PLS has been gaining more attention because of its ability to model latent constructs under conditions of nonnormality and small to medium sample sizes (Chin et al., 1996; Chin et al., 2003). PLS is similar to regression, but simultaneously models the structural paths and measurement paths (Chin et al., 1996). In other words, each indicator reflects to the latent variables and their errors. The PLS algorithm allows each indicator to vary in how much it contributes to the composite score of the latent variable, therefore, creates the interactions between variables. PLS is proposed to account for the deleterious effects of measurement error (Chin, Marcolin, and Newsted, 1996). As increasing difficulty to collect real-world data, there are an increasing number of research studies utilizing PLS to estimate their research models. In the last five years, top tier journals, such as Information System Research, MIS Quarterly, have published more than handful research papers under the estimations of PLS (Karimi, Somers, & 70
Gupta, 2004; Chin, Marcolin, Newsted, 2003; Chwelos, Benbasat, & Dexter, 2001; Wixom, & Watson, 2001; Ravichandran, & Rai, 2000). Chin et al. (2003), has especially demonstrated the interaction effects by PLS latent variable modeling. Generally speaking, all those PLS studies had the sample size under 200, some cases were even under 100 respondents. 3.4.2 The Measurement Model By accessing unidimensionality, the reliabilities of the constructs were demonstrated with Cronbach’s alpha as well as composite (construct) reliabilities. The reliability level is desirable at 0.8 for the basic study while it is acceptable at 0.7 for the exploratory study (Hair et al. 1998). Unidimensionality examines the modification indexes, residuals, and overall fit indexes. Construct validity can be examined via the assessment of each measure’s convergent and discriminant validity or factor loadings of each item that is included in a construct. Convergent validity is obtained when the average variance extracted (AVE) between the constructs exceeds 0.5. Discriminant validity can be examined by calculating confidence intervals for the estimates of the interfactor correlations (Anderson, and Gerbing, 1988; Bagozzi, and Phillips, 1982). If the confidence intervals do not include 1.0, discriminant validity is demonstrated. Using chi-square difference is another way to test discriminant validity (Bagozzi, and Phillips, 1982). The chi-square difference test (likelihood ratio test) compares the restrictive model with less restrictive models by examining the changes of the ratio of chi-square and the degrees of freedom ( χ 2 /df). If a statistically significant difference 71
appears, then discriminant validity is approved (Bagozzi, and Phillips, 1982). 3.4.3 The Structural Model The structural model illustrates relationships among the latent variables. It provides the estimation of the path coefficients that act as standardized beta weights in a multiple regression analysis. The path coefficient of an exogenous latent variable means the direct effect to an endogenous latent variable. The significance of path coefficients in the model provides support for hypothesized relationships (Bentler, 1989).
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