Using Structural Equation Modeling for Success Factor ... - ANZMAC

Using Structural Equation Modeling for Success Factor and ECSI Research: A Robustness
Comparison of Alternative Estimation Techniques.
Bradley Wilson, RMIT University, School of Applied Communication.
Christian Ringle, University of Hamburg; Faculty of Business, Economics and Social
Sciences.
Oliver Götz, University of Münster; Marketing Centrum Münster; Institute of Marketing.
Abstract
This study is one of the first to implement a Monte Carlo simulation to investigate the robustness
and precision of parameter estimates for predominantly a formative structural equation
model (SEM) specification. It is clear that such work is required in order to provide adequate
working guidelines for marketing researchers. Formative constructs feature strongly in the
area of success factor and the European Customer Satisfaction Index (ECSI) research domains.
This will help assist in selecting whether to utilise covariance-based structural equation
modeling (CBSEM) or partial least squares path modeling (PLS) methods. Understanding in
the PLS realm with adequate robustness research is many years behind the knowledge established
within CBSEM. Our study compares PLS with the performance of Maximum-
Likelihood (ML) for normal and nonnormal data scenarios. We establish that ML estimation
provides relatively robust structural and reflective measurement model estimates. PLS also
demonstrates significant performance advantages when estimating the formative model constructs
but also underestimates some parameters within the structural model. This study also
found that PLS has some advantages when estimating formative measurement models with
nonnormal data.
Literature Review
This paper aims to contribute to the body of knowledge surrounding SEM specification with
different types of measurement model specifications. We are mindful of the useful advice
provided by Boomsma and Hoogland (2001, p. 22) whom state with reference to a CBSEM
context that:
“The key objective of robustness research is to offer practical guidelines for applied
work, so as to prevent nonrobust analyses that would inevitably lead to wrong substantive
inferences. Within that framework, a predominant question is: If structural models
are to be analyzed, what estimation methods have to be preferred under what conditions?”
Measurement model specification has received heightened attention in marketing recently
(Diamantopoulos and Winklhofer 2001; Jarvis; Mackenzie, and Podsakoff 2003). In general,
the direction of indicator relationships and their causality is either in an effect (reflective) or a
cause (formative) mode (Bollen, 1989) i . Even early researchers recognised the importance of
causality from the measures to the construct, rather than vice versa (Blalock, 1971). Therefore,
formative constructs have to be modeled as a (typically linear) combination of its indicators
plus a disturbance term. The use of formative measurement models in SEM leads to some
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implications for researchers. One implication for a formative specification is that deleting one
indicator could omit a unique part of the measurement model and change the domain meaning
of the construct (Diamantopoulos and Winklhofer, 2001). Thus, some researchers state that a
formative measurement model requires a census of all indicators that determine the construct
(Bollen and Lennox 1991). Often formative indicators do not follow a multinormal distribution.
Social research often leads to nonnormal item distribution curves, with varying degrees
of skewness and kurtosis which can strongly influence the choice of SEM estimator (Browne,
1984). Two main approaches have been used to estimate formative measurement models in
SEM: the partial least squares (PLS) and the covariance-based (CBSEM) methods. However,
little attention has been devoted to the conditions in which formative measures and their estimation
method leads to precise and robust coefficients. This study is one of the first consisting
of primarily formative variables.
There are several CBSEM estimators available for analyst choice. Estimation methods include:
Unweighted Least Squares (ULS), Generalized Least Squares (GLS), Maximum Likelihood
(ML) and Asymptotic Distribution Free (ADF) estimation (Marcoulides and Hershberger,
1997). This paper focuses on ML estimation. The inclusion of formative measures in
CBSEM is well documented by Jöreskog and Sörbom (2001) and MacCallum and Brown
(1993). (Diamantopoulos 2006) recently outlined pertinent issues in formative CBSEM identification
which also supplements the work of Kline (2006) ii . Wilson, Callaghan and Stainforth
(2007) instigated these suggestions in a Confirmatory Vanishing Tetrad Analysis paper.
In contrast, the goal of PLS estimation is to maximise the variance of all dependent variables.
Therefore, the goal of PLS and CBSEM is inherently different in estimation and purpose
(Chin, 1995). However, Rigdon (2003) explains that PLS is often a nontraditional alternative
when undertaking analyses. PLS estimates become more accurate as PLS claims to operate on
the assumption of “consistency at large” (Fornell and Cha, 1994). Whilst PLS typically overestimates
structural parameters and underestimates loadings Rigdon (2003, p. 1935) states
“that this is a reasonable trade….to estimate essentially hypothetical model parameters for an
improved ability to predict the data.”
The Vilares, Almeida, and Coelho (2007) study comes the closest to a PLS Monte Carlo investigation
featuring one formative construct specification with the balance of constructs in
their research being a reflective orientation. Their scenarios include: a symmetric base model
and one with skewed data. They also use as the basis for their work the reduced form of the
European Customer Satisfaction Index (ECSI) model stating that debate exists about whether
the loyalty construct is best represented by reflective or formative indicators. They generate
1000 simulated datasets for 250 observations for 21 measured variables. (Chin; Marcolin, and
Newstead 2003)) and Hsu, Chen, and Hsieh (2006) both complete simulation studies but they
only focus on constructs with reflective specifications. Some studies ((Fornell and Bookstein
1982); Lohmöller, 1989; Tenenhaus et al., 2005) iii have CBSEM (ML estimation) and PLS estimation
comparisons but these were not for Monte Carlo studies.
Formative models have been prevalent within business and marketing success factor research
(c.f., Lee and Tsang, 2001; Höck and Ringle, 2006; Wixom and Watson, 2001). These indicators
are usually independent drivers of the success factor. The model we specify is also similar
to models that have been studied for ECSI investigations (Gronholdt, Martensen and Kristensen,
2000; Kristensen, Martensen and Gronholdt, 2000). Many studies of this nature typically
have response profiles that do not meet the normality assumption.
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Monte Carlo Study Design
The graphical model investigated is analogous to the constructs and relations in the ECSI and
the prespecified relationships are featured in Table 2 (see first column). The manifest variables
in the measurement models of the exogenous constructs are operationalised as formative
while the endogenous constructs are measured reflectively. This model is appropriate for
CBSEM (Jöreskog and Sörbom, 2001) and PLS path modeling (Lohmöller, 1989; Tenenhaus
et al., 2005). The design specification for the investigated SEM is partially based on Albers
and Hildebrand (2006) who analyse the effect of invalid scale purification. We created a correlation
matrix for data generation (Table 1). A STATISTICA 7.1 (StatSoft, 2005) macro implementation
was programmed to simulate data. The data generation process is consistent
with the procedure described by Chin, Marcolin and Newsted (2003) and Vilares, Almeida,
and Coelho (2007). The Monte Carlo simulation comprises 1000 sets of normal data whereby
each set consists of 300 cases. In addition, we carried out a separate analysis for extremely
nonnormal data regarding skewness (2) and kurtosis (8). The CBSEM as well as PLS model
estimations for each set of data provide proper solutions (convergence, model identification
and heywood cases). CBSEM results are obtained via STATISTICA while SmartPLS (Ringle,
Wende and Will, 2006) is used for the PLS path modeling.
Table 1: Correlation Matrix of Manifest Variables (Albers & Hildebrandt, 2006)
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 y1 y2 y3 y4 y5 y6
x1 1.00
x2 0.71 1.00
x3 0.72 0.65 1.00
x4 0.08 0.04 0.09 1.00
x5 -0.01 -0.05 -0.02 0.05 1.00
x6 0.02 0.03 -0.06 0.06 -0.03 1.00
x7 -0.11 -0.12 -0.06 0.00 0.02 -0.01 1.00
x8 -0.13 -0.13 -0.09 -0.05 0.01 0.06 0.10 1.00
x9 0.02 -0.03 0.00 0.06 0.00 -0.02 0.10 -0.06 1.00
x10 0.01 0.07 -0.01 0.03 0.12 -0.03 -0.02 -0.01 0.12 1.00
x11 -0.05 0.04 -0.06 0.07 0.00 0.07 0.01 -0.04 0.24 0.57 1.00
x12 0.03 0.07 -0.02 0.10 0.06 -0.02 0.02 -0.05 0.29 0.49 0.53 1.00
x13 0.03 0.05 0.01 -0.01 0.01 0.05 0.00 -0.01 0.13 0.20 0.29 0.27 1.00
y1 0.06 0.06 0.05 0.54 0.61 0.15 0.19 0.01 0.08 0.08 0.03 0.06 -0.02 1.00
y2 0.00 0.02 0.00 0.54 0.51 0.19 0.16 0.01 0.10 0.04 0.02 0.04 -0.01 0.85 1.00
y3 0.08 0.06 0.08 0.54 0.58 0.09 0.15 0.04 0.11 0.01 0.00 0.03 0.00 0.89 0.83 1.00
y4 0.06 0.07 0.04 0.33 0.30 0.29 0.36 0.04 0.33 0.37 0.39 0.42 0.32 0.58 0.53 0.55 1.00
y5 0.00 0.01 0.01 0.31 0.28 0.26 0.40 0.09 0.29 0.35 0.38 0.35 0.34 0.54 0.51 0.52 0.83 1.00
y6 0.05 0.05 0.01 0.35 0.35 0.29 0.40 0.07 0.35 0.37 0.41 0.39 0.36 0.63 0.57 0.58 0.88 0.86 1.00
Results and Conclusion
Our simulation study establishes five main findings. First, the CBSEM and PLS estimates for
the simulated sets of data are on average very close to the population parameters. ML provides
the most appropriate CBSEM estimates in our simulations study. This mirrors results
obtained in a cross-sectional study illustrating high correlations between ML estimates and
PLS estimates (Tenenhaus et al., 2005). The reader should consult Table 2 and 3 for complete
understanding of the below stated findings. Second, ML has a tendency of overestimating
while PLS has a tendency of underestimating parameters in the formative measurement mod-
832

els. Both methods perform considerably better in the formative measurement model with a
homogenous correlation pattern compared to the two with heterogeneous correlation patterns.
Third, ML has a tendency to underestimate and PLS to overestimate parameters in reflective
outer models. Fourth, ML overestimates inner relationships data while PLS underestimates
those parameters. The accuracy (mean absolute deviation, MAD) for the inner relationships
between exogenous and endogenous constructs with different kinds of measurement models
has a considerably weaker outcome, especially for PLS. Fifth, CBSEM estimates in the formative
measurement and the structural model significantly decrease in their accuracy and robustness
(mean squared error, MSE) when data is nonnormal while the performance for reflective
measurement models is not affected by the changed data characteristics. The results
for PLS show that the decrease of MSE and MAD is at much lower levels making it suitable
for nonnormal data (Table 4).
Table 2: Simulation Results for Normal Data
Mean
Mean Absolute
Mean Value Deviation
Deviation Mean Squared Error
Outer Model (Formative) ML PLS ML PLS ML PLS ML PLS
[x1]-{0.1}->(Ksi1) 0.107 0.085 0.008 -0.018 0.135 0.226 0.034 0.080
[x2]-{0.2}->(Ksi1) 0.210 0.177 0.010 -0.026 0.142 0.236 0.046 0.085
[x3]-{0.1}->(Ksi1) 0.105 0.084 -0.004 -0.023 0.137 0.230 0.053 0.079
[x4]-{0.6}->(Ksi1) 0.610 0.452 -0.003 -0.137 0.156 0.234 0.195 0.090
[x5]-{0.4}->(Ksi1) 0.421 0.308 -0.000 -0.078 0.151 0.222 0.220 0.081
[x6]-{0.4}->(Ksi2) 0.433 0.413 0.024 0.020 0.113 0.210 0.081 0.068
[x7]-{0.6}->(Ksi2) 0.649 0.600 0.040 0.000 0.144 0.179 0.112 0.052
[x8]-{0.1}->(Ksi2) 0.102 0.098 0.001 0.001 0.103 0.213 0.018 0.072
[x9]-{0.4}->(Ksi3) 0.408 0.329 0.006 -0.075 0.088 0.154 0.015 0.038
[x10]-{0.3}->(Ksi3) 0.300 0.244 -0.003 -0.057 0.089 0.150 0.015 0.036
[x11]-{0.2}->(Ksi3) 0.199 0.160 0.001 -0.035 0.085 0.146 0.013 0.033
[x12]-{0.2}->(Ksi3) 0.203 0.166 0.003 -0.030 0.093 0.145 0.015 0.033
[x13]-{0.4}->(Ksi3) 0.407 0.321 0.008 -0.073 0.095 0.148 0.018 0.035
Average(abs) 0.008 0.044 0.118 0.192 0.064 0.060
Outer Model (Reflective)
(Eta1)-{0.8}->[y1] 0.682 0.841 -0.115 0.041 0.125 0.041 0.019 0.002
(Eta1)-{0.7}->[y2] 0.648 0.816 -0.049 0.117 0.072 0.117 0.008 0.014
(Eta1)-{0.8}->[y3] 0.682 0.842 -0.114 0.042 0.124 0.042 0.019 0.002
(Eta2)-{0.8}->[y4] 0.765 0.871 -0.038 0.071 0.064 0.071 0.007 0.005
(Eta2)-{0.7}->[y5] 0.720 0.851 0.017 0.151 0.050 0.151 0.005 0.023
(Eta2)-{0.8}->[y6] 0.766 0.871 -0.036 0.072 0.062 0.072 0.006 0.005
Average(abs) 0.062 0.082 0.083 0.082 0.011 0.009
Inner Model
(Ksi1)-{0.4}->(Eta1) 0.398 0.249 -0.001 -0.025 0.048 0.151 0.007 0.025
(Ksi2)-{0.5}->(Eta1) 0.509 0.254 0.005 -0.064 0.072 0.250 0.015 0.064
(Ksi3)-{0.6}->(Eta1) 0.607 0.382 0.002 -0.051 0.057 0.221 0.008 0.051
(Eta1)-{0.6}->(Eta2) 0.597 0.580 0.001 -0.002 0.038 0.035 0.004 0.002
Average(abs) 0.002 0.036 0.054 0.164 0.009 0.036
Mean Value =
1
n
n
ˆ å q i
i = 1
;
n 1
Mean Deviation = ˆ å qi
- q ;
n i = 1
n 1
Mean Absolute Deviation = ˆ å qi
- q
n i = 1
;
1
Mean Squared Error =
n
n
2
( qˆ
i - q)
;
i = 1,...,
1000 ; θ Parameter Estimation ;
ˆ = θ =
Population
Parameter
å
i = 1
833

In conclusion, formative CBSEM provides accurate and robust parameter estimates that are in
some ways superior in comparison to PLS when dealing with normal data (Table 4). However,
in most marketing applications, we are probably dealing with relatively small sample
sizes and skewed data that may not be appropriate to provide ML robust estimates with formative
variables. ML may not be as robust to normality deviations (Bollen, 1989; Boomsma,
1983) with formative models. Consequently, PLS is recommended as the methodology of
choice with this kind of data and model specification. Although, no CBSEM convergence
problems were featured in this study, other formative models may be difficult to identify
and/or have convergence problems (Fornell and Bookstein, 1982). PLS has demonstrated advantages
here (Chin, 1998; Wilson, 2007). Future simulations must investigate different
model types with varied parameter combinations, variable numbers (item reliabilities), sample
sizes and newer CBSEM estimators that may be sensitive to categorical nonnormal variables
(Finney and DiStefano, 2006).
834

Table 3: Simulation Results for Nonnormal Data
Mean Value
Mean
Deviation Mean Absolute Deviation Mean Squared Error
Outer Model (Formative) ML PLS ML PLS ML PLS ML PLS
[x1]-{0.1}->(Ksi1) 0.104 0.084 0.004 -0.016 0.163 0.245 0.052 0.093
[x2]-{0.2}->(Ksi1) 0.215 0.178 0.015 -0.022 0.168 0.248 0.070 0.096
[x3]-{0.1}->(Ksi1) 0.110 0.084 0.010 -0.016 0.154 0.238 0.045 0.085
[x4]-{0.6}->(Ksi1) 0.612 0.453 0.012 -0.147 0.196 0.247 0.310 0.098
[x5]-{0.4}->(Ksi1) 0.418 0.307 0.018 -0.093 0.168 0.248 0.088 0.097
[x6]-{0.4}->(Ksi2) 0.445 0.412 0.045 0.012 0.150 0.229 0.264 0.084
[x7]-{0.6}->(Ksi2) 0.655 0.602 0.055 0.002 0.185 0.204 0.260 0.065
[x8]-{0.1}->(Ksi2) 0.103 0.095 0.003 -0.005 0.120 0.225 0.027 0.080
[x9]-{0.4}->(Ksi3) 0.418 0.329 0.018 -0.071 0.115 0.172 0.030 0.047
[x10]-{0.3}->(Ksi3) 0.307 0.243 0.007 -0.057 0.111 0.168 0.024 0.044
[x11]-{0.2}->(Ksi3) 0.203 0.159 0.003 -0.041 0.112 0.164 0.022 0.042
[x12]-{0.2}->(Ksi3) 0.211 0.167 0.011 -0.033 0.121 0.165 0.025 0.042
[x13]-{0.4}->(Ksi3) 0.413 0.318 0.013 -0.082 0.118 0.172 0.032 0.047
Outer Model (Reflective)
Average(abs) 0.016 0.046 0.145 0.210 0.096 0.071
(Eta1)-{0.8}->[y1] 0.682 0.842 -0.118 0.042 0.132 0.044 0.023 0.002
(Eta1)-{0.7}->[y2] 0.648 0.817 -0.052 0.117 0.083 0.117 0.011 0.014
(Eta1)-{0.8}->[y3] 0.682 0.842 -0.118 0.042 0.132 0.044 0.023 0.002
(Eta2)-{0.8}->[y4] 0.766 0.872 -0.034 0.072 0.074 0.072 0.010 0.006
(Eta2)-{0.7}->[y5] 0.720 0.851 0.020 0.151 0.066 0.151 0.008 0.023
(Eta2)-{0.8}->[y6] 0.767 0.871 -0.033 0.071 0.074 0.071 0.009 0.005
Inner Model
Average(abs) 0.063 0.082 0.094 0.083 0.014 0.009
(Ksi1)-{0.4}->(Eta1) 0.397 0.250 -0.003 -0.025 0.058 0.150 0.009 0.025
(Ksi2)-{0.5}->(Eta1) 0.503 0.255 0.003 -0.063 0.082 0.245 0.020 0.063
(Ksi3)-{0.6}->(Eta1) 0.601 0.384 0.001 -0.050 0.077 0.216 0.014 0.050
(Eta1)-{0.6}->(Eta2) 0.596 0.582 -0.004 -0.002 0.048 0.039 0.007 0.002
Mean
Value
=
Mean Squared Error
Average(abs) 0.003 0.035 0.066 0.162 0.012 0.035
1
n
1
=
n
n
å
i = 1
n
å
i = 1
qˆ
i
;
2
( qˆ
- q)
i
Mean Deviation
;
i = 1,...,
1000
n 1
= ˆ å qi
- q ;
n i = 1
n 1
Mean Absolute Deviation = ˆ å qi
- q
n i = 1
;
; θ Parameter Estimation ;
ˆ = θ = Population
Parameter
Table 4: Comparison of Simulation Results for Normal and Nonnormal Data
Relative Absolute Changes between
Normal and Non-Normal Parameter Estimations
Mean Absolute Deviation Mean Squared Error
ML PLS ML PLS
Outer Model (Formative) 0.228 0.093 0.495 0.178
Outer Model (Reflective) 0.131 0.008 0.311 0.029
Inner Model 0.229 -0.011 0.432 -0.019
Average MADnormal
- Average MADnonnormal
Relative MAD Change =
Average MAD
;
Relative MSE Change
=
Average MSE
normal
Average MSE
normal
- Average MSE
normal
835
nonnormal

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i The interested reader should consult (Bollen and Lennox, 1991; Chin, 1998; Jarvis; Mackenzie, and Podsakoff,
2003) to understand measurement model specification and directionality issues.
ii Formative model identification is a very difficult task with limited guidance presented in standard CBSEM articles,
textbooks and software manuals. There is still much research that is needed in this realm to provide guidance
for introductory and intermediate skilled modelers. We acknowledge that this is our opinion and is based on
analytical experience.
iii We cannot complete a full review of these studies with this limited presentation space. We are mindful of de-
voting more presentation space for our own results.
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