The Impact of Ignoring Time Series Processes in Linear Growth Mixture Modeling

Growth mixture modeling (GMM) is a useful statistical method for longitudinal studies because it includes features of both latent growth modeling (LGM) and finite mixture modeling. This Monte Carlo simulation study explored the impact of ignoring 3 types of time series processes (i.e., AR(1), MA(1), and ARMA(1,1)) in GMM and manipulated the separation of the latent classes, the strength of the time series process, and whether the errors conformed to the time series process in 1 or 2 latent classes. The results showed that omitting time series processes resulted in more serious bias in parameter estimation as the distance between classes increased. However, when the class distances were small, ignoring time series processes contributed to the selection of the correct number of classes. When the GMM models correctly specified the time series process, only models with an AR(1) time series process produced unbiased parameter estimates in most conditions. It was also found that among design factors manipulated, the distance between classes prominently affected the identification of the number of classes and parameter estimation.     

Situating Special Educators’ Instructional Quality and Their Students’ Outcomes within the Conditions Shaping Their Work

This investigation examined relationships among special education teachers’ working conditions (e.g., classroom characteristics, administrative support), personal characteristics (e.g., experience, certification status, self-efficacy), instructional quality, and students with disabilities’ reading achievement and behavioral outcomes. Data from the 2004–2005 administration of the Special Education Elementary Longitudinal Study were used. Confirmatory factor analysis was used to test the fit of models for five latent factors. Hybrid structural models were applied to test the hypothesis that working conditions would be positively associated with special education teachers’ self-efficacy and their instructional quality, which would, in turn, be positively associated with their students’ reading achievement and behavioral outcomes. Although the initial structural equation model tested failed to support the hypotheses, several significant relationships with theoretical and practical significance were discovered. Directions for future research and practical implications are discussed.