Conjoint models of family decision making

185

Conjoint models of family decision making Lakshman

KRISHNAMURTHI

*

The objective of this research is to develop viable approaches to modeling joint decisions. Using conjoint-analysistype preference data, three methods are developed to combine individual preferences to approximate joint preferences and predict joint decisions. The first is an equal weighting model, which is a simple average of individual members’ part-worth utihties. The second is a relative influence model, which combrnes individual utility functions using a measure of derived Influence. The third is a conflict resolution model. which combines utility functions using a measure of conflict. In addition to these three combination models, individual member models and a joint model based on the joint preferences are available. The application area in which the models are operationalized is family decision making. The decision involves choice of a job by MBA students and spouses at a major private universrty The models are first calibrated using preference data on hypothetical jobs from MBAs, spouses, and couples and then evaluated on their ability to predict the actual Job chosen,

1. Introduction Although there is an extensive literature in family decision making on identifying the relative influence of family members (e.g., Rosen and Granbois (1983)) on the role of conflict in decision making (e.g., Davis (1976), and on understanding the process of decision making and the strategies used by family members (e.g., Park (1982)), not much attention has been directed towards the modeling and prediction of joint decisions. This research takes a step in filling the gap by developing viable methods to combine individual preferences to approximate joint preferences * Lakshman Krishnamurthi is a Visiting Associate Professor of Marketing at the College of Business Administration (M/C 2.43) University of Illinois at Chicago, Box 4348. Chicago, IL 60680, USA. Intern. J. of Research in Marketing 5 (1988) 185-198 North-Holland 0167-8116/89/$3.50

and predict joint decisions. In addition, the models are calibrated and tested using data from a job choice context. Two important components of decision making which must be taken into account in the modeling of joint decisions are relative influence of family members and conflict in decision making. The preoccupation with influence is understandable because influence is a key component of group decision making (March (1955)) and has received considerable emphasis in the marketing literature. For example, Davis and Rigaux (1974) examined influence exerted by husbands and wives at three stages of the decision process for 25 purchase decisions. They found that the average relative influence across all 25 decisions changed little across the three decision stages and that a majority of the 25 decisions at the last stage, the decision stage, were joint decisions. Munsinger, Weber, and Hansen (1975) investigated agreement on relative influence of husbands and wives on seven aspects of a home purchasing decision. They found that a considerable majority of both spouses reported that they exerted equal influence in all seven aspects. More recent research in relative influence include work by Filiatrault and Ritchie (1980) and Rosen and Granbois (1983). The second key issue is conflict in decision making and its resolution. Davis (1976) identifies persuasion and bargaining as two specific strategies to resolve conflict. Spiro (1983) examined persuasion strategies used by individual spouses in making accommodative joint decisions for major durables purchases. As an outcome of a bargaining strategy, Park (1982) described a concession heuristic wherein the decision maker (DM) with the lower intensity regarding an aspect of a deci-

0 1989, Elsevier Science Publishers B.V. (North-Holland)

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L. Krishnamurthi / Conjoint models

sion gives in to the other DM. Both strategies are part of accommodative decision making in which disagreement about goals results in conflict. An example of consensual decision making where there is agreement about goals is a satisficing strategy in which a problem solving approach is taken to find a mutually satisfactory solution (Davis (1976)). Recently, an interesting framework for conflict resolution and relative influence in cooperative groups has been presented by Corfman and Lehmann (1987). Using husband-wife teams choosing between two alternatives in several product classes they find that relative preference intensity and decision history are important determinants of conflict resolution. The existing literature, however, does not offer much direction regarding how individual judgments can be combined using measures of influence and conflict to approximate group judgments and predict group decisions. Wright and Kriewall (1980) addressed the combination issue by suggesting some ways of combining individual members’ preferences to obtain the family’s preferences using conjoint analysis. Although their models did not include a measure of influence or conflict, the motivation to use the conjoint analysis framework in our research originated from theirs. The criteria used in developing the models in this paper are that they include measures of influence and conflict, that their conceptualizations be intuitive, that they be relatively simple to operationalize using conjoint data, and be in the realm of weighted linear models which are widespread in marketing. Accordingly, three combination models are developed in this paper. The first is an equal weighting model which combines individual judgments by weighting them equally. The second is a relative influence model reflecting differential influence. And the third is a conflict resolution model which combines judgments using a measure of conflict. These models are investigated in a family decision

offamrlydecision making

making context, namely the choice of a job by MBA students and their spouses at a major private university. MBAs, followed by their spouses, and later the couples together, provided preference judgments for 28 hypothetical jobs described on six attributes in a conjoint analysis format. Research participants also evaluated the job chosen and the other job offers received on the same attributes as those used in the preference task. This enabled comparison of the predictive validity offered by the combination models with that of the individual family member models and the interacting or joint model.

2. Model development The combination models developed in this section are quite general and can be applied to more than two individuals and a wide variety of tasks and groups. The only constraint is that they require conjoint analysis type preference data. However, the advantage of these data is that they allow the construction of utility functions which relate preference judgments to attributes of the decision task. 2. I. Notation The general main-effects can be formulated as K

J’(k)

k=l

p(k)=1

conjoint

model

where U,, is the derived utility of the ith individual for the jth stimulus, where i = 1, 2 ,*.*> N individuals and j = 1, 2, . . . , J stimuli, k is an attribute index, p(k) is an index for the levels of attribute k, blpck) is the part-worth for the p th level of the k th attribute for individual i, and QPckjj is a O-l dummy variable taking the value 1 for the

L. Kmhnamurrhi

/ Conpint models o/fumi!v decision making

particular attribute level and 0 otherwise. The objective of conjoint analysis iS to estimate rp(~) given the evaluations Y,, and the attrib bute levels such that uj, is a close to Y, as possible. Omitting the i subscript gives the values for the group. Several procedures are available to obtain the part-worths. Because the input evaluations are strict rankings, a non-metric algorithm LINMAP IV (Srinivasan (1981)) was selected to obtain part-worths for each individual and group. LINMAP IV offers predictive improvement over LINMAP III which was evaluated favorably in a comparison with other procedures by Jain, Acito, Malhotra, and Mahajan (1979). LINMAP scales the part-worths such that they sum to zero for each attribute. Because the partworths for each individual can be altered by any arbitrary positive linear transformation without affecting the rank order of the predicted utilities, we standardized the partworths such that the standard deviation equaled one over all the part-worths. These standardized part-worths are now invariant under any positive linear transformation of the original part-worths. The model represented by (1) is a weighted compensatory model. ’ This model formulation is commonly employed in applied work (e.g., see Wright and Kriewall (1980), Jain et al. (1979)) and is also embodied in many attitude formation theories, e.g., Fishbein’s theory. Wright and Kriewall (1980) make the important point that a compensatory model can capture non-compensatory processes fairly well, a sentiment also expressed by Curry and Menasco (1979). Support for weighted linear models in the study of group decision making has been recently offered by Steckel (1985).

’ This model does not include interactions. Interactions are rarely included in individual-level conjoint models because of limited degrees of freedom.

187

2.2. Equal weighting model (E WM) This model assigns equal weight (influence) to all individuals in the joint decision. Under equal weighting, the standardized part-worths obtained for each individual are averaged level by level. These average standardized partworths represent EWM (eq. (2)). b;c,,, = :

b,,dN,

(2)

,=l

Support for equally weighting family members comes from Davis and Rigaux (1974) and Munsinger, Weber and Hansen (1975). One example of consensual decision making is for DMs to simply pool their judgments as represented by EWM. 2.3. Relative influence model (RIM) Because influence is a key component of group decision making, it should be modeled explicitly. One way of obtaining a measure of relative influence is to directly ask group members to assess each other’s influence in different stages of decision making and in different contexts. This is popular in the family and organizational decision making literatures (e.g., Davis and Rigaux (1974). Silk and Kalwani (1982)). An alternative way of obtaining a relative influence measure is to derive it indirectly. It can be argued that the closer an individual’s preferences are to the joint preferences, the more influence the individual has had on the joint preferences because joint preferences are a result of interaction among group members. One way of operationalizing this closeness is to regress the joint rankings against the individual rankings and use the normalized beta weights for the relative influence weights r,*. However, because one would expect the individual rankings to be correlated, and highly in some cases, these regression weights will not be stable and could even be negative. We therefore adapted an alternative method suggested by Green, Carroll, and De-

L. Krishnamurthi / Conjoint models o/family decision making

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sarbo (1978) in a regression context to obtain more stable relative weights. The Green et al. method first finds an orthonormal representation of the explanatory variables such that each new variable, say z,, is best fitting in a least squares sense with the corresponding original variable xi. The dependent variable Y is regressed on the new variables zj to get unambiguous measures of importance of the Z variables. A weighting scheme is next devised to transform these importance weights in terms of the original X variables. These transformed weights are such that they are always positive and they sum to R2. The reader is referred to the original paper for a mathematical treatment. The individual standardized part-worths are multiplied by the corresponding normalized relative influence weights (r,* ) and summed to yield RIM part-worths (eq. (3)). Thus RIM is a generalization of EWM.

2.4. The conflict resolution model (CRM)

tualization. The basic premise of CRM is that, when faced with a conflict, DMs will yield to the individual who stands to gain or lose the most from the decision. This premise, which is a restatement of Park’s (1982) concession heuristic, is also supported by Corfman and Lehmann (1987) who find that the individual who cares the most has the greater impact in the resolution of the decision. In the process of yielding to this individual, the group as a whole gains more than what it would have had it yielded to some other individual. Elements of Davis’ (1976) bargaining principle are also embodied in this model. The argument is developed on the partworth utility functions obtained for each attribute for each DM. THe utility functions are piecewise linear, and the critical elements of these functions are the slopes of each segment. ’ The k th attribute has P(k) - 1 segments if it has P(K) levels. The individual with the steepest segment slope has the most to gain or lose regarding a joint decision relating to this segment. Comparisons across individuals are made by attribute, so slope comparisons are equivalent to comparing differences between utilities for attribute levels. CRM is best explained through an example. Assume there are only two DMs, X and Y. Consider an attribute with three levels and hence two segments. Let bxpckj and bypckJ represent the part-worths for X and Y respectively. Let X and Y’s part-worth functions be such that I bx2ckJ - bxlckj I > I by2ckj- bylckl 0 i.e., X’s function is steeper over segment l-2 than Y’s. In addition, let 1bx3(kj - bx2(kj I < I by3(k)- by2(k)I) i.e., Y’s function is steeper over segments 2-3 than X’s. Also, for illustrative purposes, let b,.3(kj > b..2(kl > bxlckj and by3(k) < by2(kj < bvlck,, i.e., the functions oppose each other. Suppose a decision has to be made between levels 1 and 2. There is a clear case of conflict

The conflict resolution model (CRM) differs from the influence models in its concep-

2 Piece-wise linearity is a well accepted assumption in conjoint analysis.

N

(3) The relative influence weights derived in this manner have two advantages over traditional self-report measures. First, they are obtained as a result of interaction among decision participants. This is advantageous in that notions of accommodation, power, involvement, etc., are incorporated in them. Essentially they capture some elements of the process through which DMs arrive at a joint decision. Second, because these weights are derived in a preference context they have more relevance to a choice situation than self-report measures. If there is considerable disparity in the weights reflecting disagreement with respect to the joint preferences, an accommodative type decision is likely to result. At an extreme, this might take the form of one-party dominance.

L. Krishnamurthi / Conjoint models offamrly decision making

here in that Y would like to choose an option whose value on this attribute is as close to level 1 as possible, whereas X would like to make the choice as close to level 2 as possible. According to CRM, Y should yield to X in deciding over this segment because X’s utility gain is greater than Y’s. The opposite situation prevails if a decision has to be made between levels 2 and 3. Y’s gain is greater than X’s so the conflict should be resolved by X yielding to Y in a decision over this segment. The composite part-worth function for this attribute is represented by X’s function over segment 1-2, and Y’s function over segment 2-3. The group (here X and Y) as a whole gains by resolving conflicts in this manner. Thus, CRM follows the principle of joint utility maximization. This development assumes that the decision is equally important to all the DMs. The model as described gives all the weight to that individual whose segment utilities are the largest. In principle, these segment utilities can be compared to the preference intensity measure of Corfman and Lehmann (1987). Consider a three-level attribute for which X and Y have opposing part-worth function slopes in both segments, such that X’s partworth function is marginally steeper in both segments than Y’s. According to CRM, the composite function is the same as X’s function. X and Y resolve the conflict by Y yielding to X since X would be worse off than Y if Y decides. The outcome of this model, called the O-l CRM, is inequitable because Y’s preferences have no bearing on it. Consequently, a generalization of the O-l CRM which produces a more equitable solution is necessary. Instead of giving all the weight to the individual with the greatest segment utility difference, a proportional weighting scheme is used. This scheme weights each individual in each segment by the magnitude of the individual’s segment utility difference. A weighting parameter called the conflict resolution parameter which captures a

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range of weighting schemes is used. Weighting in this way also reduces the effect of estimation errors in the part-worths which can cause reversals in choice of the larger of two slopes in the O-l CRM. The generalized CRM and use of the conflict resolution parameter is explained below using the example described earlier. Let b ,p+l,p(k) represent the segment utility calculated as the difference between the part-worth for the p + lth level and pth level of attribute k for individual i. Then, b.y2,,,, and bx32(k) are the two segment utility differences of individual X (b.y2ckj- bxlckj and bxjckj b12(k), respectively), and b.,21(k)and bv32(k)are the corresponding values for individual Y. b),21(k) and &32(k) are negative by the convention that increases in utility are considered positive while decreases are considered negative. Let ‘c’ be the conflict resolution parameter. The weighting proportion should be positive, so only the magnitudes of the segment ranges are used. Also, because individuals with larger segment utilities should be weighted more than those with smaller segment utilities, c should not be negative. According to CRM, &l(k)

1.

\

(44 which is the CRM ments 1-2;

estimated range for seg-

b’ x32(k) . @%32(k)) &32(k)

+

I $32(k)

Ic

. cby32(k))

=

%2(k),

(4’4 which is the CRM ments 2-3.

estimated range for seg-

L. Krishnnmurihr / Conjoint models of family decision making

190

If c = 0, V21(k)

=

(&21(k)

+

$21(k))/2

=

(&32(k)

+

by32(k)

and V32(k)

(5)

k2.

Thus, c = 0 leads to a simple averaging of the segment ranges and hence is equivalent to EWM. If c = 1, each composite segment is a simple weighted average of each individual’s share of the range. Asc-+cc,

because 1bx21(kJ1 > 1bv2ickJ1. A similar calculation yields by32(kJfor V,,,,,. Thus, c += cc leads to the O-l CRM. The extension to several attributes and more than two individuals is straightforward. From (4a, b) the general form of the relationship for N individuals can be compactly represented by eq. (7) below: it 1=1

1 bip+l,p(k)

1 Cbip+l,p(k) =

c+l.p(k)-

(7)

It I bip+Lp(k)I c i=l There will be as many such equations as there are attribute segments. Thus, the total number of attribute segments equals C,“=, (P(k) - 1) for the model in eq. (1). The examples considered so far show clear cases of conflict in that the part-worth functions of X and Y are opposing in nature. All the arguments developed above also hold when the functions are in the same relation to each other. The person with the smaller utility difference may be indifferent between two levels, while the one with the gI;eater utility difference will have an incentive to make the decision reflect his/her feeling on the attri-

bute. CRM then follows. The conflict resolution parameter attempts to capture an aspect of the process by which joint decisions are made. Because the process is not attribute dependent, a single parameter is derived. 2.5. Relative injluence conflict resolution model (RICRM) Each individual is treated equally in the conflict resolution model. That is, even if one individual is more influential than another, both individuals’ utility losses or gains are weighted the same. To reflect the differential influence of the individuals the standardized part-worths should be scaled by the corresponding relative weights r,*. The basic equation for RICRM is obtained from (7) as ii

r,*

1 b,p+l.p(k)

1 Cbip+l,p(k)

i=l

= t i=l

r,*

1 biP+l.p(k)

wp+l,p(k).

6)

1=

It can be seen that EWM, RIM and CRM are all special cases of RICRM. If r,* = l/N in (8) we get CRM in (7). If c = 0 in (8) we get the segment utilities for RIM in (3). If c = 0 and r,* = l/N in (8) we get the segment utilities for EWM in (2). It is easy to obtain the part-worth utilities from the segment utilities and the constraint that each attribute’s part-worths sum to zero. In the empirical application in this paper, the difference between CRM and RICRM was small except when the relative influence weights were quite discrepant. Therefore, in order to conserve space and restrict the discussion of the models to a manageable number, we will not present results of RICRM. 2.6. Estimation of c The first step is to write eq. (7) for the number of individuals and the particular attribute design used. In our application, there are two individuals - MBA and spouse -‘and

L. Krishnamurthi / Conjoint models of family decision making Table 1 Job attributes. a Job attributes

Levels

1. Geographical area in the United States

East, Midwest, West, South

2. Salary (including bonus in Expected + 20%, Expected first year of employment) b + lo%, Expected - 20% 3. Business travel (nights per month)

One night or less, 2-5 nights, 6 nights or more

4. Intellectual challenge of the job

Very stimulating and challenging; Moderately stimulating and challenging

5. People (colleagues, boss, etc.) in the company

Demanding, competitive; Flexible, easy to work with

6. Opportunity for early responsibility

A great deal; A moderate amount

,’ These six attributes were chosen as relevant for these subjects based on surveys conducted by the Business School Placement Office, an earlier study of job choice by MBAs (Montgomery and Wittink (1978)) and a pilot study conducted by the author. h A short paragraph explained what was meant by expected salary.

the attribute design is shown in table 1. There are 10 attribute segments in the design so there will be 10 segment equations of (7). We need values for Vp+l,p(k) in eq. (7) to estimate c for each MBA-spouse pair. Because CRM attempts to approximate the joint model, the joint segment ranges calculated from the joint part-worths are used for VP+l,P(k). Several values for c were tried and the value chosen was the one that rninirnized the sum of absolute deviations between the joint segment ranges and the CRM ranges. 3 The partworths for CRM were then calculated from the segment ranges by using the scaling constraint that each attribute’s part-worths sum to zero. The ordering of the attribute levels

3 c was varied in steps of 0.5 from 0 to 10. A value of 1000 was used to approximate co. Minimizing the sum of squared errors, or maximizing the correlation between the two sets of segment utilities, yielded essentially the same results.

191

shown in table 1 was used in the calculation of the segment ranges for all attributes except for ‘geographic location’. In this case, the four levels of the attribute were first arranged in terms of decreasing utility of the joint part-worths. Although this procedure is arbitrary to some extent, the ordering of the levels as given by the joint part-worths was chosen because CRM attempts to derive part-worths which approximate the joint part-worths. Another point to note is that the estimated part-worths are subject to error which can affect the estimation of c.

3. Empirical application In this section we will describe the performance and comparison of the models using the job choice application. The objective is one of model illustration rather than formal model discrimination and testing. Because the instruments used and the data collection ‘procedure are described in detail in Krishnamurtbi (1983) we will only briefly summarize the relevant parts here. 4 The preference data were collected via self-administered questionnaires in three stages, first from the MBAs, next independently from the spouses with a l-2 week delay, and finally from the couples with another l-2 week delay. MBAs were not informed that their spouses would be solicited and neither were informed that they would be approached jointly. MBAs and spouses were instructed in their individual questionnaires to complete the preference task without consultation. Each MBA, spouse, and couple ranked the same set of 28 hypothetical jobs described on six attributes from most preferred to least pre-

4 The experimental design described in that paper is not relevant for the model comparisons in this paper.

L. Krishnomurthi / Conjoint models of Jar+

192

ferred. 5 The six attributes and the specific levels of the attributes used are shown in table 1. After all the preference data were collected, couples were asked to rank the job offers received from best (the job chosen) to worst and to describe the offers on the same six attributes. The data on job offers were obtained about three months after the joint data were gathered. All three sets of preference rankings are available from 46 families. 3.1. Measure of fit

The means of the Kendall’s tau values provided by LINMAP IV are 0.90 for the MBAs, 0.89 for spouses, and 0.92 for couples. The excellent fits indicate that the main effect-only compensatory model captures the preference configuration of the subjects quite well. Also, 87% of the MBAs and spouses and 88% of the couples ranked the two identical profiles consecutively providing some measure of the data reliability. 3.2. Difference

between family

members

If the models are to discriminate at all there need to be some difference in the preference configurations of MBAs and spouses. Although the mean MBA-spouse rank correlation is 0.66, there are differences in the relative weights given to the attributes. Paired t-test of derived attribute importance weights indicate that salary and responsibility are more important to MBAs than to spouses (p < 0.05) and travel is more important to spouses than to MBAs (p < 0.06). On the two critical attributes, salary and travel, the joint importance weights are closer to MBAs on 5 A set of 27 profiles designed to be uncorrelated among the six attributes was selected from Addelman (1962). One profile was included twice, making 28 in a total, to serve as a reliability check. Clear instructions were given to aid the ranking task. It is not uncommon to use this many profiles in such conjoint analysis tasks. For example, qright and Kriewall(l980) used 32 college profiles and Jain et al. (1979) used 27 bank profiles both described on five attributes.

decision making

salary and closer to spouses on travel. A paired t-test shows that salary is more important to couples than spouses (p -C O.Ol), and travel is more important to couples than MBAs (p < 0.08). We also find that MBA and spouse preference rankings are both closer to the joint preference rankings than they are to each other, suggesting that joint preferences are the result of interactions among MBAs and spouses. However, although spouses provide preference rankings temporally closer to the joint rankings than MBAs, the mean correlation of the MBA-joint preference rankings is significantly higher than the spouse-joint correlation indicating that the MBAs had greater impact on the joint preferences. 3.3. Prediction

measures

Each model is used to predict the job actually chosen by the couple. This is the FIRST CHOICE criterion. This criterion ignores the predicted utilities of the other job offers. Therefore, we defined another measure which would include information on all the job offers. This criterion, called C *, is motivated by the objective function in LINMAP. C* is bounded between 0 and 1 and would equal 0 only when the predicted utilities rank the job offers identical to the choice set and would equal 1 when it is completely opposite. 6 The measure is invariant under any positive linear transformation of the part-worth functions (and hence the predicted utilities). The values on the two criteria for each model are provided in table 2. 3.4. Model

comparisons

To make comparisons among the models, we have to draw on accumulated research 6 Let U, be the utility of the jth ranked job ordered from most preferred to least preferred. Compute U, - q if ZJ, > CJ or fJ - Uk if U, > Uk for all possible pairs with k > j. Then B=C(CI-Li,)andG=E(U,-Uk)Vj,k,k>j,andC*=’ B/(B + G).

L. Krishnamurthi / Conjoint models o/fami!v decision making

I93

Table 2 Model performance. a MBA

Spouse

Joint

EWM

RIM

CRM

56

46

61

58

51

57

C*

0.220 c (0.286)

0.307 (0.326)

0.231 (0.279)

0.241 (0.282)

0.237 (0.269)

0.236 (0.278)

n

43

43

40

42

38

38

Criterion FIRST CHOICE

b

@)

d Although MBA, spouse, and joint preference rankings are available in 46 cases, the prediction sample size for RIM and CRM reduces to 38 because one job evaluation form was not returned, one was incomplete, one described identical job offers, and in five other cases only one job offer was reported. The prediction sample size is 40 for joint because of 2 additional cases, is 43 for MBA and spouse because of 5 additional cases, and is 42 for EWM because in four of these five cases both MBA and spouse rankings are available. h Ties have been accounted for in FIRST CHOICE by assigning a value of l/k to the job chosen if its predicted utility is the highest and tied with the predicted utilities of k - 1 other job offers reported. There were only 3 tied cases, all in the joint model. ’ Standard deviations are in parentheses.

/

evidence in the particular application area and related areas. Basically, no comparative performance results from models similar to the ones developed in this paper are available in the marketing literature. ’ Evaluation of individual, group, and combination models are more common in the social psychology literature on small group behavior. However, the groups studied are usually ad hoc groups and the tasks investigated are generally objective tasks with a known outcome in which the group members have no personal stake. In contrast, families are characterized by the long-standing nature of the relationship among the members and many family decisions are of a subjective and personally consequential nature. These differences make the generalization of findings from the social psychology literature to the family decision making literature difficult (Davis and Rigaux (1974)). The expected model comparison results are compactly summarized in table 3. ’ Although Wright and Kriewall (1980) operationalized three combination models in the context of college choice, they did not compare these models against each other but chose one model that best represented the family. They also did not compare the individual student, mother, and father models against each other, nor the best combination model with the three individual models.

3.5. Comparison results The first baseline comparison is with a random choice model. A random choice model is one in which the proportion of correct predictions is expected to be l/m, where m is the average number of job offers in that sample. Every model outperforms the random model at a, significance level of 1% or better. Formally, the test is H,: 7~= r0 where 7r0 is given by the random model and 7~ is estimated by the model being compared. The standard error is given by [ r,,(l - ~~)/n]“~ where n is the sample size for the model. This is a basic but critical test and the results indicate that the utility models are better than a pure chance model. Results are reported in table 4 on the FIRST CHOICE and C* criteria for a subset of the comparisons described in table 3. All three combination models, by incorporating the inputs of both members, are better than the Spouse model. As expected, the Joint model is also better than the Spouse model, but, contrary to expectation, the MBA model is not superior to the Spouse model although the comparison is stronger on the C* criterion. A possible reason is a lack of statistical power with the FIRST CHOICE criterion. The three combination models are a little

L. Krishnamurthi / Conjoint models of farnIb decision mukmg

194 Table 3 Model comparisons. Comparison

Expected performance

1.

EWM vs. RIM

Conceptually expect RIM better than EWM. Substantively because decision expected to be joint. differences between EWM and RIM are likely to be small. Because both are linear combinations of MBA and Spouse models, will predict correctly when MBA and Spouse predict correctly and tend to predict incorrectly when both MBA and Spouse predict incorrectly.‘. Discrimination on FIRST CHOICE possible only when either MBA or Spouse predicts correctly and the other predicts incorrectly. Expect more discrimination on C*.

2.

CRM vs. EWM

Conceptually CRM better than EWM because EWM is subset of CRM. Empirically depends on amount of conflict present. Davis (1976) claims families work to minimize conflict. Because decision is important. MBAs and spouses might compromise resulting in joint preferences being in between MBA and spouse preferences. To the extent this happens, difficult to discriminate between CRM and EWM.

3.

MBA vs. Spouse

MBA expected to be better than Spouse based on theory of comparative resources and relative investment (Davis ( 1976)).

4a. EWM, RIM. CRM By incorporating vs. Spouse than Spouse.

inputs of more influential

member (MBA),

EWM, RIM, CRM expected to predict better

4b. Joint vs. Spouse

Joint better than Spouse for same reason in 4a.

5.

Joint vs. EWM, RIM. CRM

Conceptually Joint best because of collaboration. Combination models approximate this collaboration by mathematical aggregation. Davis (1976) suggests that families want to reciprocate and accommodate and that they would satisfy rather than optimize. This indicates that EWM, and hence RIM and CRM because they are more general, may approximate the collaboration process well. :, Joint not expected to be statistically better than EWM, RIM, and CRM.

6.

Best member

Some evidence (e.g., Yetton and Bottger (1982)) suggests that a group’s best member may perform as well as the interacting group. Expect MBA to be best member because of comparative resources and relative investment (Davis (1976). .‘, Joint not expected to be better than MBA. For same reason EWM, RIM, and CRM not expected to be better than MBA.

better than the MBA model on the FIRST CHOICE criterion and slightly worse on the C* criterion. As expected the differences are not statistically significant (not reported in table 3). We argued that the MBA, on average, is the best member and that the Joint model is not expected to be better than the MBA model. As reported in table 4, this hypothesis is supported. We hypothesized that the Joint model is not likely to be superior to the three combination models which are mathematical aggregates of the individual models. The comparison of Joint versus EWM, the simplest combination model, is shown in table 4. Although numerically the Joint model is better than EWM on the FIRST CHOICE criterion the difference is not statistically significant. The results of Joint*versus RIM and CRM are similar. Operationally, the C* criterion is quite different from the

FIRST CHOICE criterion. Therefore, the convergent validity in the comparison results is reassuring. We will next briefly compare the relative influence model (RIM) and the equal weighting model (EWM) when the influence weights are discrepant and the conflict resolution model and EWM when the conflict resolution parameter ‘c’ is greater than zero. We note that these differences depend on the preference configurations of the MBA and spouse. 3.5.1. RIM

and EWM

These two models can predict differently only when the relative influence weights are discrepant. Because the C* criterion incorporates information on all the job offers it is an appropriate criterion for comparison. When the MBA is dominant we expect RIM’ to discriminate better than EWM (i.e., RIM’s

195

L. Krrshnamurthi / Conjoint models of family decision making Table 4 Model comparisons: Criteria 1 and 2. Criterion 2 (C*)

Criterion 1 (FIRST CHOICE)

Mean diff.

fb

(std. error) - 0.083 (0.034)

(sign.) -2s ( p c 0.02)

0.06

- 0.091 (0.041)

- 2.2 ( p < 0.02)

6

0.06

- 0.100 (0.047)

- 2.0 (p < 0.05)

8

7

0.05

- 0.083 (0.044)

-1.9 ( p < 0.05)

12

8

0.19

- 0.089 (0.053)

-1.7 (p < 0.07)

Joint vs. EWM

8

5

0.36

0.003 (0.038)

0-J

Jomt vs. MBA

9

6

0.25

0.014 (0.042)

(ns)

Comparison

n

r

P(k>r)

EWM vs. Spouse

6

6

0.02

RIM vs. Spouse

7

6

CRM vs. Spouse

7

JOINT vs. Spouse MBA vs. Spouse

a

* This is an exact test of correlated proportions called the McNemar test (see Hays (1973: 741)). Here r is the number of times Model A (the first model listed) is better than Model B (including ties), n is the sum of the number of times each model is better than the other, and P(k > r) is the cumulative binomial probability with p = 0.5. This test is quite powerful even for small sample size (see Srinivasan (1981)). ’ The sample size for the paired t-test varies between 38 and 43

C* will be lower). When the spouse is dominant, we speculate that this dominance may not carry through to choice based on the theory of comparative resources and relative investment. As a consequence we expect equal weighting to do just as well as RIM (i.e., RIM’s C* will be equal to or higher than EWM’s). In the MBA-dominant sub-sample (n = 13), the mean (standard deviation) of C* is 0.109 (0.123) for RIM and 0.167 (0.243) for EWM. The corresponding values for the spousedominant sub-sample (n = 11) are 0.303 (0.338) for RIM and 0.267 (0.341) for EWM. 8 Thus, numerically the values of C* are as hypothesized. Also, note that the values for C* are closer in the spouse-dominant sample because the relative weights are not very discrepant. Because of the small sample sizes, ’ Dominance was defined as the relative influence exceeding the mean + l/2 standard deviation.

weight

rather than testing the hypotheses as stated, a composite test is carried out by checking if the overall discriminating ability of RIM is significant. The test indicates that it is (t = 1.6, df = 22, p < 0.07). The value of C* for RIM in the MBA-dominant sub-sample is also significantly lower than in the spouse-dominant sub-sample (t = 1.9, df = 22, p < 0.05). 3.5.2.

CRM

and EWM

CRM differs from EWM when c > 0. In these cases, one would expect CRM to predict better than EWM (lower C*). Numerically, C* for CRM is lower than that for EWM but the difference is not statistically significant.

4. Discussion and conclusions The methodological contribution of this study is in the use of conjoint analysis to

196

L. Krishnamurthi / Conjoint models of family decision making

model family decision making, in the development of the conflict resolution model, and in the calibration of derived influence weights. The models developed are general enough to be applicable to a number of decision problems and groups of varying size. The study makes a substantive contribution to the family decision making literature by providing a modeling focus to this literature, in investigating a decision of real consequence to the individuals involved, and in comparing the two individual models with the joint model and the three combination models. The basic results are that if member preferences are fairly highly positively correlated the model of the best member, identified on the basis of comparative resources and relative investment, or the equal weighting model may be used to predict group decision almost as well as the model of the group or other combination models. Does this mean that joint modeling is unnecessary? Certainly not. The nature of the task, whether it is personally consequential or not, simple or complex; the relationship among group members, whether it is intact and long-standing like in a family or ad hoc like in a committee; and the preference configuration of the individual members and the group, for example the degree of conflict present, whether the preferences are congruent or discrepant, and whether they have a common stake in the outcome all have a bearing on model performance. It is quite clear how the job choice decision rates on these three dimensions. Recently Davis, Hoch, and Ragsdale (1986) evaluated the effect of anchoring and adjustment strategies used in inter-spousal predictions. They find that husbands and wives are very inaccurate in predicting each other’s preferences and conclude that relying on single informants could be risky. Although our study focuses on predicting joint preferences whereas theirs focuses on inJer-spousal preferences, in a broad sense their conclusion contradicts our call for using a best member

model. We believe a large part of these opposing conclusions can be explained by evaluating the decisions they studied versus the job choice decision on the three dimensions mentioned above. Because family decision making is an important area in marketing, it is useful to evaluate the results further. Davis (1976: 253) discusses three factors which are unique to families as group decision makers, namely the environment of family decision making, the maintenance needs of families, and the interrelatedness of family decisions. He claims that the distracting nature of the family environment is not conducive to high-quality decision making. There is a suggestion that families, more than other groups, are poor decision makers because they tend to simplify the issues under consideration and often ‘satisfy’ rather than ‘optimize’. Families also tend to avoid conflict, particularly if the problem seems threatening to the continuance of the group. Finally, families make decisions within the context of other decisions. This interrelatedness might make one decision look faulty when viewed in isolation but not when viewed as part of a series of decisions. The first and third factors suggest that predicting a complex family decision such as job choice may be difficult. The decisionmaking process is also dynamic, whereas the models are static. Because of significant time intervals between the preference measurement and the choice decision, learning effects and history effects could have altered the preference structure of MBAs and spouses leading to incorrect model predictions. Regarding the third factor, a spousal job decision could be interrelated with the MBA job decision. Seeking a mutually compatible solution could result in a suboptimal MBA job being selected leading to an incorrect model prediction. Despite these factors, the MBA and joint models in this study predicted correctly 56% and 61% of the actual jobs chosen. To put this in perspective, in a similar context Montgomery

197

L. Krrshnamurthi / Conjoinr models of family decision making

and Wittink (1978) predicted 48% of first choice correctly. The six attributes used in this study are a subset of their eight attributes. 9 The desire to avoid conflict, which is the second factor suggested by Davis (1976), is the chief reason for the lack of model discrimination among the combination models. Although there are 26 cases (58%) of beginning conflict there is ending conflict in only 10 of these cases (38%). lo In a study of home purchasing decisions of married couples, Park (1982) found so few cases of preference conflict that he was unable to operationalize his concession heuristic. Despite selecting choice alternatives on the basis of prior disagreement between couples, Corfman and Lehmann (1987) found that only 39% of the decisions ended in disagreement. With other intact groups, e.g., long-standing committees, or company executives who have been together for some period of time, the results could be different particularly if members have different stakes in the final outcome. There is likely to be greater degree of conflict among such group members and greater difference in relative influence. The size of the group also affects model discrimination. With larger groups, there is likely to be more conflict and greater spread in the relative influence weights. The issue, therefore, is not whether the models can discriminate among themselves. It is the context which determines discriminability. In the job choice context, the results of the model comparisons agreed with expectations except for the MBA-spouse

9 A close observation of 7 cases in which MBA, spouse, and joint models all predicted wrongly pointed to omitted attributes like company reputation or a simultaneous spousal job decision. The job chosen in 4 of these 7 cases had a lower salary and in the other 3 cases involved more travel than another essentially identical job, despite higher salary and less travel being preferred by MBA, spouse and couple. ‘“Beginmng conflict is operationalized as ‘low’ correlation between MBA and spouse rankings and ending conflict as ‘large’ difference between the relative influence weights.

comparison son.

and the CRM-EWM

4.1. Limitations search

and directions

compari-

for future

re-

We have already noted the effect on choice predictions because of the delay in gathering the choice data. There could also have been a testing effect, particularly on the MBAs, in that the preference measurement itself could have stimulated some search and information gathering and preference reconciliation with spouses prior to obtaining spouse preferences. This can affect the relative influence weights. Measurement errors in the explanatory variables (in our case MBA and spouse rankings) were also ignored in estimating r,*. This may not matter if the errors affect both weights equally. Finally, the small sample size severely restricts our ability to discriminate between the models using the FIRST CHOICE criterion. i1 A future research agenda would involve testing the models developed in this paper with different decision tasks and groups of varying compositions. Model discrimination will be further enhanced if degrees of conflict can be created through experimental conditions. Such experimental manipulations were inappropriate in this study given the real and personal decision involved. As formulated, trade-offs among attributes is not explicitly considered in the conflict resolution model. However, because the joint attribute segments are used in calibrating the parameter ‘c’, there is implicit consideration of such trade-offs. A future extension is to explicitly include such trade-offs.

‘I Such small sample sizes are not uncommon in group decision making research. Silk and Kalwani (1982) had 25 pairs of informants, Park (1982) had 48 couples, Neslin and Greenhalgh (1983) had 54 subjects, and Corfman and Lehmann (1987) had 62 couples.

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/ Conjoint models of family decision making

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