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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. 831
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
Page 1: Using Structural Equation Modeling
Page 5 and 6: In conclusion, formative CBSEM prov
Page 7 and 8: References Albers, S., Hildebrandt,
Page 9: Marcoulides, G.A., Hershberger, S.L

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