software review

Software Review

Essam Mahmoud American Graduate School of International Management

MapWise Version 2.03--Perceptual Mapping Software for Correspondence Analysis

Reviewed by Lou E. Pelton University of Mississippi

R. Keith Tudor Kennesaw State College

INTRODUCTION

Marketing research surveys which parsimoniously de- scribe choice behavior often yield data in which the preferences of respondents are unconstrained. With unconstrained data, differences in respondent preferences may not be apparent because the respondents may respond with a different number of alternatives. This type of data, referred to as "pick-any" data (Combs 1964), consists of categorical variables representing choice and non-choice. The "problem with these data is that they carry a built-in ambiguity which makes them relatively difficult to analyze" (Levine 1979, p. 85). For example, non-choice is traditionally treated as a rejection of an alternative. This treatment of multivariate data implicitly presumes that respondents are familiar with all choice alternatives, and it is clearly antithetic to real- world scenarios.

One metric technique for interpreting "pick-any" data is correspondence analysis, an exploratory data technique for visually structuring contingency tables of categorical data (Levine 1979). Since many categories are simultaneously considered, correspondence analysis extends mere detection of relationships to the identification of latent dimensions among these relationships (Hoffman and Franke 1986).

While correspondence analysis has received much atten- tion in the marketing discipline (Carroll, Green and Schaffer 1986; Hoffman and Franke 1986; Holbrook, Moore and

Journal of the Academy of Marketing Science Volume 19, Number 4, pages 383-389. Copyright �9 1991 by Academy of Marketing Science. All fights of reproduction in any form reserved. ISSN 0092-0703.

Winer 1982), marketing researchers have been forced to rely on expensive mainframe hardware and software (such as SAS or SPSSX) or memory-consuming micro computer versions for constructing joint spaces from "pick-any" data. The introduction of MapWise Version 2.03, correspondence analysis software for microcomputers, offers marketing researchers an inexpensive and efficient alternative to these products. MapWise requires 256K and is fully operational on any IBM PC/AT/XT or compatible computer. MapWise runs on both Macintosh computers if using SoftGate software and on DOS 2.1 (or later) operating systems.

HOW MAPWISE WORKS

MapWise 2.03 offers several proprietary enhancements which extend Levine's (1979) algorithm for correspondence analysis. As in any correspondence analysis, the program is predicated upon maximizing interrelationships among numerical scores which are assigned to row and column categories in a data matrix. However, MapWise scales the axes on the basis of each axis's contribution to explained variance, thus eliminating the need for drawing vectors to interpret perceptual maps (i.e. multidimensional scaling). Furthermore, the strength of the relationships can be both visually and numerically depicted using options in the mapping module.

MapWise tests the significance of all perceptual maps as significant (sign. = .05), not significant (n.s.) or not appli- cable (N/A). Significance is not appropriate if the data includes multiple mentions or incomplete data. Self-testing of significance is facilitated since MapWise reports the re- quired information: the eigenvalues and the number of active responses, row categories, and column categories.

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SOFTWARE REVIEW MAHMOUD

DATA REQUIREMENTS

Unlike other perceptual mapping techniques that require ordinal or metric data, correspondence analysis requires cross tabulations of categorical data or summarized ordinal or metric data. Categorical data may be expressed as fre- quencies or percentages whereas ordinal or metric data may be expressed as top box scores and summary statistics. The flexibility of data requirements permits a simpler research instrument and thus, may result in higher response rates.

While statistically significant results are possible with as few as 50 respondents, larger sample sizes generate more valid results (Holbrook, Moore and Winer 1986). Catego- ries with insufficient cell sizes are identified by MapWise's proprietary cell size test.

MapWise allows the users to create their data files, as well as to transfer data files from any ASCII file created by SAS, SPSSX or LOTUS, etc. with at least a nine-cell matrix. However labels and other text are deleted when Map- Wise automatically formats the data.

DATA ANALYSIS

MapWise employs an enhancement of the "pick-any" algorithm for correspondence analysis illustrated by Levine (1979). The modified algorithm yields actual proximities among and between row and column categories with a self- reported 92% to 99% accuracy. The proximity analysis option is a unique feature of MapWise which has greater face validity than the correspondence analysis procedure since this option ignores the weighing of categories. However, both procedures treat the row and column categories equally.

There is also an option for adjusting the relative sizes of subgroups to satisfy quota requirements. Goodnow (1989, p. 15) explains that "adjusting their relative sizes does not alter perceptions or the total number of responses."

TEST OF CELL SIZE

MapWise offers a proprietary test of cell size by compar- ing correspondence and proximity maps of the same data. The process of deleting categories with insufficient cell size generates a more accurate positioning of all categories. This test of cell size is a critical refinement of current correspondence analysis capabilities.

EVALUATION OF MAPWISE

Hoffman and Franke (1986, p. 214) assert "there is vir- tually no limit to the number of marketing applications for correspondence analysis," and MapWise positions both active and passive categories on a correspondence map. Rela- tionships among the active categories define the solution in the initial map and then each passive category is overlaid on the solution. Examples of the types of data, data analysis, and interpretation are illustrated in the software documentation. Some examples of applications include variables such as images, products, demographic and psychographic characteristics, and comparisons over time. Each example includes a stepwise explanation of the MapWise procedure.

To illustrate the MapWise program, data from a national study of consumers' attitudes toward generic over-the- counter pharmaceuticals are cross tabulated. The variables are shopping source, product category, and demographics, and the data is expressed as frequency counts. Shopping source alternatives include neighborhood pharmacies, chain pharmacies, grocery stores, and discount stores. The three product categories are aspirin (such as Bayer), acetamino- phen (such as Tylenol) and ibuprofen (such as Advil). Five demographic variables are gender (Male), income (Rich), martial status (Single), race (Minority) and education (Col- lege). The cross tabulation yields a 4 row by 8 column matrix and the numeric scores for each cell are reported in Table 1.

Correspondence analysis is performed to detect and interpret relationships among categories of the three variables in the data. The data analysis is fairly fast. Next MapWise graphically represented these relationships. The perceptual mapping output is saved as an ASCII file for later editing or printing. The results of the MapWise 2.03 correspondence analysis procedure are illustrated in Figure 1.

The resulting perceptual map is statistically significant, even though both axes are not significant. It is important to note that the software only uses a .05 significance level. The user must resort to sensitivity analysis for determining the effect of collapsing categories on the axes's significance. A proprietary significance chart in the User's Manual ac- commodates sensitivity analysis, relating total responses for the two active variables with their degrees of freedom. The interpretation of the data is based on the actual proximity of sources, products, and demographics. The proximity of single, minority, and male customers for analgesics to both grocery and chain pharmacy shopping sources reveals that these two sources compete for a similar market.

TABLE 1 DEMOGRAPHIC AND PRODUCT PROFILES ACROSS RETAIL SOURCES

Products Demographics

Retail Outlets ASPI ACET IBUP MALE RICH SING MINO COLL

NEIGHBOR PHAR 16 18 13 I4 27 42 41 24 CHAIN PHAR 36 24 14 19 37 56 56 31 GROCERY PHAR 21 17 9 17 29 44 44 25 DISCOUNT STORE 56 48 12 21 14 55 55 33

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SOFI'WARE REVIEW MAHMOUD

FIGURE 1 Generic Over-the-Counter Products

+100 Var iance Expla ined: X Axis --.86 Y Axis =.14

*ACET

*DISCOUNT

*ASPII

*NEIGHBOR

*GROCERY *IBUP

*College *Male

*Single *Minority

*CHAIN

Rich*

-I00 +I00

GENERIC.MXY Sign. = .05 Correspondence Analysis Vertical axis is flipped.

Copyright (c) 1988 - 90 Market ACTION Research Software, All Rights Reserved

86.1444 Percent of variance explained by the X axis 13.8556 Percent of variance explained by the Y axis 0.0000 Percent of variance explained by the Z axis

(connnued)

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FIGURE 1 (continued)

X Coordinate Y Coordinate Z Coordinate

NEIGHBOR CHAIN GROCERY DISCOUNT ASIP ACET IBUP MALE RICH SINGLE MINORITY COLLEGE

0.0755523784. -0.0506830753, 0.0000000000 0.0101286711, 0.0637569341, 0.0000000000 O.O14551O956, O.O117684234, 0.0000000000

-0.0429688357, -0.0249053835, 0.00o0o00000 -0.0244568521, 0.0389521244, 0.0000000000 -0.O118623731, -O.O526461577, 0.0000000000 O.O9217O9967, 0.0126732256, 0.0000000000 O.O5O1661444, 0.0375908427, 0.0000000000 0.1250020611, O.1371O44785, 0.0000000000 0.0612807639, 0.0446663746, 0.0000000000 O.O592866875, 0.0487527119, 0.0000000000 0.0568260583, O.O3O6881726, 0.0000000000

0.027925 Eigenvalue of the X axis 0.004491 Eigenvalue of the Y axis 0.000000 Eigenvalue of the Z axis

The Coordinate data is scaled to I00 units.

Category Horizontal Vertical Z Axis

Weight

0.1655 0.2606 0.1655 0.4085 0.4542 0.3768 0.1690 0.2500 0.3768 0.6937 0.6901 0.3979

NEIGHBOR 60.441 36.967 0.o0o CHAIN 8.1o3 -46.502 0.o00 GROCERY 11.641 -8.584 0.000 DISCOUNT -34.375 18.165 0.000 ASPI -19.565 -28.411 0.000 ACET -9.490 38.399 0.000 IBUP 73.736 -9.243 0.000 Male 40.132 -27.418 0.000 Rich I00.000 -i00.000 0.000 Single 49.024 -32.578 0.000 Minority 47.429 -35.559 0.000 College 45.460 -22.383 0.000

CONTRIBUTIONS OF ACTIVE CATEGORIES TO THE AXES: GENERIC.CXY

Correlation with Axes Contribution to Axes

Category Horizontal Vertical Z Axis Horizontal Vertical Z Axis

NEIGHBOR 0.36531 0.13665 0.00000 26.82945 12.07284 o.ooooo CHAIN 0.00657 0.21625 0.00000 0.75927 30.08255 0.00000 GROCERY 0.01355 0.00737 0.00000 0.99519 0.65091 0.00000 DISCOUNT 0.11816 0.03300 0.00000 21.41986 7.19555 0.00000 ASPI 0.03828 0.08072 0.00000 7.71553 19.57018 0.00000 ACET 0.00901 0.14745 0.00000 1.50581 29.65717 0.00000 IBUP 0.54369 0.00854 0.00000 40.77488 0.77081 0.00000

(continued)

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FIGURE I (continued)

CORR~PONDENCE MATRIX: GENERIC.CXY

Strength of Relationships Between Categories on X and Y a x e s .

NEIGHBOR CHAIN GROCERY DISCOUNT ASPI ACET IBUP

NEIGHBOR 1.00000 -0.10116 0.25388 -0,08038 -0.15481 0.21823 0.46256 CHAIN -0.10116 1.00000 0.57434 0113523 0.63051 0.03091 0.15646 GROCERY 0.25388 0.57434 1.00000 0.40511 0.58677 0.42422 0.30593 DISCOUNT -0.08038 0.13523 0.40511 1.00000 0.45374 0.64153 -0.24657 ASPI -0.15481 0.63051 0.58677 0.45374 1.00000 0.24484 -0.06459 ACET 0.21823 0.03091 0.42422 0,64153 0.24484 1.00000 -0.07183 IBUP 0.46256 0.15646 0.30593 -0,24657 -0.06459 -0.07183 1,00000 Male 0.24543 0.58328 0,61826 0.02376 0.33267 0.07873 0,57301 Rich -0,59344 -0.18850 -0,42102 -I,00000 -0.55760 -0.97241 -0.05600 Single 0,21229 0.51688 0,50351 -0.09112 0.23197 -0.02813 0,62012 Minority 0.17644 0.54376 0.49910 -0.09386 0.24697 -0.04308 0.58411 College 0.31585 0.50300 0.59175 -0.00080 0.27010 0.08418 0.65151

Male Rich Single Minority College

NEIGHBOR 0.24543 -0.59344 0.21229 0,17644 0.31585 CHAIN 0.58328 -0.18850 0.51688 0.54376 0.50300 GROCERY 0.61826 -0.42102 0.50351 0.49910 0.59175 DISCOUNT 0.02376 -I.00000 -0.09112 -0.09386 -0.00080 ASPI 0.33267 -0.55760 0.23197 0.24697 0.27010 ACET 0.07873 -0.97241 -0.02813 -0.04308 0.08418 IBUP 0.57301 -0.05600 0.62012 0,58411 0.65151 Male 1.00000 -0.05160 0 , 8 8 5 0 9 0.87781 0.91807 Rich -0.05160 1.00000 0,05528 0,07047 -0.06028 Single 0,88509 0.05528 1,00000 0,96222 0.87929 Minority 0.87781 0,07047 O,96222 1.OO000 0,85110 College 0,91807 -0.06028 0.87929 0.85110 1,00000

While the interpretation of the map follows the tenets of correspondence analysis, proximities may become difficult to measure as spatial relationships become less apparent. Although the perceptual map provides a quick, visual representation of the data, marketing researchers will want to confirm conclusions using the numerical report provided in the proprietary correspondence matrix. In contrast to the correlation matrix, the correspondence matrix reports the correspondence of all categories on all substantial axes.

In interpreting MapWise perceptual maps, it is important to remember that the proximities are two-way relationships. As such, the results depict relationships or associations, rather than causal effects.

HARDWARE AND SOFTWARE CAPABILITY

MapWise 2.03 runs on any IBM PC/AT/XT or IBM compatible computer. It also runs on Macintosh computers

using SoftGate software and a Hercules-like disk drive. While installation is possible on a floppy drive system, the dexterity of installation is facilitated by computers with a hard drive. MapWise enables the user to specify the default printer, drive and directory for running the program on a network. Modification of defaults requires the creation of a MAPWISE.SYS file for specifying default drive, printer, and directory.

Although data may be imported from SAS, SPSSX and/or LOTUS, a caveat regarding the reading of ASCII files is warranted. When MapWise formats the file, all text such as titles, labels, and headings is lost.

The capability of exporting data matrices and perceptual maps to ASCH Eles is ~n important feature of MapWise. It is extremely beneficial to have the ability to export Map- Wise files to word processing software such as WORDPER- FECT since data analysis is usually accompanied by some text. This also allows for customizing of perceptual maps with explanatory labels, subtitles, and symbols.

JAMS 387 FALL, 1991


MapWise offers a program option to plot the map on a Hewlett-Packard color plotter. The menu option allows for maps to be plotted with various foreground colors.

VENDOR SUPPORT

Market ACTION Research Software Inc. provides 30 days of free expert support for MapWise users and three months of free product updates. Also telephone support is provided which includes help in setting up your data and interpreting the results. The accuracy and ease of learning MapWise is guaranteed.

COST CONSIDERATIONS

A free demonstration disk is available from Market AC- TION Research Software Inc. The full version, which is capable of analyzing 100 by 100 tables, is available for $495. Academic site license for multiple users on a network is available for the same price. The student version, which is capable of analyzing 5 by 5 tables, is available for $9.95. Training sessions over the telephone are free and can be provided on site for an additional fee. American Express credit card charges are accepted.

RECOMMENDED PROGRAM MODIFICATIONS

Some modifications to the MapWise software package would increase its value to users. First, the tutorial that accompanies the MapWise program demonstrates the ana- lytical technique. However, the tutorial must be refined to parallel the actual screen displays. Apparently, this recom- mendation is being addressed in the documentation for the new version.

Likewise, the ability change options in the mapping module would allow the user to change his mind before running the map. This capability is already available in the data entry and analysis modules.

Alternative levels of significance would be a welcome addition to the software. This would allow researchers to set the significance level to match research objectives.

Although MapWise imports any ASCII file, the program strips off the labels when it automatically formatting the numbers. Currently, a company is developing a program that allows MapWise to automatically format ASCII files without losing the text.

APPENDIX

Information concerning MapWise can be obtained from:

Market ACTION Research Software Inc. Clarendon Arms Suite 21,

16 W. 501 58th St. Chicago, IL 60514-1740

TEL (708) 986-0830

FAX (708) 986-0801

REFERENCES

Carroll, J. Douglas, Paul E. Green and Catherine M. Schaffer. 1986. "Interpoint Distance Comparisons in Correspondence Analysis." Jour- nal of Marketing Research 23 (August): 271-280.

Coombs, C. H, 1964. A Theory of Data. New York: Dryden Press. Goodnow, Wilma Elizabeth. 1988. MapWise 2.02 User's Manual. Claren-

don Hills, IL: Market ACTION Research Software. Hoffman, Donna L. and George R. Franke. 1986. "Correspondence Analy-

sis: Graphical Representation of Categorical Data in Marketing Re- search." Journal of Marketing Research 23 (August): 213-227.

Holbrook, Morris B., William L. Moore and Russell S. Winer. 1982. "Constructing Joint Spaces from Pick-Any Data: A New Tool for Con- sumer Analysis." Journal of Consumer Research 9 (June): 99-105.

Levine, Joel H. 1979. "Joint-Space Analysis of 'Pick-Any' Data: Analysis of Choices From an Unconstrained Set of Alternatives." Psychometrika 44 (March): 85-92.

Comments by Dr. Betsy Goodnow, Market ACTION Re- search Software:

Readers of this review of MapWise (R) will greatly ap- preciate its honesty and thoroughness. If they wish to learn more about correspondence analysis, readers can call me at (708) 986-0830 to obtain for $5 a self-learning game on correspondence analysis, a reprint of a review by Jerry Pournelle in BYTE, and an article that mathematically sub- stantiates that MapWise gives users greater overall abilities in correspondence analysis.

MapWise solves the aspect ratio problem by scaling all axes proportional to their power, even when the axes are rotated or a passive category is near the border. As a result, measuring the proximity of all points on the map best repre- sents their relationships. Since MapWise positions all points, active and passive row and column points, in Eucli- dean distance, our correspondence maps are interpreted like a road map. This claim is substantiated by recreating a geographic map with 98% accuracy from a similarity matrix of the proximity of cities.

Our correspondence matrix reports the correspondence of all categories on three axes with six digit accuracy. The correspondence matrix is analogous to a multivariate correlation matrix. MapWise also tests of the accuracy of each point on the map and the significance of the map, and eliminates bias due to multiple mentions, incomplete data, or unrepresentative quotas. Proximity analysis merges row and column percents whereas correspondence analysis weighs categories to best summarize their relationships. These scientific enhancements of correspondence analysis have been legally protected since March 22, 1988.

MapWise solutions prior to these scientific enhancements are identical to symmetric correspondence analysis. The public domain algorithm for MapWise decomposes a symmetric matrix consisting of row percents and column percents in opposing quadrants and zeros in the other quadrants. In the solution, the eigenvalues report the variance among active categories explained by the axes and the eigenvectors position them as points in multidimensional space. MapWise superimposes the passive categories on the solution by weighing the coordinates by their joint occur- rences and scaling them by their eigenvalues.

Market ACTION Research Software guarantees the accu-

JAMS 388 FALL, 1991


racy and ease of MapWise 2.03. MapWise runs without a color card, graphics card, or a hard drive and is compatible with windows and a math coprocessor. MapWise reads any data file in ASCII with 3 to 100 row points and column

points and creates presentation and statistical files in ASCII. Both files are compatible with most editors, Harvard Graph- ics, Freelance, any printer able to print lines, and Hewlett Packard color plotters.

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