The purpose of this study was to assess the effects of misspecification (i.e., under-specification, over-specification, and general misspecification) of the within-person level errors in longitudinal data under quadratic, exponential, and logistic latent growth curve models and to make a contribution to the literature in this area. A Monte Carlo simulation in R uncovered a common bias pattern throughout this study. For under-specification of autocorrelated processes and general misspecification of MA as AR, the mean intercept was more likely to be downward- biased, but the linear slope and nonlinear slope for an individual tend to be upward-biased. On average, the variation of the intercept is more likely to be underestimated for under-specification of autocorrelated errors in three types of nonlinear models, whereas the variation of linear slope variance is more often to be more overestimated, Opposite results were found for over-specification and general misspecification of AR data misspecified as MA. The covariance between intercept and linear slope was downward-biased by overspecified models but upward- biased by under-specified quadratic and exponential latent growth curve models. The covariance between intercept and logistic slope was downward-biased by over-specified models, but upward-biased by under-specified models. The reverse pattern was observed for the covariance between linear slope and logistic slope, which was underestimated by under-specified logistic latent growth curve models and overestimated by over-specified logistic LGCs. Longitudinal data studies are widely conducted, and nonlinear change over time is often the focus of such studies. Rarely, do applied researchers hypothesize, a priori, stochastic effects (in this case, AR, MA, and ARMA) because such processes are primarily nuisance conditions which are not the focus of longitudinal data studies. Nevertheless, stochastic effects are widely known to be present in such data, dating at least as far back as Box and Jenkins (1978). Applied researchers encounter stochastic effects when they are force to confront correlated errors over time. By modeling the impact of various stochastic effects on parameter estimates, applied researchers are introduced to alternative models to consider as rival hypotheses when conducting longitudinal data wherein nonlinear processes are anticipated, so as to filter stochastic processes should they occur, especially as evidenced by correlated errors so common in longitudinal data.
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Doctor of Philosophy (Ph.D.)
College of Community Innovation and Education
School of Teacher Education
Education; Method, Measurement and Analysis
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Zhou, Mingming, "The Impact of Misspecification of Within-person Autocorrelated Covariance Structure on Nonlinear Latent Growth Curve Models: A Monte Carlo Simulation Study" (2021). Electronic Theses and Dissertations, 2020-. 596.