Bureau of Business Research Graduate School of Business Administration University of Michigan November 1972 AN EMPIRICAL COMPARISON OF TWO MODELS FOR PREDICTING' PREFERENCES FOR STANDARD EMPLOYMENT OFFERS Working Paper No, 67 by Raymond E. Hill Assistant Professor of Organizational Behaviovr and; I ddstfital Relations FOR DISCUSSION PURPOSE$ ONLY None of this material is to -be quoted or reproduced without the express pepmission of the Bureau of Business Research

CONTENTS Introduction. Background 4 Development of the Ideal Job Model 4 Development of the Linear Utility Model 6 Results 8 Conclusions. Appendix A 13 Appendix B 17 References 19

TABLES 1. Spearman Rhos between Predicted and Actual Rank Orders for the Ideal Job and Utility Models 9 2. Mean Spearman Rhos and Other Comparative Statistics for Ideal Job and Utility Models 11

Introduction There are two major types of job-choice models in the current literature, One may be called an ideal job model; the other is primarily a linear utility model. This study attempts to compare empirically the predictive capacity of the two types of models. The concept f:the ideal job model was developed by Peer $oelberg in a study in which graduates of the Alfred P. $loan School of Management at the Massachusetts Institute of Technology were subjects, Among several of Soelberg's conclusions ws the following. "The decision maker defines his career problem by deriving an ideal solution to it, which in turn guides his planning on a set of operational criteria for evaluating specific Job alternatives" [10o p.22 ] Soelberg also suggests that the decision maker believes a priori that he will make his decision by weighting all relevant factors with respect to each alternative job offer and then by adding up the numbers fin order to identify the best offer. It turns out, however, that the decision maker does not generally do this and that if he does add up the numbers it ise done after an '"implicit favorite" has been selected from among the alternatives. Furthermore, after the decision maker somehow selects an implicit favorite, he does not publicly announce his decision immediately but rather goes through a selective cognition process to confirm that his implicit favorite is the right choice. Soelberg calls this 'confirmation processing and further explains it as an exercise tn prejudice whereby the decision maker convinces himself of the rightness of his implicit favorite. Confirmation processing is partly a hedge against the cognitive dissonance which the decision maker will experience when he publicly announces his implicit favorite as his job choice, N,

: *23 Apparently it is easy to identify independently the favorite job alternative (once the decision maker has decided), even though the decision maker will not usually admit he has made an implicit choice. The favorite can usually be identified by considering a small number of the decision makerts most important decision criteria or dimensions of job choice, Furthermore,25 out of 29 of the graduates in the Soelberg study eventually selected as their final job choice that alternative which had been, independently identified as their favorite an average of three weeks earlier. In a study at the Carnegie Institute of Technology, Vroom was able to identify the implicit favorite using a dimensions weightingg system and reportedly predicted 28 out of 37 final job choices (76 percent) [ 12 ] Soelberg suggests. however, that an implicit favorite cannot be identified by a dimensions weighting system before the search for new alternatives has ended. It is not until after the.search has ended and an active roster of alternatives is being juggled by the decision maker that an implicit favorite can be identified by weighting and rating job-choice dimensions, Before the search is ended, Soelberg reports that the weightings on various dimensions seem to be very unreliable and shift over short periods of time, He therefore explains the occurrence of more reliable weighbtngs after the end of the soarch as part of the confirmation processing whereby the decision maker constructs a weighting function which will explain and confirm his implicit favorite. The above discussion suggests that the decision maker may arrive at his implicit favorite by making a similarity judgment between each of his alternatives and his concept of the ideal job. If this is the case, the prospects for predicting job choice using the concept of an ideal job seem worth exploring, particularly since recent developments in multidimensional

scaling techniques employ the concept of an ideal point in a decision space, The utility models, on the other hand, posit that the decision maker evaluates his alternative job offers along certain dimensions, differentially weights the dimensions, and then combines the evaluations and weights into numbers representing the utility of the various offers, Soelberg suggests that this is a postdecision phenomenon which does not generally capture the actual process of choice. Empirical work using utility models to predict job choice has been conducted by previous researchers and is probably the most widely discussed approach in the current literature[ 3,4.,5 ]. One of the most predictive utility models was developed by Huber and his associates at Wisconsin and consisted of a two-stage rating procedure. The subjects were persons seeking professional employment in the-public schools, Under the two-stage technique, the decision maker assigned utilities to different levels of various factors and weighted the importance of the factors. The utility of a given job was then represented as a linear combination of the factor ratings and weights. This two-stage rating model resulted in the accurate prediction of 60 percent of the first choices for thirty decision makers [4 ]. The predictability of first choice was also higher for a subset of persons who had experience in making job choices; those inexperienced subjects who were making their initial job choice were not as predictable as experienced decision makers were, The differences between the approaches of Soelberg and tHuber present an interesting question regarding the process of formulating preferences for jobs, The Soelberg thesis suggests an aggregate comparative judgment between each alternative job offer and some ideal job. The thrust of the work by Huber and his associates envisions a process of evaluating alternative jobs along differentially important dimensions and then adding up the numbers according to some objective function.

Background A multidimensional scaling procedure was used to construct the ideal job model for each, subject in the present research, and a two-step rating procedure was used to develop the linear utility model. The job offers studied consisted of a set of standardly described employment offers, as shown in Appendix A. These offers were extracted from descriptions of approximately one thousand actual offers made to the tsudents in the Krannert Graduate School of Industrial Administration at Purdue University. -Thus the job off ers in this study are common to all decision makers and are not the offers which each decision maker ultimately generated for actual employment. Ninety students working toward a Master of Science degree in the Krannert Graduate School of Industrial Administration in the spring of 1969 served as the subjects (decision makers)..Development of the ideal job model The ideal job model was constructed from questionnaire data which served as input to the KRUSKAL Nonmetric Multidmetrnstonal Scaling Program [ 78 ]. Input data for the ideal job model were obtained by asking the subject to make pairwise similarity judgments on all pairs of the nine standard offers. A sample pair and the similarity scale from the original questionnaire are shown in Appendix B. In addition, similarity judgments were also made between each standard and the subject s ideal job concept; an example is shown in Appendix B. Thus each subject was actually making comparative similarity judgments on ten jobs-nine standards plus an ideal,. Since there are forty-five possible pairs of ten jobs, each subject completed forty-five similarity ratings and a joint perceptualpreference space was developed for each using these data as input to the

5 -KRUSKAL multidimensional scaling procedure. This is a rather unique procedure for locating an ideal point in perceptual space because all the input data consist of similarity judgments, Ideal points are usually located by using both similarity and preference data as input to scaling algorithms [1,2]. David Klahr, however, has provided some prior empirical data to substantiate the theoretical construpct of predicting preference using multidimensionally scaled similarity judgments [6 ]. It should be pointed out that the subject never writes down or otherwise makes his ideal job concept explicit~ He is simply told to consider mentally what his ideal job would be and then to make similarity ratings between his ideal and each of the nine standards The resulting multidimensional scalifig solution is an n-dimensional space which contains nine point:repereenting s the standard jobs and a tenth point representing the ideal job, e The point representing the ideal job is referred to simply as the ideal point in the space. This process of making comparative judgments between alternatives and an ideal would seem to capture the choice phenomenon described by Soelberg [ 10 ] Under-the ideal job model, preference for a particular offer is stronger the closer the offer is to the ideal point in the decision space, Preference for a given alternative offer is then expresse as the inverse of the distance: between the given offer and the ideal point, In an n-dimensional orthogonal euclidean space, distance between any job offer, A, and the ideal point, I, is represented by the following: m II

.dAI (A,. Ii) | (1) i. where d = distance between job A and the ideal point Al Ai = coordinate of job A on axis i Ii = coordinate of the ideal point on axis i n number of dimensions in the space The above distance formula is simply an a-diLmensional extension of the Pythagorean theorem from plane-geometry. The model is thus mathematically represented as a distance function in an n-dimen sonal orthogonal space, The model predicts that the standard job closest to the ideal is the subject's first choice, the second cosesst offer is his second choice, and so forth, Thus an order of preference for the standards can be derived by calculat ng distances from the ideal in the multidimensional scaling solution space, Development of the linear utility model The data for constrauting a linea utlity representation of preference for the standards were alsp collected through questionnaires. The subjects were asked to rate the perceived desirability of each job on a sixty-point Likert-type scale with respect to the following six factors: 1, Opportunity for advancement 2, Challenge of the position 3, Salary and other economic benefits

4, Overall prestige of the position 5. Geographic location 6. Job pontent The subjects also rated the importance of each dimension to their own jobschoice on a thirteen-point Likert-type scale. The overall utility for a givqn job for a particular subject was then derived by.the following linear combinations of weights and factor rattngs: 6 Ui. utility of the 2 subject for the j job Wk;. weight assigned to the' k2 factor or the jh, job rating on the' k- factor for the j — ob Ukj Nine tility valuese or Uisr were derived for each subject since there are nine jobs. The order of preferance for jobs predicted by the model is obtained by ranking the job with thp highest utility number as first, the job with the next highest utility number as second, and so forth, The utility model was constructed using a two-stage rating pro-: cedure and is similar to the one Huber et al. determined as most predictive of actual job-choice behavior of the five they compared [ 4 ] Procedure The ninety subjects were asked to complete the ideal job model questionnaire (see Appendix B) and make the ratings for the linear utility model under supervised group conditions, Three days later they were asked to indicate their actual rank ordering of the nine standard offers. Derived

rank orderings of the offers were calculated for each subject using the two different models, and these orderings were correlated with the actual rankings using the -pearman rank order correlation coefficient (rho) [ 9, pi202 ] In additions the number and percentage of first'- choices correctly predicted by each model were tabulated. Five dimensional scaling solutions were used for the ideal job model since the goodness of fit index (s:tress) indicated a good fit between the input dOata and the five svolutions. In addition, the solutions were also highest on predictability compared to solutions of other dimensionality.:.Results Table 1. shows Spearman rhos for each oft the ni ety subjects uslng both the ideal joob model and the utility modelu Tablei2 shows mean hos for both models, as well as other gomparative statistics, and is a summarization of Table I, Table 2 indicates that ths Ideal job model is generally superior to the utility model in predicting actual preterence for the standard jobs, The average rho and number of rhos signiftqant at the 1 percent and 5 percent levels are larger for, the ideal job model? Rho must be equal to or larger than.78 to be significant at the I percent level and equal to. r greater than.60 to b'e significantp at the 5 percent _level,..The nonparametric sign test can be used; to compare the two s.amples as to centra tendency [10, p68] S A t-test between the two mean rhos was not used because the distribution of 'rhos was not normal. 'Using the nonparametric sign test for matched samplesa a Z value of -3. 3 was obtained after compring- the average rhos for the two models. This Z value was significant at the.0005 probability level and indicates a distinct difference in the predictability of the two models,

TABLE 1 Spearman Rihos between Predicted and Actual Rank Qrderrs tor the Ideal Job and Utillty Models __. _... ~_... 1.... ~.............................; ~~~~~- ~,,-~~~ —~ — *~~~i~~ll II,;c..:L::L. I II ~~~~~~~-1-I: ---- I ---- - L- --- - -1 -.. - - ---- ' -- --- 1 Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 SSpearman. Rho tdeal Mod U ty 'M-od 7~~(c*~~~-wlll~Ya~r~ -; —~rr~ --- —- ~ --- -. I " W-,4rr _q-b-r-..Y~~-w~Y~ _I~IP~*.83 093 975,80.77,72, 98 98.97 92.80,87 a38.80,78 68,83 72 ~83,70.43 02 o 93 ~88.60.77.68,77 92.87.30 63.83,72,78 88,88, 95.80.92.73 93.88,88.82.90.75 -38 960.SO..80.70 93.67 92 b 50., 28..,.73. 67 02 92:73 i 82 68 47.68 <55.58.88 ~55,60.82 077,80.33 972 955 30 73.55.85.73, 38 62 ^5.70 ~4, [ -. -....., I~

-10 -Table (cont.) Spearman Rhos between Predicted d d Actual Rank Orders tor the Ide4l Job and Utility Models __ ___ I, i, — m 04 4 4!! 14 0 - - 11.1. II 1 I -.1, I .. . -11 1. i I "....... 11 7 1:.- 11-11, -, 11 1 I 1. I.. I.,.... 1. I.. 04 O m. I I I. 1.. i 9 1; i;: id i '- I- - I.;., I;.. I F -. I;;,I;z, I."o, 1:111 o!: I - -:: 1 9 9! I I p I Im,, ".- 'I =., -m, I.,;, 1 --, —, lo 1: I I.. I I.......... " -.. I I I... 1., 9.1 I... I.., i 0 - I. I I. I I., i I I -, e. " I -,~~- ~i -r~ ~ ~ r I 7i~~l. ~. ~. Subj ect -. -... spearman khO Ide. al M6ode-u I ity -Mdel 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80,80.77.77.32 67 e 67.72 o60,67 92. 90..., 15.78 80 * 52.67.68.73 90 97.80 92.58.,83.55.92.83.80.60.97.38.70,72.88,60,20 92.73 92.88.22,55.47,78 81 82 8-3 84 85 86 87 88 89 90,54.50.37,83.70 92,995,43.87.57.73 -.07.93.82.48.88,85.73.88.82.78 -10.80 * 72.27,65 -,27.68.53 o 64.70.47,83,63.87..65.02. 65,35,90, O0,45,78.88.58,28.65 -.r ' ' 1.,7r,, II r. II 1r I m I". 1",!..R!,.,, F- Pp! -immm 1,, 11. m, 1. I -1" F I. 1..I 1.r.. I.r I.

TABLE 2 Mean Spearman Rhos and Other ComparativE Statistics for Id al Job and Utility Mod es I I.,. I.., I I,,. o,,, 1,. — -.1.... t, 1,: jj om..O. #!" o a. I- - - I i -, i. I 'i 4 " 4 I, i i: O I 4 'O.. I.... 1, 1,,, I I,,;,.., I-... 1.., , -.. -, o - 1 oo,., - - No.. 11 -.. - i,;,,.: I i... I.,.0, -...6. 4 i!;;;;;;;;; - i -, M, i i.. I I.. I, Z...: I. I II I j I.... % I. 1. I.. I 11..... I... I...1,. 11- - ---...... I i.,,..... Mean Spearman Rho Number of rhps significant at the 1% level.. (No. >/.78) Number of rhos significant a-t the 5% level (No, >/:60) Number of first choices pred icted n..V. Ideal Job 'Model e74 48 (53%) 75 (83%) 44 (49%) 90, I '. m o m m io", m U1til ty Model -62 29 (32%) 59 (66%) 34 (38%) 90 "No In addition to the mean rho>the ideal-job model is superior with regard to the number of first Qhoices accurately predicted. The ideal job model accurately predicted 44 first choices (49 percent) as compared to 34 (38 percent) for the utiity model. Ability to predict first choice among a set of alternative job offers is is important since potential uses for the models include computerized man-job matching systems. Conclusions The ideal job model as operationalized in the present research is superior to a lineat utility model for predicting preferences among a set of standard job offers. The results lend empirical evidence to Soelberg's notion that job choice involves comparative similarity judgments between alternatives and the individual's ideal job. Knowledge of the job-choice process has potential application to computerized man-job matching systems, The linear utility model has been most extensively investigated srince it is operationally feasible to adapt

* 12 -this model to computer applications. It is not as yet clear how the ideal job model could be operatiEnalized for computerized matching systems. This is an area for future research. However,.one approach might be to store a subject's description of his ideal job as well as his alternative job offers in some form amenable to computerization and then develop similarity measures between the ideal and alternative jobs for given subjects' This similarity index might be a Tanimoto matching coefficientS for instance, and the higher th simlarty, the ighe the subject s: preference for that particular job [ l, p. 185] In an article on computer-aided approaches to employment service placement and counseling, Holt and Huber note: By programming decision models into the computer which:approximate those of the persons involved, the computer can rapidly and efficiently consider' a great deal of information about many alternative jobs and candidateso In this way interviews can be proposed which hopefully are better than those resulting from manual-file searches or machine searches that seek simply acceptable:-pairings..'" of candidates and,vacancies [3, p., 573] The present study suggests that.the ideal job model'-indeed approximates the choice process involve d and is therefore worthy of further research efforts to adapt it for computer applications.

~~: '"-13 APPENDIX A Ninq Standardly tescribed Employment Offers Offer A Electronics component manufacturer Production supervision training prograul;; first-line supervisor, 1-2 years; 2nd and 3rd level supervisor, 37 years Work primarily in plants in East; start at Wilmington, Delaware Young management mediumssized firm Salary; $1 000 per month Offer B Nationwide insurance firm; systems analysis work with computer applications; work at corporate headquarters; first assignment would involve the development of a new companywide system for processing life insurance policies Chicago, Illinois Middle-aged to older management Reduced rates on all types of personal and property insurance Opportunity to move to other branches in Midwest as section manager within 3 to 5 years Salary: $950 per month Offer C International oil firm Financial and cost analysis and capital budgeting; first year primarily entails "make or buy" analysis Baton Rouge, Louisiana Later possibilities to move into either staff or line management Centralized management Salary $1,050 per month Very new facilities; new office buildings

14- I, Offer D Computer and software firm7 listed on NYSE Technical field sale. s normally progress to distric t sales manager in 5 to 10 years Automobile furnished Santa Monica, Californi a Company recreational and country club is provided free-.diniSng facilities, golf., tennis, swimming, basketball, softball,:picni iking, h iking.: Wide diversity of ages in management Decentralized operation Salary $990 per month for 1 to 2 years7 then straight commission basis Offer E Old"line industrial manufacturer; industrial gauges, pumps, gears, ball bearings and metalsstamped products Marketing analysis and new product market research; chance to move into other functional areas of management later; first project involves responsibility for conducting market potential studies of selected products Houston, Texas * Middle-aged to older management 500 employees Real estate is very reasonable Salary; $1,025 per month.r.F~II n~m w* n~u n

-15 - Offer F Small management consulting firm Work on wide variety of problems in financial analysis, marketing analysts, and operations research Special work with Negro owned businesses in Black Capitalism Program; some teaching of management techniques to groups of clients is available irn the Black Capitalism Program Middle-aged management; team approach to consulting problems; opportunity to become partner in the firm after 10 years if have the ability; one in five men makes it Cincinnati, Ohio Salary: $1,100 per month 0ffer G Work for the City of Denver, Colorado Department of City Planning and Urban Development; department is new and growing Job involves cost analysis and systems simulation; would lead to design of traffic systemns and zoning areas in 4 to 5 years; work with variety of urban problems in addition Excellent vacation plan; scenic surroundings Salary: $900 per month, covered by State Civil Service codes Offer IH Chemical concern, listed in Fortune's 500 Very selective and intensive management training program; requires trainee who is willing to work hard Trainee is rotated through all functional areas of management for two years and groomed for general management responsibilities Decentralized management structure Pphladelphia, Pennsylvania Salary; $1,125 per month

W" 16 i Offer I Pharmaceutical firm, 1,000 employees Production control and scheduling; work directly wi th viWce-president of production operations; would be responsible for new computerized production scheduling system Firm presently has plans to expand into new product area of food processing; will create several high-level positions Wide range of management ages..:. *:: Peoria, Illinois Salary: $1,075 per month... j i i I

-17 -APPENDIX B Examples of Patrwise Similarity' Judgments from Ideal Job Mdel' Questionnaire Small management consulting firm Work on wide variety of problems in financial analysis2, marketing analysis and operations research Special work with Negrpowned businesses in Black Capitalism Program; some teaching of management techniques to groups.of clientss is available *in the Black C.apitalism Program Middle-aged management; tearn approach to consulting problems; opportunity to become partner in 'the firm after 10 years if have the ability; one in five ren sak es it Cincinnati, Ohio Salary: $1,100 per smonth Work for the City of Denver, Colorado Department of City Planning and Urban Development; department is new and growing Job involves cost analysis and systems simulation; would lead to design of traffic systems and zoning areas in 4 to 5 years; work with a variety of urban problems in addition Excellent vacation plan; scenic surroundings Salary: $900 per month, covered by State Civil Service codes Please rate how similar you feel these two job offers are on the scale below by circling one. Si number. Very,Moderately Mderatel Ver Lmilar Similar'.... Di similar Dissim 1 2..3. 4,:5 6 7.',8 9 I:: 10 11 12 13 -"~ — -~- ~~ — 1~- ~I-". I IN..........,.. i",".... i": I.II'..L I 1. — ~. ' y i lar

- 18 -Chemical concern, listed: in Fortune's $00 Very selective and intensive management training program; requires trainee who is willing to work hard Trainee is rotated through all functional areas of management for two years and groomed for general management responsibilities Decentralized management structure Philadelphia, Pennsylvania Salary: $1,125 per month " I- r n w- -'I.1"" " M '"T:". - -l r4r - - - Your personal concept of the "ideal job for you, Your ideal job should reasonably be expected -to exist,. Please rate how. similar' you feel this j.Pob offer is ' to your concept 'of 'your "lideal" job:by':ci li ne number on the scal below,. Very Moderately Moderately Very Similar Similar Dissimilar Dissimilar 1 2 3 4 5 6 7..T 8 9 10 11 12 13 u

19 -REFERENCES (1) Carroll, J.D,, and Chang, Jih Jie.. "Relating Preference Data to Multidimensional Scaling Solutions via a Generalization of Coomb's Unfolding Model'"' Unpublished Working Paper Bell Telephone Laboratories, Murray Hill, N,J., 1968, (2) Doehlert, David H, "Finding the Preferred Regions in a Multidimensional Space, Paper presented at the spring meeting of the Psychometric Society, Madison, Wis,.March, 19i67. (3) Holt, Charles C., and Huber, George P, "A Computer Aided Approach to Employment Service Placement and Counseling" Management Science, XV, No. 11 (July, 1969), (4) Huber, George P, Daneshgar, R,;and Ford, David L. "An Empirical Comparison of Five Utility Models for Predicting Job Preferences. Organizational Behavior and Human Performance, VI 1971 ppa 267-832 (5) Huber, George F.; Sohney, Vinrod K.; and Ford, David L, "A Study of Subjective Evaluation Models'' Behavioral Science, XIV, No. 6 (1969). (6) Klahr, David. "Decision Making in a Complex Environment: The Use of Similarity Judgments to Predict Preferences" Management Science, XV, No, 11 (July 1969), p. 613. (7) Kruskal, J.B. "Multidimensional Scaling by Optimizing Fit to a Nonmetric Hypothesis' Psychometrika, XXIV. (March 1964), pp..i27. (8) Kruskal, J.B, "Nonmetric Multidimensional Scaling: A Numerical Method' Psychometrika, XXIX, (June 1964), pp, 115-29. (9) Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences, New York: McGraw-Hill, 1956.

I i ~20 -(10) Soelberg, Peer 0, "Unprogrammed Decision MakingS Industrial Management Review, VIIX (Spring 1967). (11) Sokal, Robert, and Sneath, Peter. Principles of Numerical Taxonomy. San Francisc: Freeman and Co., 1963 (12) Vroom, Victor H, "Organizational Choice: A Study of Pre- and Postdeclsion Processes:' Organizational Behavior and Human Performance, I (Fall 1966), p. 219,.~~~~~~~~~~~~~~~~~~~~~( — j- I — Ii-, — I