 370/165

in the Computation Center. The first of the modules, COEF-1, is concerned

with generation of the various matrices from the Student Master Research

Tape. The second, ITER -1, utilizes these matrices as a mechanism for iterat-

ing undergraduate students through the system. The third, DISAG-1, generates

projections of both graduate and adjunct students and disaggregates both

these and undergraduate projections to the departmental level.

The relationship of these modules to one another is shown in Figure VI-1

and a brief description of each is provided below.

COEF -1 Module

The COEF-1 program generates the Campus, Progression, Inter-Campus, and

Switch-Degree Matrices from the Student Mater Research Tape. Each record

on SMART is read and aggregations of enrollment are prepared for the Fall term

of each calendar year on the basis of commonality of campus, degree-level,

student-level, and college or category of enrollment as well as distributions

of the enrollment for each common group among the campus, degree-level, student-

level, and college of enrollment for the subsequent Fall term. The distributions

to terminal states are then computed as fractions of the total for the cor-

responding origin states and produced in punched-card form.

ITER -1 Module

The ITER -1 program generates projections of Fall term undergraduate enroll-

ments from the most recent historical enrollment and the projections of admissions

for as many years into the future as desired by means of the transitions matrices

VI-3

FIGURE VI-1

FLOW DIAGRAM OF MODULE INTERRELATIONSHIPS

STUDENT MASTERRESEARCH TAPE

COEF-1

Module

MOST RECENTHISTORICALENROLLMENT

J

ORGANIZATIONMATRIX

ITER-1

Module

PROJECTEDADMISSIONS FROMADMISSIONS MODEL

GRADUATEENROLLMENT PARAMETERS

DISAG-1

Module

PROJECTEDENROLLMENTS

I

generated by the COEF-1 module as applicable to the most recent year. The

summation of the enrollments of returning students and new admissions is

computed for each common group for a Fall term and then multiplied by the

appropriate coefficients in the matrices to derive enrollments for the follow-

ing Fall term. The process is then repeated for as many years into the future

as admission projections are provided. The resulting enrollments for associate

and baccalaureate students are written for output onto tape.

DISAG-1 Module

The D1SAG-1 program reads the undergraduate enrollments from the output

of 1TER-1, computes the adjunct student enrollment for each campus from the

empirical relationship, and by means of recression equations generates enroll-

ment of graduate students. These enrollmerits, which are produced for each

campus, degree-level, student-level, and college or category of enrollment

for each Fall term in the projected time-frame, are then disaggregated to the

departmental level by means of the Organization Matrix and produced in hard-

copy form, as described in the previous chapter.

COST OF OPERATION

The system as described serves two major purposes. The first is concerned

with generation of the various transition matrices employed to simulate stu-

dent movement and the second with the use of these matrices plus additional

input for projection application.

Generation of the transition matrices involves the use of the COEF-1 pro-

gram. This procedure must be carried out only once a year and is characterized

as part of, the updating process. The overall cost of operation involves an

expenditure of $110 per year.

The projection process involves the input of the matrices from the COEF-1

program, the Organization Matrix computed from the Final Distribution of Enroll-

ment Report, and a forecast of admissions ror as many years into the future as

VI-5

desired as supplied from the Admissions Model. Once the updating for a year

has been completed, the projection procedure may be conducted any number of

times without the necessity of repeating the steps involved in updating.

The cost of each projection run of ten-years duration using ITER-1 and

DISAG-1 is $35.

Shown in Table VI-1 are the operating characteristics involved in ap-

plication of the three modules as described. It is of note that the data in

this table were compiled on the basis of operation on an IBM 360/67. With

the installation of a 370/165, CPU time and cost for each module are expected

to be lower.

TABLE VI-1

OPERATING CHARACTERISTICS

CPU Time-Seconds Records Cost

COEF-1 (Baccalaureate) 350 22,000 $65

COEF-1 (Associate) 130 7,000 45

ITER-1 100 7,000 14

DISAG-1 100 21,000 21

For a run with a projected time-frame of 10 years.

VII -1

VII: FUTURE EFFORTS

An appraisal of the results of this project and the perceived use of

the model have made it desirable that consideration be given to incorporation

of certain innovations within the model. Most of these, as will be noted

below, are concerned with improvement in predictability.

Projection of Transition Rates

Explicit in the application of the basic Markov process is the assump-

tion that the transition probabilities are stable over time. An analysis

of historical data during the development proces?confirmed the general

validity of this assumption for the model in question. However, some ex-

ceptions were noted. As an entirely separate project, a multi-method

general-forecasting procedure for time-series projection has now been

developed. The procedure will be applied on a test basis to historical

time-series of transition rates. If significant improvement in predict-

ability is achieved, consideration will be given to incorporation of the

procedure within the model.

Inter-Campus Flow

Of major significance in the projection of enrollments of the campuses

of The Pennsylvania State University is the impact of student movement among

different locations. Currently, inter-campus movement is handled within the

model by a two-step process. A single-step process has now been conceived

and deemed feasible for implementation. Since application may improve the

accuracy of the projections and will permit identification of the flows be-

tween campuses, an aspect which is not possible through the existing procedure,

early consideration will be given to implementation.

VI 1-2

Graduate and Adjunct Enrollment Methodology

As indicated previously, current record limitations preclude the ap-

plication of the Markov process for determination of both graduate and

adjunct enrollments. If and when suitable records become available, the

techniques currently used within the model should be replaced by ones con-

ceptually based upon the Markov process. It is of note that the forecast

error by degree-level within administrative division of associate and

baccalaureate enrollments, which were projected by application of the Mar-

kov concept, is only 8% as contrasted to 18% for graduate and adjunct

enrollments, which do not use this methodology.

Organization Matrix

The Organization Matrices, which are used for disaggregation of enroll-

ments to the departmental level in regard to field of specialization, must

be updated annually. Currently this is done by a manual procedure from

hard-copy records, a process which is not only extremely time-consuming but

also is inherently prone to inclusion of human error. An alternative source

of data must be developed and the procedure programmed for computer operation.

To improve the efficiency of the annual updating process, an investigation

must be conducted concerning other sources of data for this purpose and the

procedure programmed for computer application.

Ref-1

REFERENCES

1 Baisuck, A. and Wallace, W. A., "A Comouter Simulation Approach toEnrollment Projection in Higher Education", Rensselaer ResearchCorporation, Rensselaer Polytechnic Institute, 1970.

2. Firmin, P. A. et al., "University Cost Structure and Behavior",Tulane University, 1967.

3. Gani, J., "Formulae for Projecting Enrollments and Degrees Awardedin Universities", Journal of Royal Statistical Society, Series A,1963.

4. "Higher Education Enrollment Projections ", Office of Program Plan-ning and Fiscal Management, State of Washington, 1970.

5. Koenig, H. E. et al., "A Systems Model for Management, Planning,and Resource Allocation in Institutions of Higher Education,Division of Engineering Research, Michigan State University,1968.

6. Lindsay, C. A. et al., "Development and Utilization of a StudentMaster Research Tape", Office of Student Affairs, The PennsylvaniaState University, 1969.

7. Lovell, C. G. "Student Flow Models: A Review and Conceptualization",N.C.H.E.M.S. at 4h,1^...C.H.E., 1971.

8. Marshall, K. T. et al., "Undergraduate Enrollments and AttendancePatterns", Administrative Studies Project, University of California1970.

Newton, R. D., "Projections of Enrollments and Degrees Awarded",Office of Vice President for Planning, The Pennsylvania State Uni-versity, 1968.

10. Oliver, R. M., "Models for Predicting riross Enrollments at The Uni-versity of California, Ford Foundation Research Program, Universityof California, 1968.

11. Richard, H. G. "Complex Linear Flow Model of Student Flow", GraduateSchool and Department of Industrial Engineering, The PennsylvaniaState University, 1969.

12. Smith, W. R., "Review of Student Flow Model", University of Californiaat Los Angeles, 1970.

Ref-2

13. Tallman, B. M. and Newton, R. D., "A :odel for Projection of Instruc-tional Activity in A Multi-Campus Lhiversity", Office of Budgetand Planning, The Pennsylvania Stab,. University, 1973.

14. Tallman, B. M. and Newton, R. D., "A Model for Projection of Under-graduate Admissions in A Multi-Campus University", Office of Budget.end Planning, The Pennsylvania State University, 1973.

15. Thonstad, T., "A Mathematical Model of the Norwegian Education System",O.E.C.D., 1967.

16. Zabrowski, E. K., et al., "Student-Te,I,Icher Population Growth Model",U. S. Office of Education, 1968:

A-1

A: COEF-1 MODULE

The user must supply in addition to the SMART tape the following card

input:

1: Parameter Card: The following information must be provided in

a right justified form in the Column positions noted.

Columns 1- 2: Number of campuses.

Columns 3- 4: Number of years of data tobe extracted.

Columns 5- 6: Number of student-levels.

Columns 7- 8: Number of terminal states incampus matrix.

Columns 9-10: Number of colleges or categoriesof enrollment.

Columns 11-12: Last two digits of last year onSMART.

Columns 13-14: Last two digits of first year ofdata to be extracted.

Columns 15-16: Degree-level (2 for associate and4 for baccalaureate).

2: Campus Name Cards: One card per campus with abbreviation and

name of campus.

Columns 1- 2: Campus abbreviation.

Columns 3-18: Campus name.

3: Terminal State Name Cards: One card per terminal state with

college code in Column 1 and abbreviation in Columns 2-4 for

colleges and with abbreviation only in Columns 2-4 for other

states.

A-2

Column 1 Columns 2-4

A AGRB AA

E BA

F ED

G ENG

H HPEJ HD

L LA

N EMS

S SCI

T DOC

V IC

GRADUATEWITHDRAW

SWITCH-DEGREETRANSFERRETAINADVANCE

The COEF-1 program produces as printed output the Campus, Progression,

Inter-Campus, and Switch-Degree Matrices for all years. In addition,

punched cards for each Matrix for the most recent year are produced.

FIGURE A-1:

MACRO FLOW CHART OF THE COEF-1 MODULE

(001)

*****

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****

****

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FIGURE

A-1:

MACRO FLOW CHART OF THE COEF-1 MODULE (continued)

(002)

7

*****

*002*

* A2 *

**

* *

* *

*****

*002*

* A3*

* A4*

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STUCFNT

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ULL PrILr (IL)

0.:55

LL_StAKCH ILAAApti..14...2.L1-1,00.1.412_24_

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ill1H-Lo,

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1)36?

Sol-1(11LII-Y-L,r(1)-Sii-d-Lut

I.

1-i-14--+-1

i-1-4.4".,

(P)

(6.146/ 101L0,Y,L,FH

Oiho

StA-(.1=1

ti;

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1.0-,=1_.

.

CALL S1-,1 (LD,PHS(1.I).2,(.,...?;122)

Li-

1,1._1

1,,

I ti

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rmLL.

..I1:-1411.ALL.LILJE_

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in

1114

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(111

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Iii

142

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with

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1,11

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r;106_171t1

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rxiiho

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1.01

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(Pr!..11

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13 -1

B: ITER-1 MODULE

The user must supply the following card input for use of the INDEX-I

module:

1: Parameter Card:

Columns 1- 2: Number of years to be projected.

Columns 3- 4: Maximum number of student-levelsfor any one degree-ley. .

Columns 5- 6: Maximum number of origin colleges forany one degree-level.

Columns 7- 8: Maximum number of terminal states inCampus and Progression Matrices forany one degree-level.

Columns 9-10: Number of campuses.

Columns 11-12: Row number of "transfer" in Campusand Progression Matrices.

Columns 13-14: Row number of "switch degree" inCampus and Progression Matrices.

Columns 15-167 Row number of "retained" in Campusand Progression Matrices.

Columns 17-18: Row number of "advanced" in Campusand Progression Matrices.

Columns 19-20. Last two digits of base year.

2: Campus Cards: One card per campus with the camp s abbreviation in

Columns 1-2 and name in Columns 3-20.

3:- Terminal State Names: One card for each row in the Campus Pro-

gression Matrices.

4: Coefficient Cards: The Matrices produced as punched output from

COEF-1 in the following order.

Campus and Progression: Baccalaureate

8-2

Inter-Campus: BaccalaureateSwitch-Degree: BaccalaureateInter-Campus: AssociateSwitch-Degree: AssociateCampus and Progression: Associate

The last card in the two sets of Campus and Progression Matrices

must have a 9 punched in Column 8.

5: Enrollment Cards: Enrollments for the base year must be read in

on cards with the following format:

Columns 3-4: Campus number equal to the order in whichthe campus is processed, which is in alpha-betic order of the campus codes.

1: Altoona2: Allentown3: Behrend4: Berks5: Beaver6: Capitol7: Delaware8: DuBois9: Fayette10: Hazleton11: Mont Alto12: McKeesport13: New Kensington14: Ogontz15: Schuylkill16: Scranton17: Shenango18: University Park19: Wilkes Barre20: York

Columns 5-6: Student-level of enrollment1, 2, 3, or 4.

Columns 7-8: College of enrollment numberequal to order in which collegesare processed.

1: Agriculture2: Arts and Architecture3: Business Administration4: Education5: Engineering6: Health and Physical Education7: Human Development8: Liberal Arts

B- 3

9: Earth and Mineral Sciences10: Science11: Division of Counseling12: Inter-College

Columns 11-15: Baccalaureate enrollment.

Columns 16-17: Associate enrollment.

The last card must have a 9 punched in Colunm 2. All fields

must be right justified.

Example:

Altoona, Freshmen, Agriculture, 41 Baccalaureate,14 Associate.

00010101000410IS014

Example:

Berks, Freshmen, Engineering, 34 Bacca;aureate,63 Associate.

100401050VV34V$V63

The ITER -1 program produces printed output of enrollment by campus,

degree-level, student-level, and college of enrollment at the undergraduate

level. In addition, a tape output is produced.

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* C4

*.x.

"'**

**.

PA

SF

INP

UT

X

C3

*.

.* LAST

*

.*Y PAR

TO

BF *. NO

PRCJECT EE?

*.

.*

*.**

Xx: * * *** * * * * * **

*YCS

* **

MEM:. CNPOLLMFNT

*FOP RASP YEAR *

FRPm CARD

INPUT

B2.

EN

RO

LLM

EN

T =

NE

W +

SW

ITC

H

DE

GR

EE

+ R

ET

AIN

ED

+ A

DV

AN

CIN

G

+ T

RA

NS

FE

R S

TU

DE

NT

S.

C2.

AD

VA

NC

ING

AN

D T

RA

NS

FE

R S

TU

-

DE

NT

S F

OR

TH

E F

OLL

OW

ING

YE

AR

. T(

// rAFG

Ou

//SUili(C17../Au,(11..

1mPLIGII

wi110

ktla

l 4,_

riI

III lv

itmt I

f-k1

),IL

ILLL

(h)

Mle

t!iN

1t1;

EK

4 IN

FU

T(2

0.4.

12,2

1.!;S

L2U

.It.1

2.21

.-S

L(12

=1J

Hrti,

REAL'.'.

?),

oli-

(.14,

uJu

.5,,TrU(2.12/.sunA2..12/.A.Lutrt241.,,.1Z).J..1Lu,riLu_./.12j

ShLdth(Ci1.4.12)./Ufill;fl

t.11.1VaLt-wCt

CWliz)

I1-1I"

ft

s(-1

Hr

1!::LH.01CL LuErhICIF

.CilLf":7

ruK

IS

Iy,a,.

1-1w,

ALL

OP.,

!APE_

I )C

Yr7iim:,

,

IL-.1

1,

1-,

Si1,11-H

IL7VrLS 1-1.

(J,klur.LLr i$

1,,

rn,r

YhAk.

1

I.

I mt.

_J.,b L.LIiL

1.r I).

_L

C.

I.

ILI

I 5t

-I

'S

1'107A

'L'

IS

14 .S.IJUt,.I

1.

'S'

IS

it

L'.1.1t-tsh

!w!)I-A.

''W L5 __a_

.L1.111_

'jr-

-; t..c

ti

o- -

Ut:

1.21

.1..V

.A,1

/"51

:::,

A ,Q

11.1

Y__

1

I.

ni-(1...nY

hr,HAILL,.,1

SO..!

I

'I", I

CI 1, I n

,uura-Lt_

cl I

--

.I

I

Nhit!t.0..

Lt-.Vt!.

H.

11-r

5P(.)11!:

IN

117.b.!

.thl- I

Iiht;

1_1.

.. 11

111-

2__C

ILL1

7.17

_1C

_LL

_3,

1.2r

11.

1,1,

.r.,1

L-'.iiL

si-C10.-!

In'

Gui

lt:J-

4f;

',"lit ni<AYS.

C C

ti Y

' t_L

ti,11

-(-4

.4S

4 '

4_14

_ C

I ta:

a L

i,T

_Kt,s

1411

NL

LALLULAILD

tII

A)1_11.-LYIN(1

11tr+i-1CAL COH--1C1t1,11

IAIKtx hY

0560

RAY 'DO C11N1111,

.0,0-0-K

to-

-AL.

SV

00E

NIS

1K

AN

SF

,EK

fm,

Liiu..Li-vtL. !LL

'S'

L C L.

_Loilu_LLVtL

:J.J__.C.LILLt

_u.tp

AK

KA

Y1114.1,

L110,1/11

irt

io-

ass.

sillut7...is

-.,1

414

I 1_

4.1:

111.

1I .

1.1.

Li)r

,, I A

l,s

I Hr

"AC

. `,1

0111

-, IS

St.'

ICI,

II (1

.1r1

111

..1I

ILo

t,-r

tu-

AS

S. s

I SI

1"

II

W3

1JI.

..

..r

(IA

L)LL

KS

.C

.

( 5

.Y

.7.1

\1st

. *L

s.. .

rui-e.,Ai(01P)

I Psi

o<A

.r-

,1{,

,i I

""-=

/-X

At-

X-,

-1-4

.,

(_=1.C;

11

)

A.,{

11,-

In.li

'11

.1(

i 1.1

=1.

21.

ICp

/-11

,-2

12

1!

-1:

L

pwl\,

111

-

0o /1

I

42.

S

2i

1314.

A t

" .1

2 .5

1,)

C C1.,,11.11±L1/1-

viiK1r0,1"N

C

00 ,O

'--I

ShOtIKS.

JJ_L .

LJ

0r,t

1)=

1

OH

L=1,

c"

1.-P1.1(C,L,k-,1)=0

I417

.111

.,LIS

.11=

11.

AUVIC.L.S,1)=0.

1141)

1251,

TRAN(C.L.S,1)=1).

1.26o

1-X71.1

SWUH(C.L,S,11=0.

S4D6(C.L.S.2)=u.

1-1.111(C.L.-S)=0

1.31,1

TC01-1-AC.L.S).

35

Du -3n L=1.2

14b

r1cF(c-.L.$)=I).

.SACuti-AL.L.S)=U.

1..;k7o

411)1/11(..L.S,1)..o.

13V..

PA

CJ-

013H -&,?

4ET1(C.L.S.11=0.

K LILIC,L.S.217=u.

TRAN1(G,L.S,1)=0.

TRAk.1.1C.1..SZ)=.11.-

SwoLl(C.L.S.1)=o.

ti..1.1"(q.

L

1'40

014

111_

14?0

I

31400

311

Cirk41,01t

Lau

----

----

----

----

----

----

----

-C C

RcAo feCHplICAL Cut-ri-ICIENTS

hAC.SPIOrNIS.

151,,

Do

RtA

v(1,

55)1

,c.L

,s,i1

1,,,p

(J).

A=

1,,)

:' )

551-

.U.R

!'...4

.1 I

bY..1

.412

1.1X

.1.1

01:5

...U

.1 /1

101'

5.0)

ity 6o

fA5(C.L.S)=1

.111

15>

iirD(,

LutrtL,L,L).1=It!,rtoi_

_

CM 111 5

1600

57

CuEr(C.L,JJ.S)=U.

5v

CuEr(G.L.!,4.1.s1=11,W)

ALU411.111

1:.(j

Il i

511

1,,,

Ir(S.,AILN)',!,

IIL

00 1-7 C=1.Ci,;

thhi,

OU

L=1,LN

LIL

wqIir(f,.,0)((a,(A.G).J=1,20).1_

hit7111<,11..1-4

4,14

474.

1.-1

-L-1

4,t*

YLt

V t-

'4-

44

01/

6.-;

6,

'fir<

i Il

66 )

(C

UL1

,14!

`'' (

J=1,

( C

Ut_

17i.

iiiu

hh C/4!.

-/.10

G11171-1-1LIF.'.16 hUk

_LU

LL_

if,"

IllC

lilsi

l 1t

1,0,1

=1,

O 1,

RI7Ao(.,%.ti5)(1CUtrAl,L,1=1,1,N)

s5

Fuk,,A1(19Y.101-5.-3,/.1ox.1/F.3)

I hit°

15,

1IH

IDo

mEA0 SwITCJ,

CoirfriC117NIN r0m tACS14JUES

C

00 97 S=1 .s1

95

CONTIN0i-

4 I

00

/,t,

L=1.L.1

mt-Lilt_Lta.EY1b_KtAL

H

1900

1,J1;

ea

FORP.Ail'IrRANR

!4C. S[001-:111-5'.10X.1Y!:AK=1,(4.10,

.IFvEL=',12)

mk

EuReAtiretrii23.12Aki

Du "A L=1,C,,

to.)

'lsifl.5x, 12 (1-5 .3.3X) I

D0 '76 L=19Lry

91

hiC.

Lr

ci ii

;.;

CHNII,Jut

1'1

OH

1.11

S=

Ici

IHS.17.0.1)qhMl(!,,2.111)111LytrICTLN)0=1.1.,

L....

11 e

s C

.A1J

1,11

4.,ii

__1_

11_1

1.1.

..1C

.1-1

1....

...L.

,_..1

+1

10)

Cuoi-ifh01-

C

11:(7P,J7t7

noL.

C 1.09

00 11,, L=1.2_

/?4,

,U

U11u

=1,51

Ifr-(s..1.1)krni 1.2.111

(1-A

(:,1

0- (

C,!.

51.c

=1.

Crn

r.S_+11-1....=1..-L.-:v-1

111

1-UR,111(2UX411/1-1.39/.10A.1,"?)

175'

'-(it 0 1-00-11L4L CLIfrt-i-1Git.:-),

1-''j<

,Iv.,.(0.,Lh011_

1)ifl

1,%n

It( I.t0.9)60 hi 131

ih(S.i.0-.2)S=S+1

00

._

4,11

,!12

/Alm-1-1COLO.N1=11.

241,1'

AC

t.hr

(CO

(75

Cu hi 12U

130

._11-(SwITCHIGu. 10 .1y0

DU 14)) C1 ,L".

ill) 14n 1=1.2

wRIlh(6,141/ICAIrtvAm(J,C),J=3.20),L

141

FURhAT( '

IC ii

mP

US

1 A

l 2 X

' AS

S10

x_.

12.14.14.1-J.t11.3-811).CCw1,4A0..(S,_14_,S=4..SA,)

DU 145 0=1.0,\

2520

145

ORIlkli,,,,o/Kul,04_,LIIJ1.1=1,11.(ALIC-L-0-1-\=.1_\,

140

Il11

U__

1_5

0 __

L

WRI)11-(6.155)HYtAR.L

(1/4

tu

WWII

fI

(11

IA

S.1

2440

245u

2460

2,01

1 I

M IJII-3"

00 160 C.I.CN

2ht,0

,16U

Viti

nt_f

a_dV

IIC

APi

N 4

- L

J =

3_, 2

0,

it- I-

EL,

_1_,

_Si

1in 1

t)CON1INOt 1=-4. 2---

-?h

it'W

k1iE

lh,1

7510

Ytr

Ak.

L2h

Ltt)

''

- Sj

. 111

X2h

'

v.t.zIT

Lb,

Hc

1I r

iAs_

._11

Ou 1-0 C=1 ,(.,

tsL

) .-

.1-=

1,t;

) .4

-4-

1 Li

..1-

`1

I

170

CuNII0t

1,40

c IND

.1

C?r2i,

21-0.

C(z.,i

CUP,H171,i:

tii,Wslat-qA7

Yv.

IS

1,11-.

1,,t7

''U'H1:

Y,AKS

iyhc:

in HI- wHtnLifho

krit.

C

00 1000 Y1 Y"

KA

1:21

_1

:ltits

(1I

N.=1

IrEKK

1)1,,N=.Z

IF(Y.t.,1.2093=10

1.

K.-1.,ITLAL1LE .v.a.H1/02LLES

.1)1.!

1.1,p42;,

810:

NS1(1)=11

On '1'10

S=1.:).,

SU

A(L

,S)=

U.

0-(1.1,1.2)Gu

hnG

TH1IL,S)=0.

TH1(2.1/41=0.

H50

C0NiP,oh.

C Cumm17.1:

-1-111)

MIHML.

C H51

RI7A01-;3./4601I.C.L.S.II,J.1

Mb))

rukmAi(4,2,2x.:151

It- I

1.(:

1).9

11;1

iI

999

;!.,

1"*

2.1h

to

,?,1

3000

AHIC

30?,,

-NS(L.L.S,2)=JJ

999

CoNIINIW2.1_1uE_1))Lii

,000

M3=5

Go ILL.6-tiA..

LOu0

N3=1,1

C C'`l 1.-111.1,I1 I

I-

SI-G-1 111"

3041,

50h).

PAC,r

'C

U1

;0(1 L=1,,LN

thJ

'uL= L Li l

5O 0

-;,111

'')=19Sro

IS hi

sc

J_E

-15

CHLUS vii71oki,11.G siiol,)!TS.

11-('i.:.07.1.11NPOI(G,L41),1)=,.ISIC,L,S.1)+40V(U.L,S.KK)+,071(C,L+

19'

I'

16)

kt_

,n

X .

/i)--

r-

,l-6.,

A' S 1,,)

320

''

1-153

S. C-

CS111111-1,1',

FMIX

S )=C1_1171-

ii.S

)1

L.L. .S.1)

CI.

ImAws,r,-( C s-I1CH

LLL-

11

I-

.j_

L.L

LI

) 661.

)

TR( L :%).--Tic()_,S)+tiql)i

.5

(C.L .R,S)

5tIA

CLj

S1U

J+I-

l'IIIt

Si).

). S21)1)

Ci."

II

340u

5,10

394) ,

IS

1,1i-

.01,t1I-K

nt-

lo

"S2 on-X1

C110 1,c

O 1)

71)

5I)m.!.,,,4*,,,)(u.3)

Li5.1,1

If-.l-.Li.:),IHVICTLL0).NIA)=,ciii-FALLI.A.0)

.52-ajII

m.

._

L..-

1-(0-1A.L.1,,NN)=S110=.410-1-(L.L.K.10

3541.

0400

C1.0\111'017

3 .)6::

T1-11 ..._..i 1( I.

(I' M.

5

C C C C

ASSOCIATE DE6REE SECTION

.51,00

3A1L1

3h2.0

DU pun C=1,CN

3640

OLI

ono

S=1..SN

It:(Y.Nt.1)INPuf(C.L.S,2)=,4S(C,L,S.2)+ADV1(C,L.S,KK)+KETI(C,L.S.KK)

Jhbu

IF(Y.LE.2.UR.L.EQ.1)INPOI(CILIS,2)=NS(C.L,S.2)

Li(lAhl(C.L.S) EL)

ii

,,.W

36,4+1

-7-NS(C.L.S,2).ADVI(C.L.S.KK),KETI(C,L,S.KK).TRANI(C.L.S.RK),

too

PA(;

3-/1

1Y9

FOR.AF('DISSI,NA, ASS. CUEhrICIEN1 mATNIX:1,5X,'C=',12,3X.'L=1,

I 2.9i

S'

37?0

IA

L

TRAWN61-w

375,,

CONPOJE.ALMANClistii.S.IOLLEALS4

CA1.10 SWITCH oEuRF.-17 STUDENTS Fuk

IHE

HILLUNINU

YEAR.

3(8.,)

sixu_

DO non 0= 1

600

END(0,51-AC-1,k)-1-C,1_,O.S)Pufl( L,S 2)

31-t

i UI

j'2G

TR1(2.S)=i1,1(P.S)+!-.-A,U(I.S),.:ACuEr(C.L.4-1,S)

Li_LA-SJ = f_k_111_,SJ +

i,f1_,_Si

SOtiiL.S).=SDH,IL.S)+EwHISI!.SI

3r70

C

"NIIM6

IS

IHL AiliMeth4

',1)-i- IS

WHit

wILL

h,

3,0u

3X7U

COLL6(st "S"

Y6AR.

'Joe,

neo,u

DU

ti!;

DU -/-)11

7.,(1

s)

II-(1..1.4t.flADVI(C.u.ONI=SACuEr(U.L.A.10

700

CONII,!(.1r

3V00

CONIIAir

.34(0

3%04.,

c_1

111\

dl!l

oE4000

LUi

C CUMmt_UI.1..LALLIOLAIL J11.-21.1....DLSTRInuLt_

t'Jw.

1Hr

It-'

l4n4k.

DU 1-'01 L=1.4

411,

ti_ .

.t31±.

1 t

1)11

,30 C=1 ,CN

I n..6.3

._S ,ntrd_1. =

t L.. S

it,

L .

SWOh(C,LIS.NO)=0.

rf-ip

2IGu HI 8.30

H.40

SviD.,tU.L.S.Nm)=Suh(L.S)*s.Acutr-lL.L.S)

).-S N.UP

Lr.0

I I

C 1,4j

IF(L.E;.1.2)S,q0A(C,L,S.No)=SDA(2.S1S.ICOEfr(C.2.S)*SDA(3.S)*SdC1iE0-(C.

4t1i:

IRA,Y1(C.L.S.4N)=IRI(L,SIIC)iE1-(C.L.S)

416,,

CulY-1-10/2-

C41mt

ut)

41,1

0

....

WRIIF(h.h500)i,-.6LNAm(S.J).J=1.2),(Tr((1,S),L=1,4)

420d

PAG

6.5.00

F.URP.1.41(",2-A8,A1,4(1-10-2.3X))

'121U

6000

CUWIN0t

4220

0UTPUT SECTION_

IY=sefiArt:AR-1

14-=

DU.

1,2D11-

WRII(b.,4001(LAmNAm(J.C1.J=3.201.1Y

.YOU

A,1

t 0441-v--11 Y

''!(1)1:

,3X.1bA 1,T12(I, ' YEAR: ' .3x. 14)

42rc.i

UH L,1" L=I

3 2

Ll=L+1

WKILLUD_.."4.11u_lt

930

FOR,A1(/,'01,8x,'LtVi:L=1,[2,125,1nACCALAI!Ktitli-1.5A,'ASSUCIAIi.

4_12u

t=1

I's

Li_AI_Alitit Alt

4., 0

111S(=1)

AISH0=11

H2SH..n

.

DU ,2o S=1,S,v

CriL.J .5.11

AlSum.,-AISIol+INpuT (CL .S '21

H2C0.5=HiS0m+11,,011,C LI.C.11

A2S0:-,=A2S0p,+141,0TIC.L1 .5.21

*(COLS.,111J=1,21.(INP01(C.L1,S.01.1.=1,2)

525

(

920

CO1\711-401:

wPriFin.,423)Kis0m.Als0m.t-Lisu,,./12s0.,,

923

HJR...AT(10CAmP0S TWIAL1,72/.1:1.10X.15.0X.1CA4PuS fOIAL1.14x.1).

=AIOX.1,/

51')

CuN11,1,:

st>to,

4ilAh

4,

fll

44Lt.

445i,

447,1

44et0

!Al 545 S=i.54

(1

1-1,

. /11

,c-i

(1

1 4

1- 1,

i- 1 1 r .1 .C.2

-I =1- / I

.I

,

1-qj

-111 IL=1-,1

885

Fliki41(1001.3)2,2x.1.110.10('0'11

CUNliN(.r

OU

is45

4Y57

141.01,(15.5h)

DU 545 K=1.,

4550)

JSI.J.(g1=1)

DU 44(1 S=I,SN

4(10t!

,ISHIn I 11 =

II1 J3-itlEnILL,1_,.s,_2j

JSU(2)...1S110(2)+INVIO(U.2.1i,,)

46%0

151.1..'(A1=1511M(31-1-1p0,11TIC.l.',.1)

41, .11

JSON(4)=JS0H(4)+INPDT(C.2.,11

!S(j-(,1-A0.-(5).1wP1.14C-.3-S.711

JS0(61=JS0.(1,1+1-11,01(L.,...:,,11

CUNLIfH1-

ISUF-.JSw,(1)+JS01,(i)+JS0,-113)+JS00(4)+JS1+JwN(n1

nrw

i_L1S))11.

1'1-0.0.4;111(0000000001.i1101

'- Ill

550

LuKil It,!'-

4/1,

,OH

C=21.??

(Si v/0 s=1,16

4 (

WR1 117115 ,Vf1:11

4(4,)

ru5mAl(?-50(,0,11

4 f-31.

970

C111\111501-

4+ (,-,k!

1000

CHN11wDr

47/,,

ENO

L,7,411

/4,

THIS IS A SLASH ASIt7KISK CAKH

Al

//uATA.F-TIFU01_011__UNLT=.124UU.OEER)4VUL=LStrcf-laml_15,HSALA,

//

DISP=(NEW,KEEP),UCB=IREChm=h,LHECL=HO,HLKSILE=32001

j/nAIA.1:T101-001 HU

UA

LL

17-l

24U

U,-

Lki

-Eki

,V-1

-11-

7--

//DISP=I(JLD.KtI7P),OL6=(KtCFN=FH.LHECL=20.BLKSILt7=320(J)

//HAIA.INPHI OU

4Hou

writ;-

C-1

C: DISAG-1 MODULE

In addition to the tape output from ITEP-1, the user must provide the

following card input:

1: Campus Cards: One card per campus. The first twenty campuses

are in campus abbreviation order as specified for ITER-1. King

of Prussia and Hershey are 21 and 22 respectively.

Columns 1- 2: Campus code.

Columns 3-18: Campus name.

2: College Cards: One card per college or category of enrollment.

The number of departments within each college is right justi-

fied in Columns 1-2. The college name follows beginning in

Column 3 with the order of colleges as shown below.

AgricultureArts and ArchitectureBusiness AdministrationEducationEngineeringHealth and Physical EducationHuman DevelopmentLiberal ArtsEarth and Mineral SciencesScienceInter-CollegeCapitolMedicineNon-Degree

3: Department Cards: The department names and associated budget and

HEGIS discipline-division code of the first college, followed by

the names of the second etc. One card per department is left

justified.

C-2

Columns 3-18: Department name.

Columns 19-26: Budget-code.

Columns 27-34: REGIS code.

4: Organization Matrix Cards: One card per department showing the

fraction of each college's enrollment, degree- level, and student-

level at a campus represented by the department.

Columns 1- 2: Campus number, right justified.

Columns 11-12: College code.

Columns 14-15: Department number, right justified.

Columns 21-25: Fraction of first year associatewith decimal point at 22.

Columns 26-30: Fraction of second year associatewith decimal point at 27.

Columns 31-35: Fraction of first year baccalaureatewith decimal point.of 32.

Columns 36-40: Fraction of second year baccalaureatewith decimal point at 37.

Columns 41-45: Fraction of third year baccalaureatewith decimal point at 42.

Columns 46-50: Fraction of fourth year baccalaureatewith decimal point at 47.

Columns 51-55: Graduate with decimal point at 52.

20X,7F5.0

5: Campus Graduate Regression Equations: These project the number

of graduate students at each campus and are prepared using library*

program POLY-2. One card per campus.

6: College Graduate Regression Equations: One card per college at

each campus having graduate enrollment with the campus number

in Columns 1-2 and the college number in Columns 3-4, where the

number represents the order in which the campus and college cards

are entered.

C -3

7: Year Card: One card for each year of enrollment.

Columns 1- 5: Planned level of graduate enrollmentright justified.

Columns 6-10: Number of campuses with graduate en-rollment constraints right justified.

Column 15: Index for type of output desired.

1 = output by campus2 = output by campus and college3 = output by campus, college, and

department

8: Graduate Constraint Cards: The number of cards will be the number

specified in Columns 6-10 of the Year Card.

Columns 1- 5: Campus number right justified.

Columns 6-10: Minimun constraint.

Columns 11-15: Maximum constraint. (Note maximunconstraint must be denoted as 99999)

In addition to the printed output of enrollment by year, campus, degree-

level, student-level, college, and department, a tape output is generated for

use into CONSUM -1 of the IA-1 model.

INITIALIZE

FIGURE C-I:

MACRO FLOW CHART OF THE DISAG-1 MODULE

(001)

******A1**********=:

,.***;=*12***********

REAO

*DATA

,

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*001*

* B1 *.k.

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* MATRIX VECTOR *

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READ UNOERGRAD

OUTPUT

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ANY

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":(7

'ENROLLMENTS

**

ENROLLMENTS

*

YEIO> 10?

...

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FROM ITER

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FINISHED?

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* STUDENTS AND

*

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4*

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FIXING

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.*

* OUTPUT CAMPUS *

*-,

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**'XI,************

*CONSTRAINT

kt

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X

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STPP

FIGURE C-1:

MACRO FLOW CHART OF THE DISAG-1 MuOULE (continued)

(002)

* Jje .=INISHEC

***

*14*

**

Al.

INCLUDING CAMPUS NAMES, NUMBER, DEPARTMENTS AND COLLEGE

NAMES, DEPARTMENT NAMES, THE ORGANIZATION MATRIX, CAMPUS

GRADUATE REGRESSION EQUATIONS, AND COLLEGE GRADUATE RE-

GRESSION EQUATIONS.

ALSO SLT YEAR=1.

A2.

AND NUMBER OF CAMPUSES WITH ENROLLMENT CONSTRAINTS AND

TYPE OF OUTPUT DESIRED FOR THIS YEAR.

C3.

VIOLATIONS.

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