Using LISREL and PLS to measure customer satisfaction

Abstract

There's a consensus that customer satisfaction is important. There have been numerous books, articles, and conferences devoted to it and its determinants. Firms have invested huge amounts in collecting satisfaction data, analyzing them, and reporting on the results. Satisfaction has been argued to be a critical component of brand equity (e.g. Aaker, 1991). Firms and managers perceive it to be related to customer retention, which is related to profitability. Governments have funded national studies to monitor it. Although other constructs have been proposed to be more important correlates of loyalty (e.g. customer value, see Gale, 1994), it is definitely the case that customer satisfaction is a central con-struct in the relationship between firms and customers. Researchers and managers have used a variety of definitions for customer sat-isfaction. Most refer to a psychological process involving prior knowledge, be-liefs, or expectations; perceived performance; and the evaluation of this informa-tion, or an affective response to it. Oliver (1997, p. 13) provides the following general definition: Satisfaction is the consumer's fulfillment response. It is a judgment that a product or service feature, or the product or service itself, provided (or is providing) a pleasurable level of consumption-related fulfillment, including levels of under-or over overfulfillment.

Full text

Using LISREL and PLS to Measure Customer
Satisfaction
Lynd D. Bacon, Ph.D.
Lynd Bacon & Associates, Ltd.
lynd.bacon@lba.com
http://www.lba.com
Seventh Annual Sawtooth Software Conference
La Jolla CA
Feb. 2-5, 1999

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Using LISREL and PLS to Measure Customer Satisfaction
Lynd D. Bacon, Ph.D.
There’s a consensus that customer satisfaction is important. There have been
numerous books, articles, and conferences devoted to it and its determinants.
Firms have invested huge amounts in collecting satisfaction data, analyzing
them, and reporting on the results. Satisfaction has been argued to be a critical
component of brand equity (e.g. Aaker, 1991). Firms and managers perceive it
to be related to customer retention, which is related to profitability. Governments
have funded national studies to monitor it. Although other constructs have been
proposed to be more important correlates of loyalty (e.g. customer value, see
Gale, 1994), it is definitely the case that customer satisfaction is a central con-
struct in the relationship between firms and customers.
Researchers and managers have used a variety of definitions for customer sat-
isfaction. Most refer to a psychological process involving prior knowledge, be-
liefs, or expectations; perceived performance; and the evaluation of this informa-
tion, or an affective response to it. Oliver (1997, p. 13) provides the following
general definition:
Satisfaction
is the consumer’s fulfillment response. It is a judgment that a
product or service feature, or the product or service itself, provided (or is
providing) a
pleasurable
level of consumption-related fulfillment, including
levels of under- or over overfulfillment.
It’s important to note that the fulfillment response Oliver refers to is
internal
to the
customer.
Satisfaction is unobservable
Unlike physical quantities like temperature or weight, the extent of a customer’s
satisfaction must be inferred. It is assessed by what Torgerson (1958) called
measurement by fiat.
Since we can’t measure it directly, we instead measure
other variables that are observable. These are sometimes called indicator, or
manifest, variables. Based on a priori grounds, or perhaps on more sophisti-
cated procedures, we ascribe meaning to what we observe based on the pre-
sumed relationship between satisfaction and our indicator variables.
Unobserved, or latent, variables are very common in marketing research. They
include real income, socioeconomic status, perceived quality, utility, brand atti-
tude, purchase intention, and loyalty. To measure them we rely on observable
indicators that are (hopefully) correlated with them.

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It’s important not to treat indicators and the latent variables that may underlie
them as being the same thing. We should observe the Chinese proverb
(Bagozzi, 1994a):
"Do not confuse the finger pointing at the moon with the moon."
Now it’s probably unlikely that many managers or researchers truly believe that
the numeric responses elicited by satisfaction measurement scales really
are
satisfaction per se. Yet the practice of reporting and modeling the observed re-
sponses while ignoring any errors in measurement that may be present, can
mislead. One reason is that estimates of the correlation between satisfaction
and other variables will be biased. Some form of correlational analysis is often
used to do what’s called "key driver analysis" (Oliver, 1997) or "revealed prefer-
ence analysis" (Hauser, 1991) in satisfaction research, so the effects of meas-
urement error have practical implications.
Effects of unreliability
The reliability of a measure is the extent to which it provides consistent results
from one application to the next, or the degree to which it is free of random error
(Vogt, 1993, p. 195). When a measure’s unreliability is not taken into account,
estimates of its correlation with other variables will be biased, and differences in
the measure across groups or over time may be obscured.
An instance of this problem that is particularly relevant to the analysis of satisfac-
tion data has to do with the effects of unmodeled measurement error in variables
used to predict satisfaction. A common form of key driver analysis consists of
deriving attribute importance by regressing a satisfaction measure on a set of
predictor variables that consist of ratings of perceived performance. Unmodeled
measurement error in the predictors will cause bias in the estimated regression
coefficients, even when the expected value for the errors is equal to zero.
This problem is well known in econometrics, and is referred to as the "errors in
variables" problem (Maddala 1977). It turns out that if only one of the predictors
has measurement error, there is downward bias in the coefficient for the less-
than-completely-reliable predictor. The coefficients of the
other
coefficients are
also biased either upwards or downwards, but the direction can be calculated if
the reliability of the predictor with error can be estimated. Thus, the effect of
having only one unreliable predictor is that
all
coefficients are biased, even those
for perfectly reliable predictors. When more than one predictor is unreliable, it is
possible to approximate the extent and direction of the bias in each coefficient,
but doing so is rather cumbersome (Maddala, 1977, p. 294), and an estimate of
each variables’ reliability is required.

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In sum, unmodeled measurement error results in biased estimates. This is even
though the expected value of the measurement error may be zero. A simple
simulated example of the effects of unmeasured can be found in Bacon
(1997a,b). See also Rigdon (1994).
Modeling latent variables
One way of dealing with measurement error is to use measurement models that
separate error from what you want to estimate. A measurement model is a de-
vice for connecting observed, or indicator, variables to one or more latent vari-
ables (LVs) such that "true" values on the latter can be separated from error. A
familiar example is the classic psychometric measurement model:
Where Yobserved is the observed value on a continuous variable for a single ob-
servation, Ytrue is the true value on the unobserved continuous variable (i.e. an
LV) for that observation, and
ζ
is a measurement error that is also unobserved.
It’s often assumed that E
ζ
=0 and cov( , )Ytrue
ζ
=0. A definition for the reliability
of Yobserved is the ratio of the variances of Ytrue and Yobserved . 1
Latent variable models are models that include measurement models for LVs.
They may also estimate relationships between the LVs. These relationships can
include multiple criterion, or endogenous, variables, as well as multiple predictor,
or exogenous, variables, and are expressed as multiple equations.
In LV models, the relationships between variables are often represented as a set
of directed or undirected "paths." The paths to each variable describe that vari-
able’s dependencies. Each directed path represents an equation, and a picture
of the paths is called a "path diagram." Path diagrams provide a concise way of
describing complex models. Figures 1 and 2 provide examples of path diagrams.
These will be discussed below.
There exists a variety of LV models, and two of the ways they differ is in terms of
whether their observed and latent variables are continuous or discrete. Exam-
ples of LV models with discrete variables include latent class models with nomi-
nal observed and LVs, and item response theory (IRT) models with nominal or
ordinal observed variables and interval or ordinal LVs. Heinen (1996) provides a
1 The unique error in the classic measurement model,
ζ
, may have more than
one source (e.g. Bollen, 1989). In some applications this may result in unreliabil-
ity not being properly accounted for, which will in turn result in biased estimators
(DeShon, 1998)
YY
observed true
=+
ζ

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summary of LV models for discrete latent or discrete observed variables.
Hagenaars (1993) describes latent class path analysis models based on the work
of Goodman, Haberman, and others. Vermunt describes models for event history
analysis (1997) and path analysis models (1996) for data with missing values.
Another type of LV model describes the variances and covariances of observed
variables, or their correlations, and these are the focus of this paper. The pre-
dominant form is called a covariance structure model (CSM), or a structural
equation model (SEM).2 The LVs in them are continuous. The observed vari-
ables are typically treated as interval-level continuous variables, although the
CSM approach has been extended to accommodate nominal and ordinal ob-
served, or "indicator," variables (Muthén 1984, 1987). The most commonly used
software for fitting CSM models is the LISREL (linear structural relations) pro-
gram developed by Jöreskog (1973). The LISREL specification extended maxi-
mum likelihood (ML) factor analysis by combining it with path analysis. General
specifications of CSMs combine measurement models for LVs, and a path model
for relationships between LVs.
At about the same time that Jöreskog was developing his ML procedures, Wold
(1973, 1980; see also Jöreskog and Wold 1982) described a set of procedures
for estimating path models with LVs that used methods based on ordinary least
squares (OLS). This approach has come to be know as the PLS approach for
structural equation modeling. It is distinct from the PLS regression method
commonly used in chemometrics to develop predictive models using intercorre-
lated inputs.3 It is also distinct from CSM methods in several respects. For sim-
plicity I'll call it PLS here. Bear in mind that both kinds of models can be used to
estimate parameters for a system of equations in LVs.
In the following two sections I describe some of the basic concepts of the CSM
and PLS approaches to structural equation modeling, and provide a simple ex-
ample of each.
CSM and PLS
Both CSM and PLS offer unique features for modeling customer satisfaction.
They provide measurement models for continuous LVs, and the ability to esti-
mate models comprised of systems of equations. As we've indicated, measure-
ment models provide a means of taking unreliability into account. Being able to
model systems of equations is important when mediating variables are present,
when endogenous variables predict other endogenous variables, or when there
2 Some authors (e.g. Bollen, 1989) call CSMs SEMs. I use CSM here because
both CSMs and PLS can be used to describe SEMs.
3 . See Frank & Friedman (1993) for a critical comparison of PLS regression to
other methods, including ridge methods, and Bacon (1997) for a simple example
of how PLS regression algorithms work.

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is "reciprocal causality" between variables. Path diagrams illustrating these fea-
tures are in Figures 1 and 2.
In Figure 1, all variables are observed, or "manifest:" there are no measurement
models. There are regression residuals, however. This model has three equa-
tions for the three dependent variables labeled purc_intent, satisfied, and
sup_brand. It is a non-recursive since the variables sup_brand and satisfied
predict each other. Figure 2 shows a recursive model with LVs perceived value,
perceived support quality, and perceived hardware quality. Each of LV is mod-
eled using observed indicator variables. These models are each like a confirma-
tory factor model with one factor. Combined they are often referred to as the
measurement model of a CSM.
CSM or PLS can be used to estimate models like those in Figures 1 and 2. They
can both accommodate measurement models, and both can estimate systems of
equations. In the case of both, the modeler must specify the form of the model.
The estimation software does not decide what paths to put in, or what indicator
variables to use for different LVs. The basic equations and other specifications
for CSM and for PLS are given in Table 1.
PLS was developed to estimate recursive models, like the one in Figure 2. It
wasn’t developed for non-recursive models. Non-recursive models have one or
more loops in them, like the loop between sup_brand and satisfied in Figure 1.
Both PLS and CSM were developed for estimating linear relationships, and so
estimating interactions between or nonlinearities in LVs has been problematic.
There have been some recent progress on this issue for CSMs (Schumacker and
Marcoulides, 1998; Arminger & Muthén, 1998) and also PLS (Chin, Marcolin &
Newsted, 1996).
CSM and PLS differ in many ways. The differences are due to what the two
methods were designed for, and the kinds of estimation procedures they use.
Table 2 lists a number of differences that are relevant to modeling satisfaction.
Here we will elaborate on some of the more important of them.
The CSM approach emphasizes estimating and testing model parameters. It
was developed out of a tradition of modeling as a way of developing and evalu-
ating theories. PLS, on the other hand, was developed to maximize predictive
accuracy (Jöreskog and Wold, 1982; Wold, 1982), while providing flexibility for
exploratory modeling. PLS doesn't require the distributional assumptions that
CSM does, and hence has been called "soft modeling" (Wold, 1980, 1982). It
was originally viewed as a complement for the LISREL approach to fitting SEMs
(Ibid.).
Fitting a CSM involves minimizing the difference between observed and pre-
dicted variance-covariance (VCV) matrices of the observed variables. An itera-
tive fitting algorithm is used to simultaneously estimate all parameters. The algo-

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rithm starts from a set of initial values for the parameters being estimated, and
then adjusts them over successive iterations until a scalar measure of the dis-
crepancy between observed and predicted has been minimized. The most
widely used procedure provides maximum likelihood (ML) estimates for parame-
ters. It requires that the observed data are distributed as multivariate normal,
and that the observations be independent. Some other estimation methods are
less restrictive. Browne’s (1982) asymptotically distribution-free (ADF) fitting cri-
terion, for example, only requires that the observed data be continuous.
In general, CSMs will be unidentified, so some of their parameters must be con-
strained. A model is unidentified when unique solutions cannot be obtained for
all of its parameters. In terms of CSMs this may mean that there are more pa-
rameters to be estimated than the number of unique elements of the VCV matrix.
Or it may mean something less obvious. Heuristics or empirical tests are typi-
cally used to determine whether a CSM is identified. The constraints serve to
reduce the number of parameters to be estimated.
LVs in CSMs are estimated basically like common factors in confirmatory factor
analysis are. Constraints must be used to set their measurement scales. The
scores on CSM LVs are not estimated directly. They may be estimated after fit-
ting a SEM by using on of several different multiple regression approaches, but
the values obtained depend on the method used. Therefore, they should be
used with some care.
PLS estimation involves estimating the parameters of a model by iterating over a
sequence of parts of the model with the goal of minimizing the residual variance
associated with all endogenous variables in the model. The model parts consist
of measurement models for the LVs, which are called "blocks," and a set of rela-
tions that connect the LVs. These are called the "outer" and "inner" models, re-
spectively, and they are analogous to the measurement and structural models of
CSMs. The data analyzed with PLS is typically a correlation matrix. The algo-
rithms used are different kinds of OLS procedures, depending on what kind of
parameter is being estimated.
As is the case with CSMs, observed variables in PLS models can be related to
LVs in one of two ways. They may be reflective indicators, meaning that in a
path diagram an arrow points to them from an LV, as in Figure 2, for example.
These are like the effects indicators in CSMs. The other kind of indicator variable
in PLS models is a formative indicator. These have an arrow pointing
towards
a
LV, and are like causal indicators in CSMs.4
The LVs in PLS are more like principal components than they are like the factor-
like LVs in CSM. The are estimated as exact weighted linear combinations of
4 Causal indicators in SEM can be difficult to use. See McCallum & Browne
(1993).

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observed variables. Parameter identification is not a problem when using PLS,
and assumptions about how the observed variables are distributed are not
needed. PLS does not require that the residuals for different observations be
distributed the same way, or that observations be independent.
Parameter estimation and inference
An important difference between CSM and PLS is in terms of their parameter es-
timates. The maximum likelihood estimates provided by CSM are just that: they
are M.V.U.E. (minimum variance unbiased estimates) under certain conditions of
regularity, assuming that the model and its assumptions is correct, and given that
the sample is large. ML estimates have several desirable characteristics, and
they are relatively robust against violations of assumptions.
PLS estimates of the scores on LVs are "consistent at large." That is, they be-
come consistent as the sample size and the number of indicators per LV both
become large. Under conditions of finite sample size and number of indicators,
the lack of complete consistency in the scores produces biased estimates of
component loadings, which relate reflective indicators to PLS LVs, and in path
coefficients. There is no closed-form solution for estimating the size of the bias
in PLS estimators (Lohm|ller, 1989; Chin, 1998a).
Lohm|ller (1989) has worked out solutions for cases involving one or two LVs
and given equal correlations between indicators. They express the bias in PLS
estimates as the ratio of each PLS estimate to its corresponding ML estimate.
This is only useful if the model used to obtain the ML estimates is in fact correct
to begin with. Chin (1998a) suggests that in general the effects of inconsistency
will be that loading estimates will tend to be biased upwards, and path coeffi-
cients will tend to be biased downward. It is theoretically possible that biases in
PLS estimates will make different coefficients appear to be the same, and coeffi-
cients that are truly the same appear different. As Chin (1998b) suggests, there
is a need for research to more broadly understand the implications of the con-
sistency at large assumption in PLS.
Ryan & Rayner (1998) provided a good example of bias in PLS estimates. They
compared PLS and CSM results across simulated data sets. They used non-
recursive models to generate their data, varying sample size and the values of
model parameters. Their models had four exogenous LVs, and one endogenous
LV. Their results indicate that the parameter estimates produced by PLS were
on average further from the true values than those from CSM models, while the
root mean squared error for the PLS models was on average smaller.
The flexibility of using PLS comes from not having to make assumptions about
how variables are distributed. This provides the freedom to use any kind of indi-
cator variables. Part of the price for this is that direct statistical tests are not
available. PLS provides no statistical tests of parameter significance, of model fit,

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or of differences between models. Inference is possible by using jackknife or
bootstrapping procedures, however.
CSMs, on the other hand, provide estimates of standard errors for estimated pa-
rameters, various tests of model fit, statistical comparisons of nested models,
and the ability to test very general linear and nonlinear constraints on parameter
values. These require distribution assumptions, of course. When the distribu-
tional assumptions are not tenable, inferences about parameters can still be en-
tertained by bootstrapping.
CSMs can be fit to data from multiple groups simultaneously so that differences
between models for the groups can be tested. They can be used to estimate
means and intercepts for LVs. Recent work on modeling multi-level (hierarchical,
or clustered) data with CSMs includes estimating individual-level coefficients
(e.g. Kaplan & Elliott, 1997; McArdle, 1998; Muthén, 1994). Muthén's (1987)
LISCOMP specification provides a means of estimating CSMs with discrete ob-
served variables. His recent work further extends the LISCOMP framework to
accommodate finite mixture models (Muthén, 1998).
A simple example
To illustrate the use of CSM and PLS models we’ll consider a very simple exam-
ple: a bivariate linear regression with LVs. The data are from a survey of 200
customers of an automotive service organization. They include ratings on four
performance attributes, and four satisfaction ratings. The four performance at-
tributes were courtesy, accessibility, speed with which routine service is com-
pleted, and cleanliness of the service location. A seven point (or six interval),
unipolar rating scale was used for each one.
The satisfaction measures included a bipolar scale with end points of very dis-
satisfied and very satisfied, and an agreement/ disagreement scale for the
statement “Overall I am very satisfied with my visit to WeLubeM.5” Each of these
two scales had eight points. The third measure was a six-point rating of satisfac-
tion relative to other automotive service providers that ranged from must less
satisfied to much more satisfied. The fourth satisfaction measure was a judg-
ment of confidence that service would be satisfactory on the next visit. The arc-
sin transform of this last variable was used for the following analyses.
ML estimation was used to fit CSM models to these data since some preliminary
analysis indicated that the observed variables didn’t depart too far from multi-
normality. The simplest useful model that could be specified involved a single
LV underlying the four performance measures, and a single satisfaction dimen-
sion. This model was estimated using a widely available CSM program (AMOS
3.61). The data consisted of the variance-covariance matrix of the eight ob-
5 Not the real name of the business.

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served variables. Judging from the fit indices obtained, and from the estimated
residuals, the fit of this model to the variance-covariance matrix is adequate. The
ML χ2 for the model is 23.09 with 19 degrees of freedom. A commonly used fit
index, the root mean square error of approximation (RSMEA), is 0.064. A heu-
ristic for RSMEA is that values between 0.05 and 0.08 indicate moderate fits.
The residuals look approximately normally distributed based on a normal quan-
tile-quantile plot. There are a number of other fit measures for CSMs.
Standardized estimates of the model’s coefficients are shown on the path dia-
gram in Figure 3. In this diagram, the observed performance indicators are la-
beled p1 through p4, and the satisfaction indicators s1 through s4. When this
model was estimated, the measurement scales for the two LVs performance
and satisfaction were set by constraining the factor loadings for p1 and s1 to be
equal to 1.0. What this does is to make the unit of measurement for each LV the
same as the unit for the observed variable with the fixed loading. An analogous
contraint was used to fix the measurement scale of zeta, the regression residual.
You'll note from the path diagram that the estimated correlation between the LVs
is 0.85, and that the standardized loadings vary from 0.51 to 0.80. All are reliably
different from zero based on their estimated standard errors. Each standardized
loading can be interpreted as the square root of the reliability coefficient for the
observed variable it is associated with. So, for example, only about 26% of the
variation in p4 is associated with the performance LV, assuming that the model is
correct.
Figure 4 shows PLS coefficients obtained by using Lohm|ller's LVPLS program.
Here again, the summary statistics indicate a reasonably good fit. The average
R2 = 0.58. The root-mean-square covariance (RMS COV) between the residuals
of the latent and manifest variables is 0.04. Like RMSEA, smaller values of RMS
COV are better. Figure 4 also shows the standardized CSM estimates from the
model in Figure 3.
You can see from Figure 4 that the point estimates of the CSM loadings are each
smaller than their PLS counterparts. Thus in this example PLS makes it look
like the LVs are somewhat better measured by their indicators than the CSM re-
sults suggest. Another difference between results is that the point estimate of
the path coefficient between the two LVs is smaller in the PLS model (0.68) than
in the CSM model (0.85). Both kinds of difference are commonly observed
(Chin, 1994) when CSMs and PLS models are compared. In this case it's not
clear which set of estimates is closer to the true parameter values. The same
pattern of differences can emerge due to bias in the PLS estimates (Ibid.).
Using CSM and PLS for satisfaction measurement

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The differences between the two methods indicate the circumstances under
which one might be preferred over the other. If you need to estimate non-
recursive models, then CSM is the method of choice. If you are in particular in-
terested in accurately predicting LV scores, then you may want to consider PLS,
since it provides a direct method for doing so.
If your primary interest is in comparing path coefficients or factor loadings, CSM
could be the better choice, given either that the necessary assumptions are ten-
able or that it’s feasible to obtain bootstrap estimates. PLS estimates of loadings
and coefficients will always be biased. The important question for any particular
application of PLS is, by how much?
Some other circumstances under which you might plan on using CSM include:
• You want to do traditional statistical inference;
• You have theory or strong domain knowledge about the causal relationships
you want to quantify, and it’s important to compare models;
• Construct validity is of high importance;
• You want to test whether models for different groups are the same.
A comparative strength of PLS is its ability to accommodate variables regardless
of their type of measurement. This feature of PLS can make it more convenient
to use on satisfaction data that have already been collected, or that will be col-
lected without consideration of what would be must suitable for the purposes of
fitting CSMs.
In the experience of this author, satisfaction data collected without regard to
plausible models or scale construction are unlikely to provide useful CSM re-
sults. As Rigdon(1998) has pointed out, there can be a substantial risk of failure
in using such a demanding analytical method when its use was not originally
considered. Regardless of recent progress towards making CSMs more flexible,
they are still a confirmatory method, and don’t lend themselves well to ad hoc
use. In the case of using either CSM or PLS, much judgment is required. They
are both relatively complicated modeling procedures, and there is often little
consensus amongst experts on how they are best applied to particular non-trivial
problems.
Neither CSM or PLS will have great utility if the data they are used on do not in-
clude measures of important variables, or if models are specified in a grossly in-
correct manner. Oliver (1997) notes that there seems to be a general disregard
of the role and importance of process variables in most customer satisfaction re-
search, and points to the common practice of only collecting data about per-
ceived performance on product attributes. It’s clear that ignoring such variables
can be very misleading. For example, there is ample empirical evidence that the

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disconfirmation of expectations either partially or fully mediates6 the effects of
perceived performance on satisfaction in many circumstances (Ibid.). Therefore,
omitting this variable from either type of model has the potential to produce pa-
rameter estimates that don’t fully reflect the true impact of variations in perceived
performance. It’s obvious that theory and prior knowledge must be used to
guide both data collection and model specification.
Both CSM and PLS can accommodate multicollinearity7 in predictors of satisfac-
tion. Multicollinearity is often a problem for satisfaction researchers who want to
do key driver analyses, since the variables they would like to use to explain
variations in satisfaction often evidence moderate to severe amounts of it. The
basic approach when using either method is to model multicollinearity in some
fashion. Using either method, you can use an LV to represent a set of highly
interrelated observed variables, assuming it makes substantive sense to do so.
Using CSMs you can also estimate covariances between LVs or between the
uniquenesses of indicator variables, or you can use generic "method" factors.
The method used should depend on what makes the most sense given what you
believe your data measure. It certainly should not be based just on what makes
a model fit the data better.
When using PLS to model multicollinear variables you can summarize interde-
pendent predictors with one or more LVs by using the predictors as reflective in-
dicators. Using them as formative indicators can prove problematic, as there is
no way of taking the interdependence between the variables into account, and
the result can be instability in the estimates obtained. More generally, standard
PLS does not provide ways of modeling undirected correlation, i.e. association
between variables that is not assumed to have a direction.8 Such relationships
are assumed to not exist when using PLS.
An important consideration for research practitioners is the availability of software
and background literature. There are at least five commercially available soft-
ware packages for fitting CSMs, and there are a few more in the public domain.
The available PLS software consists mainly of a public domain version of a pro-
gram written by Lohm|ller in the 1980’s, although a more contemporary applica-
6 A mediating variable is one that partially or fully intervenes in the path from one
variable to another (Baron & Kenny, 1986). In Figure 1, satisfied
fully
mediates
the effect of perform on purc_intent, since there is no direct path from perform
to purc_intent.
7 Multicollinearity is linear dependency between two or more variables. Substan-
tial multicollinearity makes it difficult to separate the predictive effects of vari-
ables, and results in unstable estimates. Maddala (1977) attributes the term to
Ragnar Frisch (1934).
8 It’s also the case that some of the bias PLS’s OLS estimates can be due to co-
variation between LVs and errors in equations that can’t be modeled in standard
PLS (Wothke, 1998).

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tion may soon become available (Chin, 1998b). The research literature on CSMs
is large and growing rapidly, providing a rich knowledge base for using these
models. Literature about PLS is scarce, and there have been few developments
in it over the last decade. The Appendix provides sources for software and other
resources for using CSM and PLS.
In sum, CSM and PLS offer distinct advantages as methods for analyzing satis-
faction data. They both provide a means of recognizing measurement error and
controlling its effects on the estimation of other quantities. Both methods can es-
timate systems of relationships, which provides a way of expressing the multiple
dependencies noted in the research literature on customer satisfaction. Each
provides a means of modeling multicollinearity so that its deleterious effects on
estimation can be reduced. They also differ from each other in important ways.
These include the kinds of distributional assumptions needed in order to use
them, the degree of bias in the estimates they provide, and the ease with which
inferences about models and parameters can be made.
Both methods can be demanding to use, and each requires specific knowledge
and experience on the part of the analyst. PLS was developed for applications
in which little theory is available and predictive accuracy is of paramount impor-
tance. CSM, on the other hand, was developed for theory-driven modeling. In
keeping with the philosophy that no model is correct, it may be useful (or at least
instructive) to apply both procedures when possible so that discrepancies be-
tween their results can be examined, and perhaps even be reconciled.

1998 Sawtooth Software Conference
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References
Aaker, D. (1991),
Managing Brand Equity
, New York: MacMillian Publishers.
Arminger, G. and B. Muthén (1998), "A Bayesian Approach to Nonlinear Latent
Variable Models Using the Gibbs Sampler,"
Psychometrika
, 63, 271-300.
Bacon, L. (lynd.bacon@lba.com) (1997a), "1997 ARTF SEM Tutorial Web Page,"
http://www.lba.com/art97.html, June.
------ (1997b), "Introduction to Structural Equation Modeling," Tutorial, AMA Ad-
vanced Research Techniques Forum, Monterey CA, June.
Bagozzi, R. (1994a), "Panel Discussion on Teaching CSMs," American Man-
agement Association Research Division Conference on Causal Modeling,
Purdue University, March.
------ (Editor) (1994b),
Advanced Methods of Marketing Research
, Malden MA,
Blackwell.
Baron, R. and D. Kenny (1986), "The Moderator-Mediator Variable Distinction in
Social Psychological Research,"
Journal of Personality and Social Psy-
chology
, 51, 1173-1182.
Bollen, K. and S. Long (1993),
Testing Structural Equation Models
, Thousand
Oaks CA: Sage.
Browne, M. (1982), "Covariance Structures," in
Topics in Applied Multivariate
Analysis
, ed. D. Hawkins, Cambridge: Cambridge University Press, 72-
141.
Chin, W., B. Marcolin and P. Newsted (1996), "A Partial Least Squares Latent
Variable Modeling Approach for Measuring Interaction Effects: Results
from a Monte Carlo Study and Voice Mail Emotion/Adoption Study," in
Proceedings of the Seventeenth International Conference on Information
Systems
, J. Degross, S. Jarvenpaa and A. Srinivasan, editors. Cleveland
OH, December.
Chin, Wynne (1998a), "The Partial Least Squares Approach for Structural Equa-
tion Modeling," in
Modern Methods for Business Research
, G. Marcou-
lides, editor. Mahwah NJ: Erlbaum, 275-337.
------ (1998b), Personal Communication, Impending availability of the PLS-Graph
software program, December.
DeShon, R. (1998), "A Cautionary Note on Measurement Error Corrections in
Structural Equation Models,"
Psychological Methods
, 3, 412-423.
Dillon, W., J. White, V. Rao and D. Filak (1997), "Good Science,"
Marketing Re-
search: A Magazine of Management and Applications
, 9, 22-31.
Falk, F. and N. Miller (1992),
A Primer for Soft Modeling
, Akron OH: University of
Akron Press.
Frank, I. and J. Friedman (1993), "A Statistical View of Some Chemometrics Re-
gression Tools (With Discussion),"
Technometrics
, 35, 119-148.
Frisch, R. (1934),
Statistical Confluence Analysis by Means of Complete Regres-
sion Systems
, Olso, Norway: University Institute of Economics.
Gale, B. (1994),
Managing Customer Value
, New York: Free Press.
Hagganaars, J. (1993),
Loglinear Models with Latent Variables
, Quantitative Ap-
plications in the Social Sciences, vol. 94, Thousand Oaks CA: Sage.

1998 Sawtooth Software Conference
©1999 LBA: Lynd Bacon & Associates, Ltd. All Rights Reserved
- 14 -
Hauser, J. (1991),
Comparison of Importance Measurement Methodologies and
Their Relationship to Consumer Satisfaction
, Cambridge MA: Sloan
School of Management, MIT.
Heinen, T. (1996),
Latent Class and Discrete Latent Trait Models
, Advanced
Quantitative Techniques in the Social Sciences, Thousand Oaks CA:
Sage.
Jöreskog, K. (1973), "A General Method for Estimating a Linear Structural Equa-
tion System," in
Structural Equation Models in the Social Sciences
, A.
Goldberger and O. Duncan, editors. New York: Academic Press, 85-112.
------ and H. Wold (1982), "The ML and PLS Techniques for Modeling with Latent
Variables," in
Systems Under Indirect Observation (I)
, K. Joreskog and
H. Wold, editors. Amsterdam: North-Holland.
Kaplan, D. and P. Elliott (1997), "A Didactic Example of Multilevel Structural
Equation Modeling Applicable to the Study of Organizations,"
Structural
Equation Modeling
, 4, 1-24.
Kenny, D. and C. Judd (1984), "Estimating the Nonlinear and Interactive Effects
of Latent Variables,"
Psychological Bulletin
, 96, 201-210.
Lohmöller, J. (1989),
Latent Variable Path Modeling with Partial Least Squares
,
Heidelberg: Physica-Verlag.
MacCallum, R. and M. Browne (1993), "The Use of Causal Indicators in Covari-
ance Structure Models: Some Practical Issues,"
Psychological Bulletin
,
114(3), Nov, 533-541.
Maddala, G.S. (1977),
Econometrics
, New York: McGraw-Hill.
Marcoulides, G. (Editor) (1998),
Modern Methods for Business Research
, Quan-
titative Methods Series, Mahwah NJ: Erlbaum.
------ and R. Schumacker (1996),
Advanced Structural Equation Modeling: Issues
and Techniques
, Mahwah NJ: Erlbaum.
McArdle, J. (1998), "Modeling Longitudinal Data by Latent Growth Curve Meth-
ods," in
Modern Methods for Business Research
, G. Marcoulides, editor.
Mahwah NJ: Erlbaum, 359-406.
Muthén, B. (1984), "A General Structural Equation Model with Dichotomous, Or-
dered Categorical, and Continuous Latent Variable Indicators,"
Psy-
chometrika
, 49, 115-132.
------ (1987),
LISCOMP. Analysis of Linear Structural Equations Using a Com-
prehensive Measurement Model
, Chicago IL: Scientific Software Interna-
tional.
------ (1994), "Multilevel Covariance Structure Analysis,"
Sociological Methods &
Research
, 22, 376-398.
------ (1998), Personal Communication, Extensions of the LISCOMP method in
recently available MPlus software, November.
Oliver, R. (1997),
Satisfaction: A Behavioral Perspective on the Consumer
, New
York: McGraw-Hill.
------ and W. Desarbo (1988), "Response Determinants in Satisfaction Judge-
ments,"
Journal of Consumer Research
, 14, 495-507.
Rigdon, E. (1994), "Demonstrating the Effects of Unmodeled Measurement Er-
ror,"
Structural Equation Modeling
, 1, 375-380.

1998 Sawtooth Software Conference
©1999 LBA: Lynd Bacon & Associates, Ltd. All Rights Reserved
- 15 -
------ (1998), "Structural Equation Modeling," in
Modern Methods for Business
Research
, G. Marcoulides, editor. Mahwah NJ: Erlbaum, 251-294.
Ryan, M. and B. Rayner (1998), "Estimating Structural Equation Models with
PLS," AMA Advanced Research Techniques Forum, Keystone CO, June.
Schumacker, R. and G. Marcoulides (1998),
Interaction and Nonlinear Effects in
Structural Equation Modeling
, Mahwah NJ: Erlbaum.
Torgerson, W. (1958),
Theory and Methods of Scaling
, New York: Wiley & Sons.
Vermunt, J. (1996), "Causal Log-Linear Modeling with Latent Variables and
Missing Data," U. Engel and J. Reinecke, editor. New York: de Gruyter,
35-60.
------ (1997),
Log-Linear Models for Event Histories
, Advanced Quantitative
Techniques in the Social Sciences, Thousand Oaks CA: Sage.
Vogt, W. (1993),
Dictionary of Statistics and Methodology
, Newbury Park CA:
Sage.
Wold, H. (1973), "Nonlinear Iterative Partial Least Squares (NIPALS) Modeling:
Some Current Developments," in
Multivariate Analysis- III
, P.R. Krish-
naiah, editor. New York: Academic Press, 383-487.
------ (1980), "Soft Modeling: Intermediate Between Traditional Model Building
and Data Analysis,"
Mathematical Statistics
, 6, 333-346.
------ (1982), "Soft Modeling- The Basic Design and Extensions," in
Systems Un-
der Indirect Observation (II)
, K. Jöreskog and H Wold, editors. Amster-
dam: North-Holland, 1-53.
Wothke, W. (1998), Personal Communication, Bias in OLS estimators of PLS,
June.

1998 Sawtooth Software Conference
©1999 LBA: Lynd Bacon & Associates, Ltd. All Rights Reserved
- 16 -
Appendix: Software and other resources
A variety of software programs are available for fitting CSMs. Commercial pro-
grams include LISREL from Scientific Software Inc., AMOS from Smallwaters
Corp. and SPSS Inc.; EQS from Multivariate Software, LISCOMP from Scientific
Software as well as other distributors, Mplus from Muthén and Muthén, and the
CALIS procedure in SAS. Non-commercial programs include MX and GENBLIS.
Software for PLS is quite scarce. Lohm|ller's FORTRAN program LVPLS is
available in compiled form for MS-DOS. As of this writing it can be obtained from
John ("Jack") McArdle at the University of Virginia, and from two sources in Ger-
many. The URL is:
ftp://kiptron.psyc.virginia.edu/pub/lvpls/
If you have trouble accessing this site, you might try e-mailing Fumiaki Hama-
gami at Virginia, fh3s@kiptron.psyc.virginia.edu.
Falk and Miller (1992) indicate that the FORTRAN source for LVPLS is still avail-
able from a source in Germany.
Wynne Chin at the University of Houston indicates he is developing a Windows-
based program called PLS-GRAPH for fitting PLS-SEMs. He has a web page at
http://disc-nt.cba.uh.edu/chin/indx.html
that includes some PLS background and resources.
Lohm|ller's seminal 1989 PLS book "Latent Variable Path Modeling with Partial
Least Squares" is no longer in print. Falk & Miller (1992) provide a gentle and
practical introduction to Lohm|ller's LVPLS program, as well as a conceptual
overview of soft modeling.
A number of good general references on CSMs exist. Bollen's 1989 text is semi-
nal, although somewhat dated. Bollen and Long's "Testing Structural Equation
Models" (1993) is an edited book with several useful chapters. Marcoulides &
Schumacker (1996) and Schumacker and Marcoulides (1998) cover key issues
in modeling nonlinearities, interactions, and models for change and growth. Mar-
coulide's 1998 book includes useful chapters on PLS-SEM by Chin (Chapter 10)
and on CSMs by Rigdon (Chapter 9), Kaplan (Chapter 11), and McArdle (Chap-
ter 12). The Chapters by Bagozzi & Yi, and by Fornell & Cha in Bagozzi's
1994(b) book "Advanced Methods of Marketing Research" are good introductions
to CSMs and PLS. Dillon et al. (1997) provide an accessible overview to struc-
tural equation modeling. Finally, the November 1982 issue of Journal of Market-
ing Research was dedicated to SEMs (both CSMs and PLS), and is of at least
historical interest.

1998 Sawtooth Software Conference
©1999 LBA: Lynd Bacon & Associates, Ltd. All Rights Reserved
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Figure 1. Example path diagram. Boxes are observed variables. Directed arrows show depend-
encies, e.g. satisfied depends on the three variables perform, expect_met, and sup_brand.
Ellipses labeled zeta_s, -_p, and -_n are regression errors. They aren’t in boxes because their
values are inferred, i.e. they are latent variables. The "1" next to the arrows from the zetas repre-
sent a constraint that makes the measurement scales of the zetas match that of the dependent
variable in their corresponding regression equation. This is a non-recursive model because of the
loop between satisfied and sup_brand.
Figure 2. A recursive model for how value depends on support and hardware. All three of
these variables are latent, and are estimated using measurement models having three, four, and
five indicator variables, respectively. The indicators are in squares and have arrows point to their
respective LVs. Each indicator has associated with it a measurement error named as a single
letter and digits, e.g. s1. Each of these is drawn in a circle since they are unobserved. The
curved, two headed arrow between support and hardware is a covariance. It represents an as-
sociation that isn’t directional, unlike the paths from hardware and support to value. This model
is essentially a regression model in LVs that has two predictors that are correlated.
value
Q41 v1
11
Q43 v2
1
Q38 v3
1
hardware
Q37a
p1
1
1
Q37b
p21
q39
p3
1
Q40a
p41
Q40b
p51
support
Q35a
s1
1
1
Q35b
s2
1
Q35c
s3
1
Q35d
s4
1
val_err
1
sup_brand
satisfied
purc_intent
expect_met
perform
innovative
cust_care
zeta_s
zeta_n
zeta_p
1
1
1
costs

1998 Sawtooth Software Conference
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Figure 3. Path diagram showing standardized coefficient estimates for a CSM fit using AMOS
3.61. The variance-covariance matrix of the observed variables p1…s4 was analyzed. The vari-
ables p1 through p4 are the indicators for the LV performance. s1 through s4 are the indicators
for the satisfaction LV. Zeta is a regression error. The coefficients labeling paths from the LVs to
the observed variables are estimates of standardized factor loadings. The unobserved variables
e1 through e8 are sources of variation unique to the observed variables they point to. The coeffi-
cient on the path between performance and satisfaction is the standardized regression coefficient
for performance. N=200.
Figure 4. PLS coefficients shown in larger fonts from analysis of the correlation matrix of the ob-
served variables p1…s4. The quantities in smaller font are standardized estimates from the
CSM model shown in Figure 3. The diagram is otherwise labeled like Figure 3.
performance
p1
e1
.76
p2
e2
.68 p3
e3
.72 p4
e4
.51
satisfaction
s1
e5
.80 s2
e6
.66 s3
e7
.68 s4
e8
.66
.85
zeta
performance
p1
e1
.76 p2
e2
.68 p3
e3
.72 p4
e4
.51
satisfaction
s1
e5
.80 s2
e6
.66 s3
e7
.68 s4
e8
.66
.85
zeta
.68
.82 .79 .81 .63 .85 .76 .77 .76

1998 Sawtooth Software Conference
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Table 1. Basic specifications for covariance structure and PLS models.
The basic CSM structural model expresses the relationship between endogenous LVs
η
, in-
tercepts
α
, regression coefficients Β and
Γ
, exogenous LVs
ξ
, and errors in equations
ζ
.
Where
η
,
ξ
,
α
, and
ζ
are vectors, and Βand
Γ
are matrices.
CSM measurement models connect observed indicator variables Y for endogenous LVs, and
observed indicators X for exogenous LVs:
The matrices Λcontain factor loadings for the observed variables on the LVs, and
ε
δ
, are
"uniquenesses," i.e. sources of variance other than the LVs. Their expected values are assumed
to be zero. Intercepts may also be included in the measurement models. A complete CSM
specification includes covariance matrices for the various kinds of errors and for the exogenous
LVs.
PLS has inner and outer models. The PLS inner model can be expressed as:
Where the LVs in
η
can be ordered such that Β is lower diagonal. Assumptions include
E
ζζηζξ
===00,cov, cov ,
16 16. The outer model for
reflective
indicators is:
And for
formative
indicators:
The Λ are loadings and the Π are regression coefficients. The expected values of the
ε
δ
,
are zero, and they are assumed to not covary with
η
ξ
, .
η
α
η
ξ
ζ
=+ + +Β
Γ
Y
XY
X
=
+
=+
Λ
Λ
η
ε
ξδ
η
α
η
ξ
ζ
=+ + +Β
Γ
Y
XYY
XX
=+
=+
Λ
Λ
η
ε
ξε
η
δ
ξδ
η
ξ
=+
=+
Π
ΠY
X
Y
X

1998 Sawtooth Software Conference
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The PLS specification also includes
weights
that are used to estimate the scores on
η
ξ
, . The
predicted values are obtained as, e.g.
$
ξ
=∑wx, and how the weights w are determined de-
pends on the kind of outer model used for each LV as well as the LVs role in the inner model.

1998 Sawtooth Software Conference
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Table 2. Short comparison of CSM and PLS Characteristics
Feature CSM PLS
Distribution assumptions Observed variables are MVN
for ML, GLS estimation. In-
dependent observations.
Continuously distributed ob-
served variables for
ADF/WLS.
None
Types of models that can be fit Recursive, non-recursive Recursive
Types of observed variables Continuous
Ordered discrete (using
polychoric correlations as
input, assuming robustness,
or using the LISCOMP
specification.
Continuous
Ordered and unordered dis-
crete
Type of latent variables that can
be modeled Continuous continuous
Types of indicators for latent
variables Effect- arrow from LV to indi-
cator
Causal- arrow from indicator
reflective, formative
(analogous to effect and
causal indicators, respectively)
Identification of parameters Must be considered. Heu-
ristics are available for com-
mon model forms. Other-
wise, empirical procedures
are required
Not an issue for standard PLS
models.
Effects indicators per factor Can be as few as one if the
indicator’s error is con-
strained. Otherwise, the
number depends on pa-
rameter identification re-
quirements.
One or more, but see "Con-
sistency of estimators"
Factors per indicator An observed variable can
indicate more than one LV Observed variables can only
indicate one LV
Correlation between LVs can be
estimated as undirected Yes No
Correlation between measure-
ment errors can be modeled Yes no
Estimation of means and inter-
cepts on LVs Yes No
Type of Fitting algorithm Simultaneous estimation of
parameters by minimizing
discrepancies between ob-
served and predicted VCV
matrix (or correlation matrix).
Full information methods.
Multi-stage iterative procedure
using OLS. Model is divided
into blocks whose parameters
are estimated separately. A
limited information method.

1998 Sawtooth Software Conference
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Table 2. (continued)
Feature CSM PLS
Consistency of estimators Consistent, given correct-
ness of model and appropri-
ateness of assumptions
"Consistency at Large:" Esti-
mates become consistent
when the sample size gets
large, and the number of indi-
cators/LV gets large.
Availability of statistical tests for
estimates Available and valid given key
model assumptions are ten-
able. Inference by boot-
strapping, otherwise.
Inference requires jacknifing or
bootstrapping.
Measures of fit A great variety of them. Dis-
tributional theory worked out
for some, not for others.
Some allow inferences about
nested models.
Coefficient of determination for
each equation, Q2 predictive
relevance measures. Can be
used for nested model com-
parisons with bootstrapping.
Assessing measurement model
quality Measures for assessing reli-
ability and validity are avail-
able that permit observed
variables to indicate more
than one LV
Measures of reliability and
validity are available.
Sample size requirements Larger than for multiple re-
gression. Procedures for
estimating required N and for
power analysis are available.
Small to moderate. A heuristic
is to use 10-20 observations
per parameter in the largest
model block. See "consis-
tency of estimators."
Factor indeterminancy Latent variable scores are
not estimated directly. Scale
of measurement for each
factor must be set using a
constraint.
None. Latent variable scores
are estimated as exact linear
combinations of observed
variables.
2nd-order factors can be mod-
eled Yes Yes
Estimation of random coeffi-
cients yes, for some model types No
Latent class/finite mixture mod-
eling Yes, for some model types no
Missing data Algorithms assume complete
data, but imputation can be
done w/in some available
SEM software packages.
Assumes complete data. Im-
putation using other software.