Growth curves and longitudinal models I (06)

Chair: Michael Browne, Thursday 23rd July, 9.40 - 11.00, Uppercroft, School of Pythagoras.

Betsy Feldman and Sophia Rabe-Hesketh, University of California, Berkeley, USA.  Modeling growth trajectories when dropout is informative: A simulation study. (199) ♥

Bengt Muthen and Tihomir Asparouhov, Mplus, Los Angeles, USA. Modeling with non-ignorable missing data in longitudinal studies. (065)

Andrew Pickles and Milena Falcaro, Biostatistics Group, School of Community-Based Medicine, University of Manchester, UK. Interval and non-ignorable censored observation of longitudinal cognitive data: Inferring abnormality in a context of developmental delay. (079)

Matthias von Davier, Xueli Xu, Educational Testing Service, Research and Development, Princeton NJ, USA, Claus H. Carstensen; University of Bamberg, Germany. Measuring learning and change in a longitudinal large-scale educational assessment program with generalized latent variable models. (043)

ABSTRACTS

Modeling growth trajectories when dropout is informative: A simulation study. (199)
Betsy Feldman and Sophia Rabe-Hesketh
Increasingly, educational researchers use longitudinal data to investigate effects of interventions and track progress of individual students and schools. Missing data are endemic in such studies. Approaches, such as HLM, that use maximum likelihood estimation (MLE) give consistent estimates of population values when missingness is ignorable (missing at random), but in cases of dropout from school or interventions, this assumption may not hold. This paper presents results from a simulation study investigating random-coefficientdependent missingness—a situation that arises, for instance, if individuals drop out because of declining grades. Data are simulated from a simultaneous growth and survival model in which the dropout depends on the random intercept and random coefficient of time in the linear growth curve model. The performance of several estimation methods is investigated, including MLE of the correctly specified linear growth curve model in which missing data are treated (incorrectly) as ignorable. Initial results suggest that, while bias in growth-parameter estimates varies with the proportion of missing data and dependence of missingness on the random coefficients, model misfit is not seen unless both are extreme. This study investigates bounds and limits of these effects with normally-distributed and ordinal observed outcomes.

Modeling with non-ignorable missing data in longitudinal studies. (065)
Bengt Muthen and Tihomir Asparouhov
Longitudinal studies are likely to exhibit attrition that does not fall under the typical MAR assumption. Selection modeling, pattern-mixture modeling, and shared parameter modeling have been proposed for such NMAR situations. This presentation focuses on a combination and extension of the latter two approaches. A latent class extension of pattern-mixture modeling has been proposed by Roy, where dropout time influences latent class membership. Random effect means in the growth model are obtained by mixing over the dropout classes. The Roy approach often gives a better BIC than conventional pattern-mixture modeling. The Roy approach, however, considers only latent classes related to dropout time, whereas substantively different trajectory classes may also be present as is often found in growth mixture modeling. A more general NMAR is proposed which uses two different latent class variables, one dropout-oriented and one substantively-oriented. A real-data analysis of the large-scale antidepressant clinical trial STAR*D illustrates the need for this second latent class variable. For these data, the conventional pattern-mixture modeling as well as the Roy approach overlooks substantively important trajectory classes and mixes over confounded dropout and substantive classes. The effects of covariates under modeling based on MAR, conventional pattern-mixture, Roy, and the new approach are compared.

Interval and non-ignorable censored observation of longitudinal cognitive data: Inferring abnormality in a context of developmental delay. (079)
Andrew Pickles and Milena Falcaro
There is increasing interest in using behavioural and psychological observation as a window upon underlying neurobiological process. Identifying the onset of abnormality is often key. Reports of the onset of milestones and abnormality are often subject to interval censoring, and Falcaro & Pickles have described a framework for fitting latent covariance structure models to multivariate profiles of such interval censored reports. However, in a developmental context behavioural abnormality is also subject to another form of censoring, namely that the production of the abnormal behaviour may require a certain stage of development of the behaviour itself to have been achieved. Prior to this stage, observation of abnormality is not possible even if the underlying neurobiological developmental anomaly has occurred. We present a method to allow the joint modelling of delay and abnormality. We parameterise the thresholds of a multivariate (multi-response) ordinal response model to allow variation in the precision of reported onset and milestones, consider the scope for accounting for recall error, and explore identification issues. We apply the methods to data on language loss in autism, to estimate the onset distribution of the underlying neurobiological anomaly, doing so both before and after account has been taken of the censoring due to delay in language development.

Measuring learning and change in a longitudinal large-scale educational assessment program with generalized latent variable models. (043)
Matthias von Davier, Xueli Xu and Claus H. Carstensen
A general latent variable modeling framework was used to specify multidimensional IRT (MIRT) models for longitudinal data with the following two variations: A model that handles repeated measurements as multiple, correlated variables over time (Andersen, 1985) as well as a model that assumes one common variable over time points, and additional orthogonal variables quantifying the change (Embretson, 1991). These two models were compared in the analyses presented in this paper. In addition, a model with a single two-dimensional ability distribution was compared to extensions of the Andersen and Embretson approaches assuming multiple populations, where the ability distributions of the MIRT models used were allowed to vary across subpopulations defined by school type. Moreover, a hierarchical mixture distribution variant of the (Andersen and Embretson) MIRT models was specified in the framework and compared to the above alternatives. These types of models are growth mixture models that allow for variation of the mixing proportions across clusters in a hierarchically organized sample. In order to illustrate the models presented in this paper, they were applied to the PISA-I-PLUS data for assessing learning and change across multiple subpopulations. PISA-I-PLUS is a longitudinal study conducted as a national addition to the Program for International Student Assessment (PISA). The results indicate that (1) the model with baseline ability and additional change variables (Embretson-type model) with multiple group assumptions provides better fit to the data than the other models investigated in this paper; and (2) that the higher performing group has larger improvement at time point 2 than the lower performing group.