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Description
In order to analyze data from an instrument administered at multiple time points it is a common practice to form composites of the items at each wave and to fit a longitudinal model to the composites. The advantage of using composites of items is that smaller sample sizes are required in contrast to second order models that include the measurement and the structural relationships among the variables. However, the use of composites assumes that longitudinal measurement invariance holds; that is, it is assumed that that the relationships among the items and the latent variables remain constant over time. Previous studies conducted on latent growth models (LGM) have shown that when longitudinal metric invariance is violated, the parameter estimates are biased and that mistaken conclusions about growth can be made. The purpose of the current study was to examine the impact of non-invariant loadings and non-invariant intercepts on two longitudinal models: the LGM and the autoregressive quasi-simplex model (AR quasi-simplex). A second purpose was to determine if there are conditions in which researchers can reach adequate conclusions about stability and growth even in the presence of violations of invariance. A Monte Carlo simulation study was conducted to achieve the purposes. The method consisted of generating items under a linear curve of factors model (COFM) or under the AR quasi-simplex. Composites of the items were formed at each time point and analyzed with a linear LGM or an AR quasi-simplex model. The results showed that AR quasi-simplex model yielded biased path coefficients only in the conditions with large violations of invariance. The fit of the AR quasi-simplex was not affected by violations of invariance. In general, the growth parameter estimates of the LGM were biased under violations of invariance. Further, in the presence of non-invariant loadings the rejection rates of the hypothesis of linear growth increased as the proportion of non-invariant items and as the magnitude of violations of invariance increased. A discussion of the results and limitations of the study are provided as well as general recommendations.
ContributorsOlivera-Aguilar, Margarita (Author) / Millsap, Roger E. (Thesis advisor) / Levy, Roy (Committee member) / MacKinnon, David (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2013
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. 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