Browsing by Subject "Growth curve modeling"

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Estimating a three-level latent variable regression model with cross-classified multiple membership data
(2014-08) Leroux, Audrey Josée; Beretvas, Susan Natasha
The current study proposed a new model, termed the cross-classified multiple membership latent variable regression (CCMM-LVR) model, to be utilized for multiple membership data structures (for example, in the presence of student mobility across schools) that provides an extension to the three-level latent variable regression model (HM3-LVR). The HM3-LVR model is beneficial for testing more flexible, directional hypotheses about growth trajectory parameters and handles pure clustering of participants within higher-level units. However, the HM3-LVR model involves the assumption that students remain in the same cluster (school) throughout the duration of the time period of interest. The CCMM-LVR model, on the other hand, appropriately models the participants’ changing clusters over time. The first purpose of this study was to demonstrate use and interpretation of the CCMM-LVR model and its parameters with a large-scale longitudinal dataset that had a multiple membership data structure (i.e., student mobility). The impact of ignoring mobility in the real data was investigated by comparing parameter estimates, standard error estimates, and model fit indices for the two estimating models (CCMM-LVR and HM3-LVR). The second purpose of the dissertation was to conduct a simulation study to try to understand the source of potential differences between the two estimating models and find out which model’s estimates were closer to the truth given the conditions investigated. The manipulated conditions in the simulation study included the mobility rate, number of clustering units, number of individuals (i.e., students) per cluster (here, school), and number of measurement occasions per individual. The outcomes investigated in the simulation study included relative parameter bias, relative standard error bias, root mean square error, and coverage rates of the 95% credible intervals. Substantial bias was found across conditions for both models, but the CCMM-LVR model resulted in the least amount of relative parameter bias and more efficient estimates of the parameters, especially for larger numbers of clustering units. The results of the real data and simulation studies are discussed, along with the implications for applied researchers for when to consider using the CCMM-LVR model versus the misspecified HM3-LVR model.
Modeling achievement in the presence of student mobility : a growth curve model for multiple membership data
(2010-08) Grady, Matthew William, 1981-; Beretvas, Susan Natasha; Dodd, Barbara G.; Pituch, Keenan A.; Whittaker, Tiffany A.; Mahometa, Michael J.
The current study evaluated a multiple-membership growth curve model that can be used to model growth in student achievement, in the presence of student mobility. The purpose of the study was to investigate the impact of ignoring multiple school membership when modeling student achievement across time. Part one of the study consisted of an analysis of real longitudinal student achievement data. This real data analysis compared parameter estimates, standard error estimates, and model-fit statistics obtained from a growth curve model that ignores multiple membership, to those obtained from a growth model that accounts for multiple school membership via the MMREM approach. Part two of the study consisted of a simulation study designed to determine the impact of ignoring multiple membership and the accuracy of parameter estimates obtained under the two modeling approaches, under a series of data conditions. The goal of the study was to assess the importance of incorporating a more flexible MMREM approach when modeling students’ academic achievement across time. Overall, the results of the current study indicated that the Cross-classified multiple membership growth curve model (CCMM-GCM) may provide more accurate parameter estimates than competing approaches for a number of data conditions. Both modeling approaches, however, yielded substantially biased estimates of parameters for some experimental conditions. Overall, results demonstrate that incorporating student mobility into achievement growth modeling can result in more accurate estimates of schools effects.