The Annual Meeting of the RSAI – The Israeli Branch, Tel-Aviv University, January 10, 2010

Development and estimation of a semi-compensatory residential choice model with a flexible error structure

Sigal Kaplan, Shlomo Bekhor, Yoram ShiftanFaculty of Civil and Environmental Engineering, Technion

Motivation

When faced with

many

alternatives,

people apply a

sequence of non-

compensatory

heuristics

followed by a

compensatory

evaluation

(Payne , 1976).

• are mostly Multinomial logit• necessitate exogenous choice set formation• choice set formation independent of individual

characteristics

Motivation

Semi-compensatory models:• are based on Manski’s (1977) formula

• have 2J-1 theoretical choice sets for J alternatives• are estimated only for a few alternatives• involve thresholds that are independent of individual

characteristics• do not account for correlation patterns and population

heterogeneity

Residential choice models:

q qqS G

P i G P i S P S G

Research objectives

To develop a semi-compensatory model for residential choice

To accommodate correlations across alternatives and random taste

heterogeneity in the model

Model formulation

Universal realm of alternatives

Chosen alternative

Viable choice set

Preferencestructure

Utility maximization

Unmanageablechoice set

No choice

Overtly specified criteria thresholds

Conjunctiveheuristic

Abort?

NoYes

Choice set formation

stage

Choice

stage

Model formulation

Observed choice i Observed choice set S

| | |q q q q qP i G P i S P S G

Proposed model:

Nested logit or random coefficients logit

Multidimensional mixed ordered-response model

Observed combination of criteria thresholds

that yield the choice set S

Model formulation

MMOP-NL model:

1

111

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,1

1 ' /

1 ,

' '1 1 1 1 1 11

1

1

e e, , , ln

e

...

...

qir

j ri r

q r

sq

j s

q s

k m q

q Kqk

d

XX

Q j S j Bk k s

Nq i S X

l j S j B

M d

q q m q qmm

m

LL

Z Z

' '

1

1 1, ,

k m qK

KKk

M d

K Kq Kq m K Kq Kqm

K q Kq q Kq

Z Z

d d

Model formulation

MMOP-RCL:

1

111

'

'1

' '1 1 1 1 1 11

1

' '1

1

1

e, , , ln |e

...

...

, ,

qi

i

jq

q

k m q

q Kqk

k m qK

KKk

d

XQ

k k s Xq i S

j S

M d

q q m q qmm

M d

K Kq Kq m K Kq Kqmm

K q

LL f d

Z Z

Z Z

1Kq q Kqd d

Empirical context

Positive• Demand for public

transport• Revitalization of

city center• Local economic

growth• Local employment

generationNegative• Demand for

private cars• Formation of

seasonal communities

• Competition with low income groups in the rental market

Regional impact of students:

Survey design

Product: rental apartmentsPopulation: Technion’s studentsSurvey type: stated preference Survey duration: 1 month

Survey method: web-based

Incentive: 23 prizes ($1000) Technion campus

Survey design

Utility-based choice stage Rank three most preferred

apartments from the choice set

Conjunctive choice set formation

Criteria thresholds specification (e.g., price, rooms, noise level,

parking)

Questionnaire socio-economic, price

perceptions, travel attitudes and study preferences

Questionnaire socio-economic, price

perceptions, travel attitudes and study preferences

Conjunctive choice set formation

Criteria thresholds specification (e.g., price, rooms, noise level,

parking)

Utility-based choice stage Rank three most preferred

apartments from the choice set

Verification

No

No

Yes

Respondent’s criteria

thresholds and chosen apartment

Synthetically generated apartment

dataset 3 < j <100

Verification

Yes

SQL query

YesNo

Database

Respondent’s information

Survey design

Model specification

Three criteria are represented in the estimated model:• apartment sharing• neighborhood • monthly rent price

Universal realm of alternatives: 200 apartments• adjacent to campus with little employment or leisure• far from campus with leisure activities, shopping and jobs

Explanatory variables:• personal characteristics • apartment attributes

Nested structure: floor numberTaste variation: renovation status, view and security bars.

Model estimation resultsVariable description

est. t-stat. est. t-stat. est. t-stat.

Married 1.823 8.88 1.823 8.88 1.822 8.86Male -0.775 -5.85 -0.775 -5.83 -0.773 -5.83Age (years) 0.026 2.75 0.026 2.75 0.026 2.74Daily car availability 0.537 3.91 0.537 3.91 0.539 3.92Daily trip frequency to campus -0.635 -5.04 -0.634 -5.04 -0.633 -5.02Study on-campus for better communication -0.155 -3.95 -0.155 -3.95 -0.154 -3.93$ 750 - 1000 0.756 3.71 0.756 3.70 0.753 3.69$1000 - 1750 0.931 5.18 0.930 5.18 0.93 5.17Roommates -0.918 -5.13 -0.918 -5.13 -0.922 -5.15Alone 1.073 4.47 1.073 4.46 1.07 4.45Spouse 1.354 8.25 1.353 8.24 1.351 8.22Haifa suburbs -0.851 -2.96 -0.851 -2.96 -0.852 -2.96Haifa outskirts -1.266 -6.59 -1.267 -6.59 -1.265 -6.59

Price-quality ratio consciousness (factor) -0.395 -7.55 -0.395 -7.54 -0.395 -7.53Age (years) 0.055 4.37 0.055 4.36 0.055 4.36Daily car availability 0.696 5.51 0.696 5.50 0.698 5.51Medical campus 0.774 3.40 0.774 3.40 0.776 3.40$ 750 - 1500 0.637 4.26 0.637 4.25 0.636 4.23> $1500 0.995 5.76 0.995 5.76 0.994 5.75Part-time job -0.558 -3.46 -0.558 -3.46 -0.558 -3.45Difference in job opportunities 0.113 3.36 0.113 3.36 0.113 3.36Difference in green space availability 0.299 7.33 0.299 7.32 0.299 7.30Study on-campus to improve efficiency (factor) -0.187 -5.68 -0.188 -5.68 -0.188 -5.68Daily trip frequency to campus -0.461 -3.74 -0.461 -3.74 -0.460 -3.74

MMOP-MNL MMOP-NL MMOP-RCL

Apartment sharing threshold

Location threshold

Model estimation resultsVariable description

est. t-stat. est. t-stat. est. t-stat.

Married 0.928 7.30 0.928 7.29 0.926 7.28Male -0.393 -4.87 -0.393 -4.86 -0.393 -4.85Age (years) 0.052 3.82 0.052 3.81 0.052 3.81$ 500-750 0.362 3.51 0.361 3.51 0.361 3.5$ 750-1500 0.854 7.05 0.853 7.04 0.853 7.02Part-time job 0.148 1.76 0.149 1.77 0.148 1.76Daily car availability 0.337 3.61 0.337 3.61 0.337 3.61Price-knowledge (factor) 0.160 6.07 0.160 6.07 0.161 6.06> 4 apartment changes -0.547 -3.24 -0.548 -3.24 -0.547 -3.24Daily trip frequency to campus -0.533 -5.82 -0.533 -5.80 -0.533 -5.79currently reside with roommates -0.330 -2.72 -0.330 -2.71 -0.329 -2.70currently reside with alone/parents 0.258 2.13 0.258 2.12 0.260 2.13currently reside with spouse 0.847 6.63 0.847 6.62 0.847 6.62Haifa – upper class neighborhoods 0.210 1.74 0.210 1.73 0.208 1.72Center of Israel 0.754 6.52 0.755 6.53 0.754 6.52Non-motorized modes preference (factor) -0.038 -1.66 -0.038 -1.66 -0.038 -1.66Travel minimization preference (factor) -0.083 -3.12 -0.083 -3.11 -0.083 -3.09Cut-off point 200 a - - - - - -

250 -0.295 -0.70 -0.296 -0.71 -0.297 -0.71350 0.330 0.79 0.329 0.78 0.328 0.78350 0.735 1.75 0.733 1.74 0.732 1.74400 1.051 2.49 1.049 2.49 1.048 2.48450 1.691 3.99 1.689 3.98 1.688 3.97500 2.353 5.54 2.351 5.53 2.349 5.52550 3.239 7.61 3.236 7.59 3.232 7.59600 3.583 8.39 3.580 8.38 3.577 8.37650 4.115 9.66 4.111 9.64 4.108 9.63700 4.328 10.14 4.325 10.13 4.321 10.12

MMOP-MNL MMOP-NL MMOP-RCL

Price threshold

Model estimation results

Rent price and neighborhood 0.415 fixed 0.415 fixed 0.415 fixedRent price and apartment sharing 0.674 fixed 0.674 fixed 0.674 fixedNeighborhood and apartment sharing 0.313 fixed 0.313 fixed 0.313 fixed

Rent price (monthly) -0.001 -2.04 -0.001 -2.19 -0.001 -2.62Number of rooms 0.584 12.00 0.453 8.81 0.634 12.04Number of roommates -0.394 -4.64 -0.364 -5.03 -0.363 -3.76Walking time to campus -0.083 -15.95 -0.062 -10.55 -0.089 -15.91Quiet apartment 1.475 25. 90 1.134 11.52 1.507 24.3Parking 0.298 4.43 0.257 4.70 0.346 4.89Floor -0.071 -3.09 -0.073 -2.78 -0.067 -2.74Smoking allowed -0.385 -5.16 -0.31 -5.05 -0.412 -5.26Security bars (mean) 0.185 3.63 0.104 2.51 0.209 3.58Security bars (standard deviation) - - - - 0.213 0.23Stunning view (mean) 0.377 6.65 0.267 4.79 -1.369 -1.71Stunning view (standard deviation) - - - - 4.517 3.02Renovated (mean) 0.565 9.49 0.468 7.88 0.356 2.82Renovated (standard deviation) - - - - 2.19 4.70Air conditioner 0.290 5.01 0.223 4.77 0.321 5.27Solar water heater 0.442 5.43 0.348 5.30 0.453 5.36λ1 Non ground floor apartment - - 0.802 14.19 - -λ2 Ground floor apartment - - 0.638 8.30 - -Number of observationsNumber of parametersLog-likelihood at zeroLog-likelihood at estimatesMcFadden’s adjusted R2 0.473

Correlation across thresholds

Utility function

189368 70 71

-20431.414-10710.708 -10700.996 -10692.686

0.472 0.473

-20431.414 -20431.414

1893 1893

Conclusions

The model estimation results shows the importance of incorporating a flexible error structure into semi-compensatory modelsThe proposed model is a viable option for real-world applications and it can be readily incorporated within activity-based models and joint residential and transportation models.

The proposed semi-compensatory model:• is applicable to large universal realms• includes a probabilistic choice set formation dependent on

individual characteristics• includes a flexible error structure

Thank you!The Annual Meeting of the RSAI – The Israeli branch, Tel-Aviv University, January 10, 2010