Growth curves and longitudinal models II (07)

Chair: Gregory Palardy , Thursday 23rd July, 11.30 - 12.50, Castlereagh Room, Fisher Building.

Gregory J. Palardy, University of California, Riverside, USA. A multilevel piecewise crossed random effects growth model. (066)

Xinyuan Song, Lee Sikyum, and Hser Yihing, Chinese University of Hong Kong. Bayesian analysis of multivariate latent curve models with nonlinear longitudinal latent effects. (033)

Silvia Cagnone and Silvia Bianconcini, Department of Statistics, University of Bologna, Italy. A general multivariate latent growth model with applications in student achievements. (084)

Sy-Miin Chow, Niansheng Tang, Ying Yuan, Xinyuan Song and Hongtu Zhu, University of North Carolina at Chapel Hill, USA. Bayesian estimation of semi-parametric nonlinear dynamic latent variable models using the Dirichlet process prior. (057)

ABSTRACTS

A multilevel piecewise crossed random effects growth model. (066)
Gregory J. Palardy
This paper extends the linear crossed random effects growth model (Raudenbush, 1993) to the multilevel and piecewise specification and shows the new model’s application for estimating teacher effects on student learning across grade levels when students encounter a series of teachers over time. In this three-level model, repeated measurements of student achievement at level one are cross-classified in students and classrooms at level two, both of which are nested in schools at level three. Piecewise-linear growth trajectories are fit to the repeated measurements within grade levels and during summer, allowing the trajectories to vary across segments. A comparison of results from the new piecewise and the former linear specifications suggest that the latter will inflate the magnitude of the teacher effect when student learning trajectories are not linear across segments, which is surprising common given the expected summer drop in learning. The results have important implications to efforts to build data systems for studying or evaluating teacher effectiveness, suggesting that more than one annual achievement measurement is essential.

Bayesian analysis of multivariate latent curve models with nonlinear longitudinal latent effects. (033)
Xinyuan Song, Lee Sikyum, and Hser Yihing
In longitudinal study, investigators often measure multiple variables at multiple time points and are interested in investigating individual differences in patterns of change on those variables. Furthermore, in behavioral and psychological sciences, investigators often deal with latent variables that cannot be observed directly and should be measured by two or more manifest variables. Longitudinal latent variables occur when manifest variables are measured at multiple time points. Our primary interests are in studying dynamic change of longitudinal latent variables and exploring possible interactive effect among latent variables. Much of the existing research in longitudinal study focuses on studying change in a single observed variable at different time points. In this article, we propose a novel latent curve model (LCM) for studying the dynamic change of multivariate manifest and latent variables and their linear and interaction relationships. The proposed LCM has the following useful features: First, it can handle multivariate variables for exploring the dynamic change of their relationships, while conventional LCMs usually consider change in a univariate variable. Second, it accommodates both first-order and second-order latent variables and their interactions to explore how changes in latent attributes interact to produce a joint effect on the growth of an outcome variable.

A general multivariate latent growth model with applications in student achievements. (084)
Silvia Cagnone and Silvia Bianconcini
The evaluation of the formative process in the University system has been assuming an ever increasing importance in the European countries. Within this context the analysis of student performance and capabilities plays a fundamental role. In this work we propose a multivariate latent growth model for studying the performances of a cohort of students of the University of Bologna. The model proposed is innovative since it is composed by: (1) multivariate growth models that allow to capture the different dynamics of student performance indicators over time and (2) a factor model that allows to measure the general latent student capability. The flexibility of the model proposed allows its applications in several fields such as socio-economic settings in which personal behaviours are studied by using panel data.

Bayesian estimation of semi-parametric nonlinear dynamic latent variable models using the Dirichlet process prior. (057)
Sy-Miin Chow, Niansheng Tang, Ying Yuan, Xinyuan Song and Hongtu Zhu
Parameters in time series and other dynamic models often show complex restrictions in range and their distributions may deviate substantially from multivariate normal, or other standard parametric distributions. To approximate such distributions nonparametrically, we use the truncated Dirichlet process (DP) as the prior distribution in a series of linear and nonlinear Bayesian dynamic latent variable models. This is equivalent to specifying the prior distribution to be a mixture distribution composed of an unknown number of discrete point masses. Using a set of ordinal daily diary data as the basis of our modeling example, we developed a nonlinear vector autoregressive model with interaction between latent variables and used the DP as nonparametric prior for the dynamic parameters in our model. The stick-breaking prior and the blocked Gibbs sampler are used to enable efficient simulation of posterior samples of parameters. Additional Metropolis-Hasting procedures are also embedded within the Gibbs sampler to allow sampling from other non-standard densities implicated in the model. We discuss the strengths and limitations of the proposed approach in approximating distributions of different functional forms.