Market segmentation for customer satisfaction ... - Wiley Online Library

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY Appl. Stochastic Models Bus. Ind., 2005; 21:303–309 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/asmb.554

Market segmentation for customer satisfaction studies via a new latent structure multidimensional scaling model Jianan Wu1,*,y and Wayne S. DeSarbo2,z 1

2

A. B. Freeman School of Business, Tulane University, New Orleans, LA 70118, U.S.A. Smeal College of Business, Pennsylvania State University, University Park, PA 16802, U.S.A.

SUMMARY It has been well documented in the marketing literature that customer satisfaction is critical to any businesses’ success. However, it is far less clear as on how marketers comprehend customer differences in customer satisfaction evaluations, and leverage such understanding in forming their marketing strategies. Only recently have researchers begun to explore the notion of individual or segment differences in the formation of overall satisfaction judgments. To extend the exploration of unobserved customer heterogeneity in customer satisfaction studies with multiple attributes, we propose a latent structure multidimensional scaling (MDS) model to visually depict unobserved customer heterogeneity with respect to the theoretical components of customer satisfaction judgments. Our model is developed on the basis of the well-established expectancy–disconfirmation theory of customer satisfaction. We describe the proposed MDS model and discuss the technical aspects of the model structure and maximum likelihood estimation. Copyright # 2005 John Wiley & Sons, Ltd. KEY WORDS:

customer satisfaction; market segmentation; latent structure analysis; multidimensional scaling

INTRODUCTION Customer satisfaction has become a fundamental construct in marketing given its importance and established relationship with customer retention and firm profitability [1]. There is an abundant marketing literature concerning the determinants of customer satisfaction judgments, mostly from an aggregate market perspective [2]. Such studies focus upon the impacts of various response determinants (e.g. performance, expectation, disconfirmation, attribution, equity, etc.) on satisfaction judgments, and report that these impacts on satisfaction are heterogeneous and are often dependent upon the product/service class under investigation [3]. Recent studies argue that even within a given product/service class, unobserved customer heterogeneity still exists and the recognition of such heterogeneity helps marketers to form their targeted marketing strategies

*Correspondence to: Jianan Wu, A. B. Freeman School of Business, Tulane University, New Orleans, LA 70118, U.S.A. y E-mail: [email protected] z E-mail: [email protected]

Copyright # 2005 John Wiley & Sons, Ltd.

304

J. WU AND W. S. DESARBO

(e.g. References [4, 5]). In addition, visually depicting satisfaction determinants has been managerially desirable. For example, the well-known importance–performance chart has been extensively adopted for market performance analysis in a variety of commercial satisfaction studies. This approach visually depicts an attribute’s performance against it’s importance in a two-dimensional plot. Unfortunately, such an approach not only ignores both sources of the heterogeneities discussed above, but also ignores how other important determinants (e.g. expectation, disconfirmation), together with performance, relate to overall satisfaction. In addition, it fails to capture correlations amongst the attributes. We propose a stochastic latent structure multidimensional scaling model which visually depicts unobserved customer heterogeneity with respect to these theoretical components of customer satisfaction. That is, we devise a spatial market segmentation procedure whose inner structure reflects the theoretical process upon which such satisfaction judgments are elicited.

THE MODEL The legions of authors cited in the review work of Reference [6] on customer satisfaction suggests that the expectancy–disconfirmation paradigm is the most consistently and most widely adopted paradigm in marketing literature for understanding the determinants of customer satisfaction judgments. Based on this evidence, we have adopted the expectancy–disconfirmation paradigm in our proposed stochastic MDS model, where the primary determinants of overall satisfaction judgments are performance, expectation, and disconfirmation (e.g. Reference [3]). In this paradigm, an individual’s expectation is negatively disconfirmed when the product performs worse then expected, and positively confirmed when the product performs better than expected. In general, satisfaction results from positive confirmation, and dissatisfaction results from negative disconfirmation. We use this general framework to model the relationship between performance, expectation, disconfirmation, and overall satisfaction. Let PEim = observed perceived performance rating on attribute m for subject i; CSim = observed expectations rating on attribute m for subject i; DSim = observed disconfirmation rating on attribute m for subject i; OSi = observed overall satisfaction for subject i. These are the observed data where i ¼ 1; . . . ; I and m ¼ 1; . . . ; M are the indices for subjects/ consumers and attributes, respectively. Following a scalar products/vector MDS model (e.g. Reference [7]), we assume that the each attribute and each satisfaction determinant can be visually depicted in a common T dimensional vector space. Let amt = attribute m vector location on dimension t; ft|s = performance vector location on dimension t for segment s; jt|s = expectations vector location on dimension t for segment s; ct|s = disconfirmation vector location on dimension t for segment s; where t ¼ 1; . . . ; T and s ¼ 1; . . . ; S are the indices for the derived dimensions of the common space and the derived latent/unknown segments respectively. The inner product structure of the Copyright # 2005 John Wiley & Sons, Ltd.

Appl. Stochastic Models Bus. Ind., 2005; 21:303–309

MARKET SEGMENTATION FOR CUSTOMER SATISFACTION

305

vector model in the common T dimensional space suggests that conditional on consumer i being in segment s, T T T X X X ftjs amt ; cimjs ¼ jtjs amt ; and dimjs ¼ ctjs amt pimjs ¼ t

t

t

represent the ‘model’ performance, expectations, and disconfirmation of attribute m for consumer i respectively (cf. Reference [7]). The corresponding stochastic specifications for performance, expectation, and disconfirmation are thus given by T X ftjs amt þ eimjs ð1Þ PEimjs ¼ pimjs þ eimjs ¼ t

CSimjs ¼ cimjs þ Zimjs ¼

T X

jtjs amt þ Zimjs

ð2Þ

ctjs amt þ ximjs

ð3Þ

t

DSimjs ¼ dimjs þ ximjs ¼

T X t

To model overall satisfaction, we take the following three important characteristics into consideration. First, the expectancy–disconfirmation paradigm dictates that satisfaction is a function of performance, expectation, and disconfirmation. We posit that overall satisfaction is a linear function of overall performance and overall expectation. This specification has been widely adopted in the literature. For example, Reference [6] posits that overall satisfaction as a linear function of overall expectation. Reference [4] specifies overall satisfaction as a linear function of performance, expectation, disconfirmation, attribution, and equity. Reference [2] posits that overall satisfaction is a linear function of both overall expectation and overall performance. Reference [1] specifies overall satisfaction as a linear function of quality and expectation. Second, we further posit that overall satisfaction is an increasing and concave function of overall disconfirmation, indicating that customers’ dissatisfaction from not having their expectations met is greater than their satisfaction from an equivalent amount of positive confirmation. This asymmetry is a well supported finding in customer satisfaction and service quality research in particular [2], and in psychology in general [8]. To achieve that, we assume a modified exponential functional relationship between overall satisfaction and overall disconfirmation to capture this asymmetry. Third, to operationalize overall performance, overall expectation, and overall disconfirmation, we follow a composite approach as in Reference [9]. The composite measure of each construct is obtained by averaging the measures of the construct over the attributes. Reference [9] shows that the overall measure and the composite measure over attributes are highly correlated (with correlations between 0.77 and 0.83). Let the composite measure of performance, expectation, and disconfirmation be X X X PE i ¼ PEim =M; CS i ¼ CSim =M; DS i ¼ DSim =M m

m

m

Then, our overall satisfaction model is specified as OSijs ¼ us PE i þ vs CS i þ ws ð1 eks DSi Þ=ks þ zijs Copyright # 2005 John Wiley & Sons, Ltd.

ð4Þ


306


where ks > 0 is a segment constant which captures the degree of the asymmetry for disconfirmation DS i on overall satisfaction and includes the linear treatment of DS i as a limiting case when ks approaches 0. Note, if we attribute-mean-centre performance, attribute expectation, attribute disconfirmation, and overall satisfaction, we do not need a constant term in (4). We assume that for any consumer i and attribute m, ðeimjs ; Zimjs ; ximjs Þ may be correlated (e.g. consumer i who has a high expectation for attribute m may also tend to render high performance evaluations on attribute m). We thus model ðeimjs ; Zimjs ; ximjs Þ via a multivariate normal distribution 0 1 eimjs B C B Zimjs C N3 ð0; Ds Þ ð5Þ @ A ximjs where Ds is the variance–covariance matrix of ðeimjs ; Zimjs ; ximjs Þ for segment s and attribute m, and eimjs ; Zimjs ; ximjs are IID across attributes and individuals. We further assume that, conditional on eimjs ; Zimjs ; ximjs ; zijs Nð0; s2s Þ

ð6Þ

Our complete segment level model framework is thus given by expressions (1)–(6).

MODEL ESTIMATION The conditional likelihood of the ith customer belonging to segment s can be specified as Lijs ðPEim ; CSim ; DSim ; OSi Þ ¼ Lijs ðOSi jPEim ; CSim ; DSim Þ Lijs ðPEim ; CSim ; DSim Þ M Y 0 1 2 1 1 2 pffiffiffiffiffiffiffiffi eðXim mmjs Þ Ds ðXim mmjs Þ=2 ¼ pffiffiffiffiffiffi eðOSi ys Þ =2ss 3=2 jDs j 2pss m¼1 ð2pÞ

where 0 ys ¼ us PE i þ vs CS i þ ws ð1 eks DSi Þ=ks ;

PEim

0 PT

1

B C C Xim ¼ B @ CSim A DSim

t¼1

and

ð7Þ

ftjs amt

1

BP C B C mmjs ¼ B Tt¼1 jtjs amt C @ A PT c a t¼1 tjs mt ð8Þ

The unconditional likelihood is then Li ðPEim ; CSim ; DSim ; OSi jamt ; ftjs ; jtjs ; ctjs ; Ds ; ss ; us ; vs ; ws ; ks ; ls Þ ¼

S X

ls Lijs

ð9Þ

s¼1



307


where ls represents the relative size (mixing proportion) of segment s. Therefore, the complete log-likelihood function across all consumers is ! I S X X ð10Þ LLðPEim ; CSim ; DSim ; OSi jamt ; ftjs ; jtjs ; ctjs ; Ds ; ss ; us ; vs ; ws ; ks ; ls Þ ¼ ln ls Lijs i

s¼1

Thus, in our proposed stochastic MDS model, given observed data PEim, CSim, DSim, and OSi, we estimate the parameters amt ; ftjs ; jtjs ; ctjs ; Ds ; ss ; us ; vs ; ws ; ks and ls : To ensure that D1 (hence Ds) is positive definite in the s decomposition for D1 s : 0 c11js B 1 0 Ds ¼ Cs Cs where Cs ¼ B @0 0

estimation, we utilize the Cholesky c12js

c13js

1

c22js

C c23js C A

0

c33js

ð11Þ

with cijjs 2 ð1; 1Þ and further enforce the positivity of the diagonal elements via an exponential function as reparameterization. We use a modified E-M algorithm (cf. References [10–12]) to estimate the full model (1)–(6) by iteratively maximizing expression (10) over specified values of T and S.

THE SPATIAL REPRESENTATION The performance vector fs ¼ ðftjs Þ; the expectation vector js ¼ ðjtjs Þ; and the disconfirmation vector cs ¼ ðctjs Þ can be all spatially represented simultaneously in the derived T-dimensional space together with common attribute coordinates am ¼ ðamt Þ: In addition, we estimate and depict the satisfaction vector in this same T-dimensional space. Let os ¼ ðotjs Þ be the satisfaction vector in the same T-dimensional space, then the attribute satisfaction can be written as X Simjs ¼ otjs amt þ Bimjs with EðBimjs Þ ¼ 0 ð12Þ t

On the other hand, using the first order approximation of the modified exponential function in Equation (4), we have OSijs ¼ us PE i þ vs CS i þ ws ð1 eks DSi Þ=ks þ zijs ¼ us

¼

1 X 1 X 1 X PEim þ vs CSim þ ws DSim þ zijs M m M m M m

X 1 m

¼

X

M

ðus PEim þ vs CSim þ ws DSim Þ þ zijs

Simjs þ zijs

ð13Þ

m



308


where Simjs ¼ 1=Mðus PEim þ vs CSim þ ws DSim Þ: Using the vector model framework in Equations (1)–(3), we have ! X X X 1 us Simjs ¼ ft amt þ vs jt amt þ ws ct amt þ dimjs M t t t ¼

X 1 us ft þ vs jt þ ws ct amt þ dimjs M t

ð14Þ

where dimjs ¼ 1=Mðus eimjs þ vs Zimjs þ ws ximjs Þ; and Eðdimjs Þ ¼

1 ðus Eðeimjs Þ þ vs EðZimjs Þ þ ws Eðximjs ÞÞ ¼ 0 M

ð15Þ

Comparing the two expressions of the attribute satisfaction in (12) and in (14), (15), we obtain the estimated satisfaction vector as 1 us fs þ vs js þ ws cs os ¼ ð16Þ M As constructed, the proposed formulation is a special type of latent structure MDS spatial model (see Reference [11] for a review of such procedures). It is important to note that unlike any existing spatial methodology (traditional or latent structure MDS), this is the only such methodology that has been tailored to accommodate customer satisfaction modeling based upon well-established behavioural theory. Much of the technical specification in expressions (1)–(16) is based on the theoretical and empirical behavioural research concerning the impact of disconfirmation, expectation, and performance on customer satisfaction. Although a direct comparison with other existing spatial methodology would be difficult given different likelihood functions and the inability to perform predictive validation (where membership in a given segment must be known a priori), a number of nested special cases can be tested against our full model exposition. By utilizing zero parameter restrictions, we can compare the overall fit of the full model described above versus special cases where one or more constructs in Equation (4) are dropped. By utilizing equality restrictions, we can test for equality of the impacts across constructs. In addition, with the use of appropriate constraints, we can compare the non-spatial specifications (e.g. Reference [4]) versus ours. For all such nested model tests, we can utilize either the standard likelihood ratio chi-square tests given prescribed values of S and T, and/or the BIC/CAIC information heuristics discussed below.

IDENTIFICATION ISSUES There are two major issues concerning model identification: (1) the identification of parameters relating to mixture distributions; and (2) the identification of parameters related to such a spatial bilinear MDS model (cf. Reference [12]). Because the joint distribution of the three error terms for satisfaction determinants is trivariate normal with non-singular covariance matrices and the error term for the overall satisfaction is normal, the associated mixture is identified [13]. Regarding the second identification issue, the derived configuration for each market segment can be orthogonally rotated (including scale indeterminacies) without changing the resulting projections and scalar products. Thus, there are TðT 1Þ=2 indeterminacies per segment. Copyright # 2005 John Wiley & Sons, Ltd.



309

MODEL SELECTION HEURISTICS The number of free parameters estimated in our model is N ¼ MT þ 3ST þ 10S þ ðS 1Þ TðT 1Þ=2: The common information heuristics used for model selection (S and T) utilized here are the CAIC and BIC. CAIC ¼ 2LL þ ðln I þ 1ÞN and BIC ¼ 2LL þ ðln IÞN; where LL is the log-likelihood of the model and N is the number of free parameters of the model. One utilizes these penalized likelihood function measures in model selection by choosing the model solution which renders minfBIC or CAICg:

CONCLUSIONS The expressed position in this manuscript is that market segmentation for customer satisfaction should reflect customer heterogeneity in terms of the behavioural process underlying the elicitation of such judgments. We have devised a new latent structure spatial methodology whose internal structure is driven by the expectancy–disconfirmation process of customer satisfaction. Unlike traditional data analytic methods for market segmentation (e.g. cluster analysis, CHAID, CART, etc.), we have developed heuristics for identifying the appropriate number of market segments. In addition, given the Maximum Likelihood Estimation (MLE) finite mixture framework, one can employ asymptotic statistical theory for large samples to investigate the stochastic nature of the derived parameter estimates. Additional research in terms of concomitant variable reparameterization, structural equation generalizations, hierarchical Bayes formulations, and commercial applications are fertile areas for future investigation.

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