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Interaction effects in multilevel models

Description
Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand…

Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain.
ContributorsMazza, Gina L (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
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Robustness of Latent variable interaction methods to nonnormal exogenous indicators

Description
For this thesis a Monte Carlo simulation was conducted to investigate the robustness of three latent interaction modeling approaches (constrained product indicator, generalized appended product indicator (GAPI), and latent moderated structural equations (LMS)) under high degrees of nonnormality of the exogenous indicators, which have not been investigated in previous literature.…

For this thesis a Monte Carlo simulation was conducted to investigate the robustness of three latent interaction modeling approaches (constrained product indicator, generalized appended product indicator (GAPI), and latent moderated structural equations (LMS)) under high degrees of nonnormality of the exogenous indicators, which have not been investigated in previous literature. Results showed that the constrained product indicator and LMS approaches yielded biased estimates of the interaction effect when the exogenous indicators were highly nonnormal. When the violation of nonnormality was not severe (symmetric with excess kurtosis < 1), the LMS approach with ML estimation yielded the most precise latent interaction effect estimates. The LMS approach with ML estimation also had the highest statistical power among the three approaches, given that the actual Type-I error rates of the Wald and likelihood ratio test of interaction effect were acceptable. In highly nonnormal conditions, only the GAPI approach with ML estimation yielded unbiased latent interaction effect estimates, with an acceptable actual Type-I error rate of both the Wald test and likelihood ratio test of interaction effect. No support for the use of the Satorra-Bentler or Yuan-Bentler ML corrections was found across all three methods.
ContributorsCham, Hei Ning (Author) / West, Stephen G. (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2010