The product indicator approach to estimation of latent interaction effects: Testing of a new method

Ezgi Ayturk, Fordham University


Latent factor interaction is an extension of multiple regression models with interaction effects between predictors. In a latent factor interaction model, there are interactions between latent factors to the outcome variables. Product Indicator (PI) approach is one of the procedures of estimating latent interaction effects in the structural equation modeling (SEM; e.g. Kenny & Judd, 1984; see also Algina & Moulder, 2001; Joreskog & Yang, 1996; Marsh, Wen, & Hau, 2004; Wall & Amemiya, 2001). In this approach, indicators of a latent factor are multiplied with that of a second one to generate the (product) indicators of the interaction term, which is represented by a new latent factor. The interaction term, then, is treated as a separate factor predicting the outcome variable. The purpose of this study was to test a new method which combines the merits of the item-level and parcel-level indicators when forming PIs under the unconstrained PI approach. A Monte Carlo simulation study was conducted to test the efficiency of the new proposed method of forming PIs for testing interaction effects of latent factors. Specifically, the aim of this study was to test whether using 1 or 2 best indicators in addition to a parcel of the remaining indictors to form PIs is more effective than forming PIs with selected individual items or sole parcels in terms of having less biased parameter estimates, better convergence rates, greater power, and better Type I error rates. The robustness of methods was also tested under varying levels of non-normality, and indicator level of measurement. A secondary purpose of the study was to compare the performances of random and purposive allocations of items to parcels when forming PIs.

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Recommended Citation

Ayturk, Ezgi, "The product indicator approach to estimation of latent interaction effects: Testing of a new method" (2016). ETD Collection for Fordham University. AAI10192866.