Article: Latent Variable Interactions With Ordered-Categorical Indicators: Comparisons of Unconstrained Product Indicator and Latent Moderated Structural Equations Approaches

Methods to handle ordered-categorical indicators in latent variable interactions have been developed, yet they have not been widely applied. This article compares the performance of two popular latent variable interaction modeling approaches in handling ordered-categorical indicators: unconstrained product indicator (UPI) and latent moderated structural equations (LMS). We conducted a simulation study across sample sizes, indicators' distributions and category conditions. We also studied four strategies to create sets of product indicators for UPI. Results supported using a parceling strategy to create product indicators in the UPI approach or using the LMS approach when the categorical indicators are symmetrically distributed. We applied these models to study the interaction effect between third- to fifth-grade students' social skills improvement and teacher-student closeness on their state English language arts test scores.

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References

1.

Foldnes N, Hagtvet K . The choice of product indicators in latent variable interaction models: post hoc analyses. Psychol Methods. 2014; 19(3):444-57. DOI: 10.1037/a0035728. View

2.

Marsh H, Wen Z, Hau K . Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction. Psychol Methods. 2004; 9(3):275-300. DOI: 10.1037/1082-989X.9.3.275. View

3.

Cham H, West S, Ma Y, Aiken L . Estimating Latent Variable Interactions With Non-Normal Observed Data: A Comparison of Four Approaches. Multivariate Behav Res. 2013; 47(6):840-876. PMC: 3583564. DOI: 10.1080/00273171.2012.732901. View

4.

Cham H, Reshetnyak E, Rosenfeld B, Breitbart W . Full Information Maximum Likelihood Estimation for Latent Variable Interactions With Incomplete Indicators. Multivariate Behav Res. 2016; 52(1):12-30. PMC: 5489914. DOI: 10.1080/00273171.2016.1245600. View

5.

Yang C, Nay S, Hoyle R . Three Approaches to Using Lengthy Ordinal Scales in Structural Equation Models: Parceling, Latent Scoring, and Shortening Scales. Appl Psychol Meas. 2010; 34(2):122-142. PMC: 2877522. DOI: 10.1177/0146621609338592. View

6.

Rhemtulla M, Brosseau-Liard P, Savalei V . When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychol Methods. 2012; 17(3):354-73. DOI: 10.1037/a0029315. View

7.

Song X, Lee S . Maximum Likelihood Analysis of Nonlinear Structural Equation Models With Dichotomous Variables. Multivariate Behav Res. 2016; 40(2):151-77. DOI: 10.1207/s15327906mbr4002_1. View

8.

Foldnes N, Olsson U . A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix. Multivariate Behav Res. 2016; 51(2-3):207-19. DOI: 10.1080/00273171.2015.1133274. View

9.

Little T, Rhemtulla M, Gibson K, Schoemann A . Why the items versus parcels controversy needn't be one. Psychol Methods. 2013; 18(3):285-300. PMC: 3909043. DOI: 10.1037/a0033266. View

10.

Rizopoulos D, Moustaki I . Generalized latent variable models with non-linear effects. Br J Math Stat Psychol. 2007; 61(Pt 2):415-38. DOI: 10.1348/000711007X213963. View

11.

Cohen J . A power primer. Psychol Bull. 2009; 112(1):155-9. DOI: 10.1037//0033-2909.112.1.155. View