Testing Moderating Effects in PLS Path Models. An Illustration of Available Procedures

Along with the development of scientific disciplines, namely social sciences, hypothesized relationships become increasingly more complex. Besides the examination of direct effects, researchers are more and more interested in moderating effects. Moderating effects are evoked by variables whose variation influences the strength or the direction of a relationship between an exogenous and an endogenous variable. Investigators using partial least squares path modeling need appropriate means to test their models for such moderating effects. We illustrate the identification and quantification of moderating effects in complex causal structures by means of Partial Least Squares Path Modeling. We also show that group comparisons, i.e. comparisons of model estimates for different groups of observations, represent a special case of moderating effects by having the grouping variable as a categorical moderator variable. We provide profound answers to typical questions related to testing moderating effects within PLS path models: 1. How can a moderating effect be drawn in a PLS path model, taking into account that the available software only permits direct effects? 2. How does the type of measurement model of the independent and the moderator variables influence the detection of moderating effects? 3. Before the model estimation, should the data be prepared in a particular manner? Should the indicators be centered (by having a mean of zero), standardized (by having a mean of zero and a standard deviation of one), or manipulated in any other way? 4. How can the coefficients of moderating effects be estimated and interpreted?And, finally: 5. How can the significance of moderating effects be determined? Borrowing from the body of knowledge on modeling interaction effect within multiple regression, we develop a guideline on how to test moderating effects in PLS path models. In particular, we create a graphical representation of the necessary steps to take and decisions to make in the form of a flow chart. Starting with the analysis of the type of data available, via the measurement model specification, the flow chart leads the researcher through the decisions on how to prepare the data and how to model the moderating effect. The flow chart ends with the bootstrapping, as the preferred means to test significance, and the final interpretation of the model outcomes.

[1]  G. McClelland,et al.  Misleading Heuristics and Moderated Multiple Regression Models , 2001 .

[2]  Jost Reinecke.  Interaktionseffekte in Strukturgleichungsmodellen mit der Theorie des geplanten Verhaltens: Multiple Gruppenvergleiche und Produktterme mit latenten Variablen , 1999 .

[3]  L. Cronbach.  Statistical tests for moderator variables: flaws in analyses recently proposed , 1987 .

[4]  Subhash Sharma,et al.  Identification and Analysis of Moderator Variables , 1981 .

[5]  Jan-Bernd Lohmöller,et al.  Latent Variable Path Modeling with Partial Least Squares , 1989 .

[6]  Traci Carte,et al.  In Pursuit of Moderation: Nine Common Errors and Their Solutions , 2003, MIS Q..

[7]  Wynne W. Chin,et al.  A Partial Least Squares Latent Variable Modeling Approach for Measuring Interaction Effects: Results from a Monte Carlo Simulation Study and an Electronic - Mail Emotion/Adoption Study , 2003, Inf. Syst. Res..

[8]  Michel Tenenhaus,et al.  PLS path modeling , 2005, Comput. Stat. Data Anal..

[9]  Fan Yang,et al.  Nonlinear structural equation models: The Kenny-Judd model with Interaction effects , 1996 .

[10]  S. West,et al.  Multiple Regression: Testing and Interpreting Interactions. , 1994 .

[11]  R. Lennox,et al.  Conventional wisdom on measurement: A structural equation perspective. , 1991 .

[12]  J. Jaccard,et al.  Interaction effects in multiple regression , 1992 .

[13]  J. Elashoff,et al.  Multiple Regression in Behavioral Research. , 1975 .

[14]  Donald W. Marquardt,et al.  Comment: You Should Standardize the Predictor Variables in Your Regression Models , 1980 .

[15]  Wynne W. Chin,et al.  A Partial Least Squares Latent Variable Modeling Approach for Measuring Interaction Effects: Results from a Monte Carlo Simulation Study and Voice Mail Emotion/Adoption Study , 1996, ICIS.

[16]  Edward E. Rigdon,et al.  A Comparative Review of Interaction and Nonlinear Modeling , 1998 .

[17]  J. M. Cortina,et al.  Interaction, Nonlinearity, and Multicollinearity: implications for Multiple Regression: , 1993 .

[18]  D. A. Kenny,et al.  Estimating the nonlinear and interactive effects of latent variables. , 1984 .

[19]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[20]  Frank M. Bass,et al.  Pooling Issues and Methods in Regression Analysis with Examples in Marketing Research , 1975 .

[21]  Donald W. Marquardt,et al.  A Critique of Some Ridge Regression Methods: Comment , 1980 .

[22]  D. A. Kenny,et al.  The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. , 1986, Journal of personality and social psychology.

[23]  G. Chow.  Tests of equality between sets of coefficients in two linear regressions (econometrics voi 28 , 1960 .

[24]  H. Winklhofer,et al.  Index Construction with Formative Indicators: An Alternative to Scale Development , 2001 .

[25]  Kent W. Smith,et al.  Decreasing Multicollinearity , 1979 .

[26]  Christian Homburg,et al.  Personal characteristics as moderators of the relationship between customer satisfaction and loyalty—an empirical analysis , 2001 .

[27]  Richard L. Tate,et al.  Limitations of Centering for Interactive Models , 1984 .

[28]  R. Moos,et al.  Methodological issues in estimating main and interactive effects: examples from coping/social support and stress field. , 1984, Journal of health and social behavior.

[29]  Jacob Cohen.  Partialed products are interactions; partialed powers are curve components. , 1978 .

[30]  Cheryl Burke Jarvis,et al.  A Critical Review of Construct Indicators and Measurement Model Misspecification in Marketing and Consumer Research , 2003 .

[31]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .