Chapter 2
Response-Based Segmentation Using Finite
Mixture Partial Least Squares
Theoretical Foundations and an Application
to American Customer Satisfaction Index Data
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
Abstract When applying multivariate analysis techniques in information systems
and social science disciplines, such as management information systems (MIS) and
marketing, the assumption that the empirical data originate from a single homogeneous population is often unrealistic. When applying a causal modeling approach,
such as partial least squares (PLS) path modeling, segmentation is a key issue in coping with the problem of heterogeneity in estimated cause-and-effect relationships.
This chapter presents a new PLS path modeling approach which classifies units on
the basis of the heterogeneity of the estimates in the inner model. If unobserved
heterogeneity significantly affects the estimated path model relationships on the aggregate data level, the methodology will allow homogenous groups of observations
to be created that exhibit distinctive path model estimates. The approach will, thus,
provide differentiated analytical outcomes that permit more precise interpretations
of each segment formed. An application on a large data set in an example of the
American customer satisfaction index (ACSI) substantiates the methodology’s effectiveness in evaluating PLS path modeling results.
Christian M. Ringle
Institute for Industrial Management and Organizations, University of Hamburg, Von-Melle-Park
5, 20146 Hamburg, Germany, e-mail: cringle@econ.uni-hamburg.de, and Centre for Management and Organisation Studies (CMOS), University of Technology Sydney (UTS), 1-59 Quay
Street, Haymarket, NSW 2001, Australia, e-mail: christian.ringle@uts.edu.au
Marko Sarstedt
Institute for Market-based Management, University of Munich, Kaulbachstr. 45, 80539 Munich,
Germany, e-mail: sarstedt@bwl.lmu.de
Erik A. Mooi
Aston Business School, Aston University, Room NB233 Aston Triangle, Birmingham B47ET, UK,
e-mail: e.a.mooi@aston.ac.uk
R. Stahlbock et al. (eds.), Data Mining, Annals of Information Systems 8,
c Springer Science+Business Media, LLC 2010
DOI 10.1007/978-1-4419-1280-0 2,
19
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Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
2.1 Introduction
2.1.1 On the Use of PLS Path Modeling
Since the 1980s, applications of structural equation models (SEMs) and path modeling have increasingly found their way into academic journals and business practice.
Currently, SEMs represent a quasi-standard in management research when it comes
to analyzing the cause–effect relationships between latent variables. Covariancebased structural equation modeling [CBSEM; 38, 59] and partial least squares analysis [PLS; 43, 80] constitute the two matching statistical techniques for estimating
causal models.
Whereas CBSEM has long been the predominant approach for estimating SEMs,
PLS path modeling has recently gained increasing dissemination, especially in the
field of consumer and service research. PLS path modeling has several advantages
over CBSEM, for example, when sample sizes are small, the data are non-normally
distributed, or non-convergent results are likely because complex models with many
variables and parameters are estimated [e.g., 20, 4]. However, PLS path modeling should not simply be viewed as a less stringent alternative to CBSEM, but
rather as a complementary modeling approach [43]. CBSEM, which was introduced
as a confirmatory model, differs from PLS path modeling, which is predictionoriented.
PLS path modeling is well established in the academic literature, which appreciates this methodology’s advantages in specific research situations [20]. Important
applications of PLS path modeling in the management sciences discipline are provided by [23, 24, 27, 76, 18]. The use of PLS path modeling can be predominantly
found in the fields of marketing, strategic management, and management information systems (MIS). The employment of PLS path modeling in MIS draws mainly
on Davis’s [10] technology acceptance model [TAM; e.g., 1, 25, 36]. In marketing,
the various customer satisfaction index models – such as the European customer
satisfaction index [ECSI; e.g., 15, 30, 41] and Festge and Schwaiger’s [18] driver
analysis of customer satisfaction with industrial goods – represent key areas of PLS
use. Moreover, in strategic management, Hulland [35] provides a review of PLS
path modeling applications. More recent studies focus specifically on strategic success factor analyses [e.g., 62].
Figure 2.1 shows a typical path modeling application of the American customer
satisfaction index model [ACSI; 21], which also serves as an example for our study.
The squares in this figure illustrate the manifest variables (indicators) derived from
a survey and represent customers’ answers to questions while the circles illustrate
latent, not directly observable, variables. The PLS path analysis predominantly focuses on estimating and analyzing the relationships between the latent variables in
the inner model. However, latent variables are measured by means of a block of
manifest variables, with each of these indicators associated with a particular latent
variable. Two basic types of outer relationships are relevant to PLS path modeling:
formative and reflective models [e.g., 29]. While a formative measurement model
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
21
has cause–effect relationships between the manifest variables and the latent index
(independent causes), a reflective measurement model involves paths from the latent
construct to the manifest variables (dependent effects).
The selection of either the formative or the reflective outer mode with respect to
the relationships between a latent variable and its block of manifest variables builds
on theoretical assumptions [e.g., 44] and requires an evaluation by means of empirical data [e.g., 29]. The differences between formative and reflective measurement
models and the choice of the correct approach have been intensively discussed in
the literature [3, 7, 11, 12, 19, 33, 34, 68, 69]. An appropriate choice of measurement model is a fundamental issue if the negative effects of measurement model
misspecification are to be avoided [44].
= latent variables
Perceived
Quality
= manifest variables (indicators)
Perceived
Value
Customer
Expectations
Overall
Customer
Satisfaction
Customer
Loyalty
Fig. 2.1 Application of the ACSI model
While the outer model determines each latent variable, the inner path model
involves the causal links between the latent variables, which are usually a hypothesized theoretical model. In Fig. 2.1, for example, the latent construct “Overall Customer Satisfaction” is hypothesized to explain the latent construct “Customer Loyalty.” The goal of prediction-oriented PLS path modeling method is to minimize the
residual variance of the endogenous latent variables in the inner model and, thus,
to maximize their R2 values (i.e., for the key endogenous latent variables such as
customer satisfaction and customer loyalty in an ACSI application). This goal underlines the prediction-oriented character of PLS path modeling.
22
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
2.1.2 Problem Statement
While the use of PLS path modeling is becoming more common in management
disciplines such as MIS, marketing management, and strategic management, there
are at least two critical issues that have received little attention in prior work. First,
unobserved heterogeneity and measurement errors are endemic in social sciences.
However, PLS path modeling applications are usually based on the assumption that
the analyzed data originate from a single population. This assumption of homogeneity is often unrealistic, as individuals are likely to be heterogeneous in their
perceptions and evaluations of latent constructs. For example, in customer satisfaction studies, users may form different segments, each with different drivers of
satisfaction. This heterogeneity can affect both the measurement part (e.g., different latent variable means in each segment) and the structural part (e.g., different
relationships between the latent variables in each segment) of a causal model [79].
In their customer satisfaction studies, Jedidi et al. [37] Hahn et al. [31] as well as
Sarstedt, Ringle and Schwaiger [72] show that an aggregate analysis can be seriously misleading when there are significant differences between segment-specific
parameter estimates. Muthén [54] too describes several examples, showing that if
heterogeneity is not handled properly, SEM analysis can be seriously distorted. Further evidence of this can be found in [16, 66, 73]. Consequently, the identification of
different groups of consumers in connection with estimates in the inner path model
is a serious issue when applying the path modeling methodology to arrive at decisive
interpretations [61]. Analyses in a path modeling framework usually do not address
the problem of heterogeneity, and this failure may lead to inappropriate interpretations of PLS estimations and, therefore, to incomplete and ineffective conclusions
that may need to be revised.
Second, there are no well-developed statistical instruments with which to extend and complement the PLS path modeling approach. Progress toward uncovering
unobserved heterogeneity and analytical methods for clustering data have specifically lagged behind their need in PLS path modeling applications. Traditionally,
heterogeneity in causal models is taken into account by assuming that observations
can be assigned to segments a priori on the basis of, for example, geographic or
demographic variables. In the case of a customer satisfaction analysis, this may be
achieved by identifying high and low-income user segments and carrying out multigroup structural equation modeling. However, forming segments based on a priori
information has serious limitations. In many instances there is no or only incomplete substantive theory regarding the variables that cause heterogeneity. Furthermore, observable characteristics such as gender, age, or usage frequency are often
insufficient to capture heterogeneity adequately [77]. Sequential clustering procedures have been proposed as an alternative. A researcher can partition the sample
into segments by applying a clustering algorithm, such as k-means or k-medoids,
with respect to the indicator variables and then use multigroup structural equation modeling for each segment. However, this approach has conceptual shortcomings: “Whereas researchers typically develop specific hypotheses about the relationships between the variables of interest, which is mirrored in the structural equation
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
23
model tested in the second step, traditional cluster analysis assumes independence
among these variables” [79, p. 2]. Thus, classical segmentation strategies cannot
account for heterogeneity in the relationships between latent variables and are often inappropriate for forming groups of data with distinctive inner model estimates
[37, 61, 73, 71].
2.1.3 Objectives and Organization
A result of these limitations is that PLS path modeling requires complementary
techniques for model-based segmentation, which allows treating heterogeneity in
the inner path model relationships. Unlike basic clustering algorithms that identify clusters by optimizing a distance criterion between objects or pairs of objects, model-based clustering approaches in SEMs postulate a statistical model for
the data. These are also often referred to as latent class segmentation approaches.
Sarstedt [74] provides a taxonomy (Fig. 2.2) and a review of recent latent class
segmentation approaches to PLS path modeling such as PATHMOX [70], FIMIXPLS [31, 61, 64, 66], PLS genetic algorithm segmentation [63, 67], Fuzzy PLS Path
Modeling [57], or REBUS-PLS [16, 17]. While most of these methodologies are in
an early or experimental stage of development, Sarstedt [74] concludes that the finite mixture partial least squares approach (FIMIX-PLS) can currently be viewed as
the most comprehensive and commonly used approach to capture heterogeneity in
PLS path modeling. Hahn et al. [31] pioneered this approach in that they also transferred Jedidi et al.’s [37] finite mixture SEM methodology to the field of PLS path
modeling. However, knowledge about the capabilities of FIMIX-PLS is limited.
PLS Segmentation Approaches
Path Modelling
Segmentation Tree
Distance-based
PLS Typological
Regression Approaches
PLS Typological Path
Modeling
Fuzzy PLS Path Modeling
FIMIX-PLS
PLS Genetic Algorithm
Segmentation
Response-based Units
Segmentation in PLS
Fig. 2.2 Methodological taxonomy of latent class approaches to capture unobserved heterogeneity
in PLS path models [74]
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Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
This chapter’s main contribution to the body of knowledge on clustering data
in PLS path modeling is twofold. First, we present FIMIX-PLS as recently implemented in the statistical software application SmartPLS [65] and, thereby, made
broadly available for empirical research in the various social sciences disciplines.
We thus present a systematic approach to applying FIMIX-PLS as an appropriate and necessary means to evaluate PLS path modeling results on an aggregate
data level. PLS path modeling applications can exploit this approach to responsebased market segmentation by identifying certain groups of customers in cases
where unobserved moderating factors cause consumer heterogeneity within inner model relationships. Second, an application of the methodology to a wellestablished marketing example substantiates the requirement and applicability of
FIMIX-PLS as an analytical extension of and standard test procedure for PLS path
modeling.
This study is particularly important for researchers and practitioners who can exploit the capabilities of FIMIX-PLS to ensure that the results on the aggregate data
level are not affected by unobserved heterogeneity in the inner path model estimates.
Furthermore, FIMIX-PLS indicates that this problem can be handled by forming
groups of data. A multigroup comparison [13, 32] of the resulting segments indicates whether segment-specific PLS path estimates are significantly different. This
allows researchers to further differentiate their analysis results. The availability of
FIMIX-PLS capabilities (i.e., in the software application SmartPLS) paves the way
to a systematic analytical approach, which we present in this chapter as a standard
procedure to evaluate PLS path modeling results.
We organize the remainder of this chapter as follows: First, we introduce the PLS
algorithm – an important issue associated with its application. Next, we present a
systematic application of the FIMIX-PLS methodology to uncover unobserved heterogeneity and form groups of data. Thereafter, this approach’s application to a
well-substantiated and broadly acknowledged path modeling application in marketing research illustrates its effectiveness and the need to use it in the evaluation
process of PLS estimations. The final section concludes with implications for PLS
path modeling and directions regarding future research.
2.2 Partial Least Squares Path Modeling
The PLS path modeling approach is a general method for estimating causal relationships in path models that involve latent constructs which are indirectly measured
by various indicators. Prior publications [80, 43, 8, 75, 32] provide the methodological foundations, techniques for evaluating the results [8, 32, 43, 75, 80], and
some examples of this methodology. The estimation of a path model, such as the
ACSI example in Fig. 2.1, builds on two sets of outer and inner model linear equations. The basic PLS algorithm, as proposed by Lohmöller [43], allows the linear
relationships’ parameters to be estimated and includes two stages, as presented in
Table 2.1.
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
25
Table 2.1 The basic PLS algorithm [43]
Stage 1: Iterative estimation of latent variable scores
#1
Inner weights
if Yj and Yi are adjacent
sign cov(Yj ; Yi )
vji =
0
otherwise
#2
Inside approximation
Ỹj := ∑ vji Yi
i
#3
Outer weights; solve for
Mode A
ykjn = w̃kj Ỹjn + ekjn
Ỹjn = ∑ w̃kj ykjn + djn Mode B
kj
#4
Outside approximation
Yjn := ∑ w̃kj ykj n
kj
Variables:
y = manifest variables (data)
Y = latent variables
d = validity residuals
e = outer residuals
Parameters:
v = inner weights
w = weight coefficients
Indices:
i = 1, . . . , I for blocks of manifest variables
j = 1, . . . , J for latent variables
kj = 1, . . . , K for manifest variables counted within block j
n = 1, . . . , N for observational units (cases)
Stage 2: Estimation of outer weights, outer loadings, and inner path model
coefficients
In the measurement model, manifest variables’ data – on a metric or quasi-metric
scale (e.g., a seven-point Likert scale) – are the input for the PLS algorithm that
starts in step 4 and uses initial values for the weight coefficients (e.g., “+1” for all
weight coefficients). Step 1 provides values for the inner relationships and Step 3
for the outer relationships, while Steps 2 and 4 compute standardized latent variable scores. Consequently, the basic PLS algorithm distinguishes between reflective
(Mode A) and formative (Mode B) relationships in step 3, which affects the generation of the final latent variable scores. In step 3, the algorithm uses Mode A to
obtain the outer weights of reflective measurement models (single regressions for
the relationships between the latent variable and each of its indicators) and Mode B
for formative measurement models (multiple regressions through which the latent
variable is the dependent variable). In practical applications, the analysis of reflective measurement models focuses on the loading, whereas the weights are used to
analyze formative relationships. Steps 1 to 4 in the first stage are repeated until convergence is obtained (e.g., the sum of changes of the outer weight coefficients in
step 4 is below a threshold value of 0.001). The first stage provides estimates for the
26
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
latent variable scores. The second stage uses these latent variable scores for ordinary
least squares (OLS) regressions to generate the final (standardized) path coefficients
for the relationships between the latent variables in the inner model as well as the
final (standardized) outer weights and loadings for the relationships between a latent
variable and its block of manifest variables [32].
A key issue in PLS path modeling is the evaluation of results. Since the PLS algorithm does not optimize any global scalar function, fit measures that are well known
from CBSEM are not available for the nonparametric PLS path modeling approach.
Chin [8] therefore presents a catalog of nonparametric criteria to separately assess
the different model structures’ results. A systematic application of these criteria is
a two-step process [32]. The evaluation of PLS estimates begins with the measurement models and employs decisive criteria that are specifically associated with the
formative outer mode (e.g., significance, multicollinearity) or reflective outer mode
(e.g., indicator reliability, construct reliability, discriminant validity). Only if the
latent variable scores show evidence of sufficient reliability and validity is it worth
pursuing the evaluation of inner path model estimates (e.g., significance of path
coefficients, effect sizes, R2 values of latent endogenous variables). This assessment
also includes an analysis of the PLS path model estimates regarding their capabilities to predict the observed data (i.e., the predictive relevance). The estimated
values of the inner path coefficients allow the relative importance of each exogenous latent variable to be decided in order to explain an endogenous latent variable
in the model (i.e., R2 value). The higher the (standardized) path coefficients – for
example, in the relationship between “Overall Customer Satisfaction” and “Customer Loyalty” in Fig. 2.1 – the higher the relevance of the latent predecessor variable in explaining the latent successor variable. The ACSI model assumes significant
inner path model relationships between the key constructs “Overall Customer Satisfaction” and “Customer Loyalty” as well as substantial R2 values for these latent
variables.
2.3 Finite Mixture Partial Least Squares Segmentation
2.3.1 Foundations
Since its formal introduction in the 1950s, market segmentation has been one of
the primary marketing concepts for product development, marketing strategy, and
understanding customers. To segment data in a SEM context, researches frequently
use sequential procedures in which homogenous subgroups are formed by means
of a priori information to explain heterogeneity, or they revert to the application of
cluster analysis techniques, followed by multigroup structural equation modeling.
However, none of these approaches is considered satisfactory, as observable characteristics often gloss over the true sources of heterogeneity [77]. Conversely, the
application of traditional cluster analysis techniques suffers from conceptual shortcomings and cannot account for heterogeneity in the relationships between latent
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
27
variables. This weakness is broadly recognized in the literature and, consequently,
there has been a call for model-based clustering methods.
In data mining, model-based clustering algorithms have recently gained increasing attention, mainly because they allow researchers to identify clusters based on
their shape and structure rather than on proximity between data points [50]. Several approaches, which form a statistical model based on large data sets, have been
proposed. For example, Wehrens et al. [78] propose methods that use one or several samples of data to construct a statistical model which serves as a basis for a
subsequent application on the entire data set. Other authors [e.g., 45] developed
procedures to identify a set of data points which can be reasonably classified into
clusters and iterate the procedure on the remainder. Different procedures do not derive a statistical model from a sample but apply strategies to scale down massive
data sets [14] or use reweighted data to fit a new cluster to the mixture model [49].
Whereas these approaches to model-based clustering have been developed within a
data mining context and are thus exploratory in nature, SEMs rely on a confirmatory
concept as researchers need to specify a hypothesized path model in the first step of
the analysis. This path model serves as the basis for subsequent cluster analyses but
is supposed to remain constant across all segments.
In CBSEM, Jedidi et al. [37] pioneered this field of research and proposed the
finite mixture SEM approach, i.e., a procedure that blends finite mixture models
and the expectation-maximization (EM) algorithm [46, 47, 77]. Although the original technique extends CBSEM and is implemented in software packages for statistical computations [e.g., Mplus; 55], the method is inappropriate for PLS path
modeling due to unlike methodological assumptions. Consequently, Hahn et al.
[31] introduced the finite FIMIX-PLS method that combines the strengths of the
PLS path modeling method with the maximum likelihood estimation’s advantages
when deriving market segments with the help of finite mixture models. A finite
mixture approach to model-based clustering assumes that the data originate from
several subpopulations or segments [48]. Each segment is modeled separately and
the overall population is a mixture of segment-specific density functions. Consequently, homogeneity is no longer defined in terms of a set of common scores, but at
a distributional level. Thus, finite mixture modeling enables marketers to cope with
heterogeneity in data by clustering observations and estimating parameters simultaneously, thus avoiding well-known biases that occur when models are estimated
separately [37]. Moreover, there are many versatile or parsimonious models, as well
as clustering algorithms available that can be customized with respect to a wide
range of substantial problems [48].
Based on this concept, the FIMIX-PLS approach simultaneously estimates the
model parameters and ascertains the heterogeneity of the data structure within a
PLS path modeling framework. FIMIX-PLS is based on the assumption that heterogeneity is concentrated in the inner model relationships. The approach captures
this heterogeneity by assuming that each endogenous latent variable ηi is distributed
as a finite mixture of conditional multivariate normal densities. According to Hahn
et al. [31, p. 249], since “the endogenous variables of the inner model are a function
of the exogenous variables, the assumption of the conditional multivariate normal
28
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
distribution of the ηi is sufficient.” From a strictly theoretical viewpoint, the imposition of a distributional assumption on the endogenous latent variable may prove
to be problematic. This criticism gains force when one considers that PLS path
modeling is generally preferred to covariance structure analysis in circumstances
where assumptions of multivariate normality cannot be made [4, 20]. However, recent simulation evidence shows the algorithm to be robust, even in the face of distributional misspecification [18]. By differentiating between dependent (i.e., endogenous latent) and explanatory (i.e., exogenous latent) variables in the inner model,
the approach follows a mixture regression concept [77] that allows the estimation of
separate linear regression functions and the corresponding object memberships of
several segments.
2.3.2 Methodology
Drawing on a modified presentation of the relationships in the inner model (Table
2.2 provides a description of all the symbols used in the equations presented in this
chapter.),
Bηi + Γξi = ζi ,
(2.1)
it is assumed that ηi is distributed as a finite mixture of densities fi|k (·) with K
(K < ∞) segments
K
ηi ∼
∑ ρk fi|k (ηi |ξi , Bk , Γk , Ψk ),
(2.2)
k=1
whereby ρk > 0 ∀k, ∑Kk=1 ρk = 1 and ξi , Bk , Γk , Ψk depict the segment-specific
vector of unknown parameters for each segment k. The set of mixing proportions
ρ determines the relative mixing of the K segments in the mixture. Substituting
fi|k (ηi |ξi , Bk , Γk , Ψk ) results in the following equation:1
K
ηi ∼ ∑ ρk
k=1
1
(2π)M/2
|Ψk |
′
−1 ˜
1 ˜
e− 2 ((I−Bk )ηi +(−Γk )ξi ) Ψk ((I−Bk )ηi +(−Γk )ξi ) .
(2.3)
Equation 2.4 represents an EM formulation of the complete log-likelihood (lnLc )
as the objective function for maximization:
I
LnLC = ∑
K
I
K
∑ zik ln( f (ηi |ξi , Bk , Γk , Ψk )) + ∑ ∑ zik ln(ρk )
i=1 k=1
(2.4)
i=1 k=1
An EM formulation of the FIMIX-PLS algorithm (Table 2.3) is used for statistical computations to maximize the likelihood and to ensure convergence in this
model. The expectation of Equation 2.4 is calculated in the E-step, where zik is 1
1
Note that the following presentations slightly differ from Hahn et al.’s [31] original paper.
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
29
Table 2.2 Explanation of symbols
Am
am
Bm
bm
γam mk
βbm mk
τmk
ωmk
c
fi|k (·)
I
i
J
j
K
k
M
m
Nk
Pik
R
S
V
Xmi
Ymi
zik
ζi
ηi
ξi
B
Γ
I˜
∆
Bk
Γk
Ψk
ρ
ρk
Number of exogenous variables as regressors in regression m
exogenous variable am with am = 1, . . . , Am
number of endogenous variables as regressors in regression m
endogenous variable bm with bm = 1, . . . , Bm
regression coefficient of am in regression m for class k
regression coefficient of bm in regression m for class k
((γam mk ), (βbm mk ))′ vector of the regression coefficients
cell(m × m) of Ψk
constant factor
probability for case i given a class k and parameters (·)
number of cases or observations
case or observation i with i = 1, . . . , I
number of exogenous variables
exogenous variable j with j = 1, . . . , J
number of classes
class or segment k with k = 1, . . . , K
number of endogenous variables
endogenous variable m with m = 1, . . . , M
number of free parameters defined as (K − 1) + KR + KM
probability of membership of case i to class k
number of predictor variables of all regressions in the inner model
stop or convergence criterion
large negative number
case values of the regressors for regression m of individual i
case values of the regressant for regression m of individual i
zik = 1, if the case i belongs to class k; zik = 0 otherwise
random vector of residuals in the inner model for case i
vector of endogenous variables in the inner model for case i
vector of exogenous variables in the inner model for case i
M × M path coefficient matrix of the inner model for the relationships between
endogenous latent variables
M × J path coefficient matrix of the inner model for the relationships between
exogenous and endogenous latent variables
M × M identity matrix
difference of currentlnLc and lastlnLc
M ×M path coefficient matrix of the inner model for latent class k for the relationships
between endogenous latent variables
M × J path coefficient matrix of the inner model for latent class k for the relationships
between exogenous and endogenous latent variables
M × M matrix for latent class k containing the regression variances
(ρ1 , . . . , ρK ), vector of the K mixing proportions of the finite mixture
mixing proportion of latent class k
iff subject i belongs to class k (or 0 otherwise). The mixing proportion ρk (i.e.,
the relative segment size) and the parameters ξi , Bk , Γk , and Ψk of the conditional
probability function are given (as results of the M-step), and provisional estimates
(expected values) E(zik ) = Pik , for zik are computed according to Bayes’s [5] theorem (Table 2.3).
30
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
Table 2.3 The FIMIX-PLS algorithm
set random starting values for Pik ; set lastlnLC = V ; set 0 < S < 1
// run initial M-step
// run EM-algorithm until convergence
repeat do
// the E-step starts here
if ∆ ≥ S then
ρ f (ηi |ξi ,B ,Γ ,Ψ )
Pik = K k ρi|k f (η |ξk,B k,Γ k,Ψ ) ∀i, k
∑k=1 k i|k
i
i
k
k
k
lastlnLC = currentlnLC
// the M-step starts here
∑I
P
ρk = i=1I˜ ik ∀k
determine Bk , Γk , Ψk , ∀k
calculate currentlnLC
∆ = currentlnLC − lastlnLC
until ∆ < S
Equation 2.4 is maximized in the M-step (Table 2.3). This part of the FIMIXPLS algorithm accounts for the most important changes in order to fit the finite
mixture approach to PLS path modeling, compared to the original finite mixture
structural equation modeling technique [37]. Initially, we calculate new mixing
proportions ρk through the average of the adjusted expected values Pik that result
from the previous E-step. Thereafter, optimal parameters are determined for Bk , Γk ,
and Ψk through independent OLS regressions (one for each relationship between
the latent variables in the inner model). The ML estimators of coefficients and
variances are assumed to be identical to OLS predictions. We subsequently apply
the following equations to obtain the regression parameters for endogenous latent
variables:
Ymi = ηmi
and
Xmi = (Emi , Nmi )′
(2.5)
Emi =
{ξ1 , ..., ξAm }, Am ≥ 1, am = 1, ..., Am ∧ ξam is regressor of m
0/ else
(2.6)
Nmi =
{η1 , ..., ηBm } Bm ≥ 1, bm = 1, ..., Bm ∧ ηbm is regressor of m
0/ else
(2.7)
The closed-form OLS analytic formula for τmk and ωmk is expressed as follows:
−1 ′
Xm PkYm )
τmk = Xm′ Pk Xm )
(2.8)
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
31
k
ωmk = (Ym − Xm τmk )′ ((Ym − Xm τmk ) Pk ) /Iρ
(2.9)
As a result, the M-step determines the new mixing proportions ρk , and the
independent OLS regressions are used in the next E-step iteration to improve the
outcomes of Pik . The EM algorithm stops whenever lnLC no longer improves
noticeably, and an a priori-specified convergence criterion is reached.
2.3.3 Systematic Application of FIMIX-PLS
To fully exploit the capabilities of the approach, we propose the systematic approach to FIMIX-PLS clustering as depicted in Fig. 2.3. In FIMIX-PLS step 1,
the basic PLS algorithm provides path modeling results, using the aggregate set of
data. Step 2 uses the resulting latent variable scores in the inner path model to run
the FIMIX-PLS algorithm as described above. The most important computational
results of this step are the probabilities Pik , the mixing proportions ρk , class-specific
estimates Bk and Γk for the inner relationships of the path model, and Ψk for the
(unexplained) regression variances.
Step 1
Standard PLS path modeling: the basic PLS algorithm
provides path model estimates on the aggregate data level
Scores of latent variables in the inner path model
are used as input for the FIMIX-PLS procedure
Step 2
Number of
classes K = 2
FIMIX-PLS
Number of
classes K = 3
FIMIX-PLS
Number of
classes K = 4
FIMIX-PLS
…
FIMIX-PLS
Evaluation of results and
identification of an appropriate number of segments
Step 3
Step 4
Ex post analysis and
selection of an explanatory variable for segmentation
A-priori segmentation of data and
segment-specific estimation of the PLS path model
Evaluation and interpretation of segment-specific PLS results
Fig. 2.3 Analytical steps of FIMIX-PLS
32
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
The methodology fits each observation with the finite mixture’s probabilities Pik
into each of the predetermined number of classes. However, on the basis of the
FIMIX-PLS results, it must be specifically decided whether the approach detects
and treats heterogeneity in the inner PLS path model estimates by (unobservable)
discrete moderating factors. This objective is explored in step 2 by analyzing the
results of different numbers of K classes (approaches to guide this decision are presented in the next section).
When applying FIMIX-PLS, the number of segments is usually unknown. The
process of identifying an appropriate number of classes is not straightforward.
For various reasons, there is no statistically satisfactory solution for this analytical procedure [77]. One such reason is that the mixture models are not asymptotically chi-square distributed and do not allow the calculation of the likelihood
ratio statistic with respect to obtaining a clear-cut decision criterion. Another reason is that the EM algorithm converges for any given number of K classes. One
never knows if FIMIX-PLS stops at a local optimum solution. The algorithm should
be started several times (e.g., 10 times) for each number of segments for different starting partitions [47]. Thereafter, the analysis should draw on the maximum log-likelihood outcome of each alternative number of classes. Moreover, the
FIMIX-PLS model may result in the computation of non-interpretable segments
for endogenous latent variables with respect to the class-specific estimates Bk and
Γk of the inner path model relationships and with respect to the regression variances Ψk when the number of segments is increased. Consequently, segment size
is a useful indicator to stop the analysis of additional numbers of latent classes to
avoid incomprehensible FIMIX-PLS results. At a certain point, an additional segment is just very small, which explains the marginal heterogeneity in the overall
data set.
In practical applications, researchers can compare estimates of different segment
solutions by means of heuristic measures such as Akaike’s information criterion
(AIC), consistent AIC (CAIC), or Bayesian information criterion (BIC). These information criteria are based on a penalized form of the likelihood, as they simultaneously take a model’s goodness-of-fit (likelihood) and the number of parameters
used to achieve that fit into account. Information criteria generally favor models
with a large log-likelihood and few parameters and are scaled so that a lower value
represents a better fit. Operationally, researchers examine several competing models
with varying numbers of segments and pick the model which minimizes the value
of the information criterion. Researchers usually use a combination of criteria and
simultaneously revert to logical considerations to guide the decision.
Although the preceding heuristics explain over-parameterization through the integration of a penalty term, they do not ensure that the segments are sufficiently separated in the selected solution. As the targeting of markets requires segments to be
differentiable, i.e., the segments are conceptually distinguishable and respond differently to certain marketing mix elements and programs [40], this point is of great
practical interest. Classification criteria that are based on an entropy statistic, which
indicates the degree of separation between segments, can help to assess whether the
analysis produces well-separated clusters [77]. Within this context, the normed en-
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
33
tropy statistic [EN; 58] is a critical criterion for analyzing segment-specific FIMIXPLS results. This criterion indicates the degree of all observations’ classification and
their estimated segment membership probabilities Pik on a case-by-case basis and
subsequently reveals the most appropriate number of latent segments for a clear-cut
segmentation:
ENK = 1 −
[∑i ∑k −Pik ln(Pik )]
Iln(K)
(2.10)
The EN ranges between 0 and 1 and the quality of the classification commensurates with the increase in ENK . The more the observations exhibit high membership
probabilities (e.g., higher than 0.7), the better they uniquely belong to a specific
class and can thus be properly classified in accordance with high EN values. Hence,
the entropy criterion is especially relevant for assessing whether a FIMIX-PLS solution is interpretable or not. Applications of FIMIX-PLS provide evidence that EN
values above 0.5 result in estimates of Pik that permit unambiguous segmentation
[66, 71, 72].
An explanatory variable must be uncovered in the ex post analysis (step 3) in situations where FIMIX-PLS results indicate that heterogeneity in the overall data set
can be reduced through segmentation by using the best fitting number of K classes.
In this step, data are classified by means of an explanatory variable, which serves
as input for segment-specific computations with PLS path modeling. An explanatory variable must include both the similar grouping of data, as indicated by the
FIMIX-PLS results, and the interpretability of the distinctive clusters. However, the
ex post analysis is a very challenging FIMIX-PLS analytical step. Ramaswamy et al.
[58] propose a statistical procedure to conduct an ex post analysis of the estimated
FIMIX-PLS probabilities. Logistic regressions, or in the case of large data sets,
CHAID analyses, and classification and regression trees [9] may likewise be applied
to identify variables that can be used to classify additional observations in one of the
designed segments. While these systematic searches uncover explanatory variables
that fit the FIMIX-PLS results well in terms of data structure, a logical search, in
contrast, mostly focuses on the interpretation of results. In this case, certain variables
with high relevance with respect to explaining the expected differences in segmentspecific PLS path model computations are examined regarding their ability to form
groups of observations that match FIMIX-PLS results.
The process of identifying an explanatory variable is essential for exploiting
FIMIX-PLS results. The findings are also valuable to researchers to confirm that
unobserved heterogeneity in the path model estimates is not an issue, or they allow this problem to be dealt with by means of segmentation and, thereby, facilitate multigroup PLS path modeling analyses [13, 32] in step 4. Significantly different group-specific path model estimations impart further differentiated interpretations of PLS modeling results and may foster the origination of more effective
strategies.
34
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
2.4 Application of FIMIX-PLS
2.4.1 On Measuring Customer Satisfaction
When researchers work with empirical data and do not have a priori segmentation
assumptions to capture heterogeneity in the inner PLS path model relationships,
FIMIX-PLS is often not as clear-cut as in the simulation studies presented by Ringle
[61] as well as Esposito Vinzi et al. [16]. To date, research efforts to apply FIMIXPLS and assess its usefulness with respect to expanding the methodological toolbox
were restricted by the lack of statistical software programs for this kind of analysis.
Since such functionalities have recently been provided as a module in the SmartPLS
software, FIMIX-PLS can be applied more easily to empirical data, thereby increasing our knowledge of the approach and its applicability. As a means of presenting
the benefits of the method for PLS path modeling in marketing research, we focus
on customer satisfaction to identify and treat heterogeneity in consumers through
segmentation. However, the general approach of this analysis can be applied to any
PLS application such as the various TAM model estimations in MIS.
Customer satisfaction has become a fundamental and well-documented construct
in marketing that is critical with respect to demand and for any business’s success
given its importance and established relation with customer retention and corporate
profitability [2, 52, 53]. Although it is often acknowledged that there are no truly
homogeneous segments of consumers, recent studies report that there is indeed substantial unobserved customer heterogeneity within a given product or service class
[81]. Dealing with this unobserved heterogeneity in the overall sample is critical
for forming groups of consumers that are homogeneous in terms of the benefits that
they seek or their response to marketing programs (e.g., product offering, price discounts). Segmentation is therefore a key element for marketers in developing and
improving their targeted marketing strategies.
2.4.2 Data and Measures
We applied FIMIX-PLS to the ACSI model to measure customer satisfaction as presented by Fornell et al. [21] in the Journal of Marketing but used empirical data from
their subsequent survey in 1999.2 These data are collected quarterly to assess customers’ overall satisfaction with the services and products that they buy from a number of organizations. The ACSI study has been conducted since 1994 for consumers
of 200 publicly traded Fortune 500 firms as well as several US public administration
and government departments. These firms and departments comprise more than 40%
of the US gross domestic product. The sample selection mechanism ensures that all
2
The data were provided by Fornell, Claes. AMERICAN CUSTOMER SATISFACTION INDEX,
1999 [Computer file]. ICPSR04436-v1. Ann Arbor, MI: University of Michigan. Ross School of
Business, National Quality Research Center/Reston, VA: Wirthlin Worldwide [producers], 1999.
Ann Arbor, MI: Inter-University Consortium for Political and Social Research [distributor], 200606-09. We would like to thank Claes Fornell and the ICPSR for making the data available.
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
35
types of organizations are included across all economic sectors considered. For the
1999 survey, about 250 consumers of each organization’s products/services were
selected via telephone. Each call identified the person in the household (for household sizes >1) whose birthday was closest, after which this person (if older than 18
years) was asked about the durables he or she had purchased during the last 3 years
and about the nondurables purchased during the last month. If the products or services mentioned originated from one of the 200 organizations, a short questionnaire
was administered that contained the measures described in Table 2.4.
The data-gathering process was carried out in such a manner that the final data
were comparable across industries [21]. The ACSI data set has frequently been used
in diverse areas in the marketing field, using substantially different methodologies
such as event history modeling or simultaneous equations modeling. However, past
research has not yet accounted for unobserved heterogeneity.
Table 2.4 Measurement scales, items, and descriptive statistics
Construct
Items
Overall Customer
Satisfaction
Overall satisfaction
Expectancy disconfirmation (performance falls short of or exceeds
expectations)
Performance versus the customer’s ideal product or service in the category
Customer
Expectations
of Quality
Overall expectations of quality (prior to purchase)
Expectation regarding customization, or how well the product fits the
customer’s personal requirements (prior to purchase)
Expectation regarding reliability, or how often things would go wrong
(prior to purchase)
Perceived Quality
Overall evaluation of quality experience (after purchase)
Evaluation of customization experience, or how well the product fits the
customer’s personal requirements (after purchase)
Evaluation of reliability experience, or how often things have gone wrong
(after purchase)
Perceived Value
Rating of quality given price
Rating of price given quality
Customer
Complaints
Has the customer complained either formally or informally about the
product or service?
Customer Loyalty
Likelihood rating prior to purchase
Covariates
Age
Average = 43, Standard deviation = 15, minimum = 18, maximum = 84
Gender
42% male, 58% female
Education
Less than high school = 4.8%, high school graduate = 21.9%,
some college = 34.6%,
college graduate = 23.1%, post graduate = 15.5%
Race
White = 82.4%, Black/African American = 7.2%, American
Indian = 1.1%, Asian or Pacific Islander = 1.8%, other race = 3.7%
Total Annual
Family Income
Under $20.000 = 13.5%, $20.000−$30.000 = 13.9%,
$30.000− $40.000 = 14.9%, $40.000−$60.000 = 22.3%,
$60.000−$80.000 = 15.1%, $80.000−$100.000 = 8.4%,
Over $100.000 = 11.9%
36
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
To illustrate the capabilities of FIMIX-PLS, we used data from the first quarter of 1999 (N = 17, 265). To ensure the validity of our analysis, we adjusted the
data set by carrying out a missing value analysis. In standard PLS estimations,
researchers frequently revert to mean replacement algorithms. However, when replacing relatively high numbers by missing values per variable and case by mean
values, FIMIX-PLS will most likely form its own segment of these observations.
Consequently, we applied case-wise replacement. As this procedure would have led
to the exclusion of a vast number of observations, we decided to reduce the original ACSI model as presented by Fornell et al. [21]. Consequently, we excluded two
items from the “Customer Loyalty” construct, as they had a high number of missing
values. Furthermore, we omitted the construct “Customer Complaints,” measured
by a binary single item, because we wanted to use this variable as an explanatory
variable in the ex post analysis (step 3 in Fig. 2.3).
As our goal is to demonstrate the applicability of FIMIX-PLS regarding empirical data and to illustrate a cause–effect relationship model with respect to customer
satisfaction, we do not regard the slight change in the model setup as a debilitating
factor. Consequently, the final sample comprised N = 10, 417 observations. Figure 2.1 illustrates the path model under consideration.
Fornell et al. [21] identified the three driver constructs “Perceived Quality,” “Customer Expectations of Quality,” and “Perceived Value,” which are measured by three
and two reflective indicators, with respect to “Overall Customer Satisfaction.” The
ACSI construct itself directly relates to the “Customer Loyalty” construct. Both latent variables also employ a reflective measurement operationalization. Table 2.4
provides the measurement scales and the items used in our study plus various descriptive statistics of the full sample.
2.4.3 Data Analysis and Results
Methodological considerations that are relevant to the analysis include the assessment of the measures’ reliability, their discriminant validity. As the primary concern
of the FIMIX-PLS algorithm is to capture heterogeneity in the inner model, the focus of the comparison lies on the evaluation of the overall goodness-of-fit of the
models. Nevertheless, as the existence of reliable and valid measures is a prerequisite for deriving meaningful solutions, we also deal with these aspects.
As depicted in Fig. 2.3, the basic PLS algorithm [43] is applied to estimate the
overall model by using the SmartPLS 2.0 [64] in step 1. To evaluate the PLS estimates, we follow the suggestions by Chin [8] and Henseler et al. [32]. On assessing
the empirical results, almost all factor loadings exhibit very high values of above
0.8. The smallest loading of 0.629 still ranges well above the commonly suggested
threshold value of 0.5 [35], thus supporting item reliability. Composite reliability is
assessed by means of composite reliability ρc and Cronbach’s α. Both measures’
values are uniformly high around 0.8, thus meeting the stipulated thresholds [56].
To assess the discriminant validity of the reflective measures, two approaches are
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
37
applied. First, the indicators’ cross loadings are examined, which reveals that no
indicator loads higher on the opposing endogenous constructs. Second, the Fornell
and Larcker [22] criterion is applied, in which the square root of each endogenous
construct’s average variance extracted (AVE) is compared with its bivariate correlations with all opposing endogenous constructs [cp. 28, 32]. The results show that
in all cases, the square root of AVE is greater than the variance shared by each construct and its opposing constructs. Consequently, we can also presume a high degree
of discriminant validity with respect to all constructs in this study.
The central criterion for the evaluation of the inner model is the R2 . Whereas
ACSI exhibits a highly satisfactory R2 value of 0.777, all other constructs show
only moderate values of below 0.5 (Table 2.8).
In addition to the evaluation of R2 values, researchers frequently revert to
the cross-validated redundancy measure Q2 (Stone–Geisser test), which has been
developed to assess the predictive validity of the exogenous latent variables and
can be computed using the blindfolding procedure. Values greater than zero imply
that the exogenous constructs have predictive relevance for the endogenous construct under consideration, whereas values below zero reveal a lack of predictive
relevance [8]. All Q2 values range significantly above zero, thus indicating the exogenous constructs’ high predictive power. Another important analysis concerns the
significance of hypothized relationships between the latent constructs. For example,
“Perceived Quality” as well as “Perceived Value” exert a strong positive influence
on the endogenous variable “Overall Customer Satisfaction,” whereas the effect of
“Customer Expectations of Quality” is close to zero. To test whether path coefficients differ significantly from zero, t values were calculated using bootstrapping
with 10,417 cases and 5000 subsamples [32]. The analysis reveals that all relationships in the inner path model exhibit statistically significant estimates (Table 2.8).
In the next analytical step, the FIMIX-PLS module of SmartPLS was applied
to segment observations based on the estimated latent variable scores (step 2 in
Fig. 2.3). Initially, FIMIX-PLS results are computed for two segments (see settings
in Fig. 2.4). Thereafter, the number of segments is increased sequentially. A comparison of the segment-specific information and classification criteria, as presented in
Table 2.5, reveals that the choice of two groups is appropriate for customer segmentation purposes. All relevant evaluation criteria increase considerably in the ensuing
numbers of classes.
The choice of two segments is additionally supported by the EN value of 0.504.
As illustrated in Table 2.6, more than 80% of all our observations are assigned to
one of the two segments with a probability Pik of more than 0.7. These probabilities
decline considerably with respect to higher numbers of K classes, which indicates
an increased segmentation fuzziness that is also depicted by the lower EN. An EN
of 0.5 or higher for a certain number of segments allows the unambiguous segmentation of data.
Next, observations are assigned to each segment according to their segment
membership’s maximum probability. Table 2.7 shows the segment sizes with respect
to the different segment solutions, which allows the heterogeneity that affects the
analysis to be specified: (a) As the number of segments increases, the smaller seg-
38
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
Fig. 2.4 PLS path modeling and FIMIX-PLS settings in SmartPLS
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
39
Table 2.5 Information and classification criteria for varying K
K
1nL
AIC
BIC
CAIC
EN
2
3
4
5
6
−44, 116.354
−46, 735.906
−47, 276.720
−49, 061.353
−50, 058.503
88,278.708
93,541.811
94,647.440
98,240.706
100,259.006
88,445.486
93,795.563
94,988.246
98,668.527
100,773.840
88,468.486
93,830.563
95,035.246
98,727.527
100,844.840
0.504
0.431
0.494
0.447
0.443
Table 2.6 Overview of observations’ highest probability of segment membership
Pik
K=2
K=3
K=4
K=5
K=6
[0.9, 1.0]
[0.8, 0.9)
[0.7, 0.8)
[0.6, 0.7)
[0.5, 0.6)
[0.4, 0.5)
[0.3, 0.4)
[0.2, 0.3)
[0.1, 0.2)
[0, 0.1)
0.510
0.211
0.118
0.090
0.071
0.158
0.279
0.182
0.153
0.142
0.076
0.009
0.134
0.237
0.195
0.173
0.151
0.087
0.022
0.001
0.054
0.093
0.253
0.225
0.198
0.147
0.030
0.046
0.061
0.171
0.198
0.236
0.225
0.061
0.002
Sum
1.000
1.000
1.000
1.000
1.000
Table 2.7 Segment sizes for different numbers of segments
K
ρ1
ρ2
2
3
4
5
6
0.673
0.179
0.592
0.534
0.079
0.327
0.219
0.075
0.036
0.313
ρ3
0.602
0.075
0.245
0.449
ρ4
0.258
0.096
0.037
ρ5
0.089
0.081
ρ6
∑ ρk
0.041
1.000
1.000
1.000
1.000
1.000
k
ment is gradually split up to create additional segments, while the size of the larger
segment remains relatively stable (about 0.6 for K ∈ {2, 3, 4} and 0.5 for K ∈ {5, 6}).
(b) The decline in the outcomes of additional numbers of classes based on the EN
criterion allows us to conclude that the overall set of observations regarding this
particular analysis of the ACSI consists of a large, stable segment and a small fuzzy
one. (c) FIMIX-PLS cannot further reduce the fuzziness of the smaller segment.
In the process of increasing the number of segments, FIMIX-PLS can still identify the larger segment with comparably high probabilities of membership but
is ambivalent when processing the small group with heterogeneous observations.
Consequently, the probability of membership Pik declines, resulting in decreasing
40
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
EN values. This indicates methodological complexity in the process of assigning
the observations in this data set to additional segments. FIMIX-PLS computation
forces observations to fit within a given number of K classes. As a result, FIMIXPLS generates outcomes that are statistically problematic for the segment-specific
estimates Bk and for Γk , i.e., regarding the inner relationships of the path model,
and for Ψk , i.e., regarding the regression variances of endogenous latent variables.
In this example, results exhibiting inner path model relationships and/or regression
variances above one are obtained with respect to K = 7 classes. Consequently, the
analysis of additional numbers of classes can stop at this juncture in accordance
with the development of segment sizes in Table 2.7.
Table 2.8 presents the global model and FIMIX-PLS results of two latent segments. Before evaluating goodness-of-fit measures and inner model relationships,
all outcomes with respect to segment-specific path model estimations were tested
with regard to reliability and discriminant validity. The analysis showed that all
measures satisfy the relevant criteria for model evaluation [32]. As in the global
model, all paths are significant at a level of 0.01.
When comparing the global model with the results derived from FIMIX-PLS, one
finds that the relative importance of the driver constructs “Overall Customer Satisfaction” differs quite substantially within the two segments. For example, the global
model suggests that the perceived quality is the most important driver construct with
Table 2.8 Global model and FIMIX-PLS results of two latent segments
FIMIX-PLS
Global
k=1
k=2
t[mgp]
Customer Expectations of Quality
→ Perceived Quality
Customer Expectations of Quality
→ Perceived Value
Customer Expectations of Quality
→ Overall Customer Satisfaction
Perceived Quality
→ Overall Customer Satisfaction
Perceived Quality
→ Perceived Value
Perceived Value
→ Overall Customer Satisfaction
Overall Customer Satisfaction
→ Customer Loyalty
0.556∗∗∗
0.807∗∗∗
0.258∗∗∗
26.790∗∗∗
(56.755)
0.072∗∗∗
(7.101)
0.021∗∗∗
(3.294)
0.557∗∗∗
(63.433)
0.619∗∗∗
(62.943)
0.394∗∗∗
(44.846)
0.687∗∗∗
(93.895)
(168.463)
0.218∗∗∗
(16.619)
0.117∗∗∗
(14.974)
0.425∗∗∗
(50.307)
0.582∗∗∗
(46.793)
0.455∗∗∗
(62.425)
0.839∗∗∗
(208.649)
(13.643)
−0.107∗∗∗
(6.982)
−0.068∗∗∗
(6.726)
0.633∗∗∗
(49.038)
0.544∗∗∗
(42.394)
0.308∗∗∗
(21.495)
0.481∗∗∗
(31.794)
ρk
R2Perceived Quality
R2Perceived Value
R2Overall Customer Satisfaction
R2Customer Loyalty
1.000
0.309
0.439
0.777
0.471
0.673
0.651
0.591
0.848
0.704
0.327
0.067
0.277
0.679
0.231
t[mgp] = t-value for multi-group comparison test
∗∗∗ sig. at 0.01, ∗∗ sig. at 0.05, ∗ sig. at 0.1
15.571∗∗∗
14.088∗∗∗
10.667∗∗∗
1.899∗∗
7.922∗∗∗
19.834∗∗∗
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
41
respect to customer overall satisfaction. As “Perceived Quality” describes an ex post
evaluation of quality, companies should emphasize product and service quality and
their fit with use, which can be achieved through informative advertising. However, in the first segment of FIMIX-PLS, the most important driver construct with
respect to customer satisfaction is “Perceived Value.” In addition, also “Customer
Expectations of Quality” exerts an increased positive influence on customer satisfaction. Likewise, both segments differ considerably with regard to the relationships
between the three driver constructs “Perceived Quality,” “Customer Expectations of
Quality,” and “Perceived Value.”
However, only significant differences between the segments offer valuable interpretations for marketing practice. Consequently, we performed a multigroup comparison to assess whether segment-specific path coefficients differ significantly. The
PLS path modeling multigroup analysis (PLS-MGA) applies the permutation test
(5000 permutations) as described by [13] and which has recently been implemented
as an experimental module in the SmartPLS software.
Multigroup comparison results show that all paths differ significantly between
k = 1 and k = 2. Thus, consumers in each segment exhibit significantly different
drivers with respect to their overall satisfaction, which allows differentiated marketing activities to satisfy customers’ varying wants better. At the same time, all
endogenous constructs have increased R2 values, ranging between 2% (“Overall
Customer Satisfaction”) and 49% (“Perceived Quality”) higher than in the global
model. These were calculated as the sum of each endogenous construct’s R2 values
across the two segments, weighted by the relative segment size.
The next step involves the identification of explanatory variables that best characterize the two uncovered customer segments. We consequently applied the QUEST
[42] and Exhaustive CHAID [6] algorithm, using SPSS Answer Tree 3.1 on the
covariates to assess if splitting the sample according to the sociodemographic variables’ modalities leads to a statistically significant discrimination in the dependent
measure. In the latter, continuous covariates were first transformed into ordinal predictors. In both approaches, “age” and “total annual family income” showed the
greatest potential for meaningful a priori segmentation, with Exhaustive CHAID
producing more accurate results. The result is shown in Fig. 2.5. The percentages
in the nodes denote the share of total observations (as described in the root node)
with respect to each segment. These mark the basis of the a priori segmentation of
observations based on the maximum percentages for each node.
Segment one (nk1 = 6, 314) comprises middle-aged customers (age ∈ (28, 44])
with a total annual family income between $40,000 and less than $100,000. Furthermore, customers aged 44 and above belong to this segment. Segment two (nk2 =
4,103) consists of young customers (age ≤ 28) as well as middle-aged customers
with a total annual family income of less than $40,000 or more than $100,000. The
resulting classification corresponds to 56.878% of the FIMIX-PLS classification.
In addition to this clustering according to sociodemographic variables, we used the
behavioral variable “Customer Complaints” (Table 2.4) to segment the data. Segment one (nk1 = 7,393) represents customers that have not yet complained about
a product or service, whereas segment two (nk2 = 3,023) contains customers who
42
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
Fig. 2.5 Segmentation tree results of the exhaustive CHAID analysis
have complained in the past (consistency with FIMIX-PLS classification: 62.811%).
Table 2.9 documents the results of the ex post analysis. The evaluation of the PLS
path modeling estimates [8] with respect to these four a priori segmented data sets
confirms that the results are satisfactory.
Similar results as those with the FIMIX-PLS analysis were obtained with regard to the ex post analysis using the Exhaustive CHAID algorithm. Again, the
goodness-of-fit measures of the first segment exhibit increased values. Furthermore,
the path coefficients differ significantly between the two segments. For example, the
large segment exhibits a substantial relationship between “Customer Expectations
of Quality” and “Overall Customer Satisfaction,” which is highly relevant from a
marketing perspective. With respect to this group of mostly older consumers, satisfaction is also explained by expected quality, which can potentially be controlled by
marketing activities. For example, non-informative advertising (e.g., sponsorship
programs) can primarily be used as a signal of expected product quality [39, 51].
However, it must be noted that with respect to the global model, the differences are
less pronounced than those in the FIMIX-PLS analysis. Even though there are several differences observable, the path coefficient estimates are more balanced across
the two segments, thus diluting response-based segmentation results. Similar figures result with respect to the ex post analysis based on the variable “customer
complaints.”
Despite the encouraging results of the ex post analysis, the analysis showed that
the covariates available in the ACSI data set only offer a limited potential for meaningful a priori segmentation. Even though one segment’s results improved, the dif-
Ex Post CHAID
Ex Post Cust. Compl.
Global
k=1
k=2
t[mgp]
k=1
K=2
t[mgp]
Customer Expectations of Quality
→ Perceived Quality
Customer Expectations of Quality
→ Perceived Value
Customer Expectations of Quality
→ Overall Customer Satisfaction
Perceived Quality
→ Overall Customer Satisfaction
Perceived Quality
→ Perceived Value
Perceived Value
→ Overall Customer Satisfaction
Overall Customer Satisfaction
→ Customer Loyalty
0.556∗∗∗
(56.755)
0.072∗∗∗
(7.101)
0.021∗∗∗
(3.294)
0.557∗∗∗
(63.433)
0.619∗∗∗
(62.943)
0.394∗∗∗
(44.846)
0.687∗∗∗
(93.895)
0.575∗∗∗
(45.184)
0.072∗∗∗
(5.511)
0.036∗∗∗
(4.334)
0.548∗∗∗
(45.653)
0.635∗∗∗
(50.417)
0.400∗∗∗
(34.377)
0.677∗∗∗
(68.975)
0.526∗∗∗
(29.956)
0.067∗∗∗
(3.581)
−0.002
(0.252)
0.572∗∗∗
(35.861)
0.599∗∗∗
(36.269)
0.384∗∗∗
(24.571)
0.698∗∗∗
(57.207)
2.599∗∗∗
0.589∗∗∗
(50.844)
0.089∗∗∗
(6.169)
0.047∗∗∗
(5.336)
0.517∗∗∗
(45.217)
0.519∗∗∗
(35.082)
0.402∗∗∗
(35.728)
0.616∗∗∗
(58.929)
0.511∗∗∗
(29.224)
0.071∗∗∗
(4.025)
−0.001
(0.094)
0.578∗∗∗
(35,806)
0.659∗∗∗
(43,397)
0.390∗∗∗
(23,599)
0.705∗∗∗
(57.805)
3.457∗∗∗
ρk
R2Perceived Quality
R2Perceived Value
R2Overall Customer Satisfaction
R2Customer Loyalty
1
0.309
0.439
0.777
0.471
0.606
0.331
0.461
0.793
0.459
0.394
0.277
0.406
0.752
0.488
0.710
0.347
0.332
0.713
0.380
0.246
2.761∗∗∗
1.283∗
1.716∗∗
0.819
1.440∗
0.290
0.261
0.488
0.798
0.497
0.825
3.252∗∗∗
3.179∗∗∗
6.518∗∗∗
0.608
6.237∗∗∗
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
Table 2.9 Inner model path coefficients with t values and goodness-of-fit measures
t[mgp] = t-value for multi-group comparison test
sig. at 0.01, ∗∗ sig. at 0.05, ∗ sig. at 0.1
∗∗∗
43
44
Christian M. Ringle, Marko Sarstedt, and Erik A. Mooi
ferences between the segments were considerably smaller when compared to those
of the FIMIX-PLS results.
2.5 Summary and Conclusion
Unobserved heterogeneity and measurement errors are common problems in social
sciences. Jedidi et al. [37] have addressed these problems with respect to CBSEM.
Hahn et al. [31] have further developed their finite mixture SEM methodology for
PLS path modeling, which is an important alternative to CBSEM for researchers
and practitioners. This chapter introduced and discussed the FIMIX-PLS approach,
as it has recently been implemented in the software application SmartPLS. Consequently, researchers from marketing and other disciplines can exploit this approach
to response-based segmentation by identifying certain groups of customers. We
demonstrate the potentials of FIMIX-PLS by applying the procedure on data from
the ACSI model. We thus extend prior research work on this important model by
explaining unobserved heterogeneity in the inner model path estimates. Moreover,
we show that, contrary to existing work on the same data set, there are different
segments, which has significant implications.
Our example application demonstrates how FIMIX-PLS reliably identifies an appropriate number of customer segments, provided that unobserved moderating factors account for consumer heterogeneity within inner model path relationships. In
this kind of very likely situation, FIMIX-PLS enables us to identify two segments
with distinct inner model path estimates that differ substantially from the aggregatelevel analysis. For example, unlike in the global model, “Customer Expectations of
Quality” exerts a pronounced influence on the customers’ perceived value. Furthermore, the FIMIX-PLS analysis achieved a considerably increased model fit in the
larger segment.
In the course of an ex post analysis, two explanatory variables (“Age” and “Total Annual Family Income”) were uncovered. An a priori segmentation based on
the exhaustive CHAID analysis results, followed by segment-specific path analyses yielded similar findings as the FIMIX-PLS procedure. The same holds for segmenting along the modalities of the behavioral variable “Customer Complaints.”
These findings allow marketers to formulate differentiated, segment-specific marketing activities to better satisfy customers’ varying wants. Researchers can exploit
these additional analytic potentials where theory essentially supports path modeling
in situations with heterogeneous data. We expect that these conditions will hold true
in many marketing-related path modeling applications.
Future research will require the extensive use of FIMIX-PLS on marketing examples with heterogeneous data to illustrate the applicability and the problematic
aspects of the approach from a practical point of view. Researchers will also need
to test the FIMIX-PLS methodology by means of simulated data with a wide range
of statistical distributions and a large variety of path model setups to gain additional
implications. Finally, theoretical research should provide satisfactory improvements
2 Response-Based Segmentation Using Finite Mixture Partial Least Squares
45
of problematic areas such as convergence to local optimum solutions, computation
of improper segment-specific FIMIX-PLS results, and identification of suitable explanatory variables for a priori segmentation. These critical aspects have been discussed, for example, by Ringle [61] and Sarstedt [74]. By addressing these deficiencies, the effectiveness and precision of the approach could be extended, thus further
extending the analytical ground of PLS path modeling.
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