Dynamic and longitudinal models II (08)

Chair: Matthias von Davier, Thursday 23rd July, 14.55 - 16.15, Boys Smith Room, Fisher Building. 

Harry Garst, University of Amsterdam, The Netherlands. A general longitudinal model formulated as a higher factor model. (214)

Lee Sik-Yum, Song Xinyuan and Hser Yihing, Department of Statistics, Chinese University of Hong Kong. A two-level structural equation model approach for analyzing multivariate longitudinal responses. (023)

Michael Browne and Guangjian Zhang, Ohio State University, USA. Capabilities of DyFA: A computer program for dynamic factor analysis. (219)

Ingmar Visser, University of Amsterdam, The Netherlands, Maarten Speekenbrink, University College London, UK. DepmixS4: A framework for modelling discrete change. (229)


A general longitudinal model formulated as a higher factor model. (214)
Harry Garst
A general longitudinal model will be introduced and it will be shown how several well-known models can be treated as special cases of the general longitudinal model. The general longitudinal model is a special higher order factor model. The hierarchy of longitudinal models will be used to show that different classes of models (e.g., autoregressive models and latent growth curve models) are based upon different assumptions of the underlying change processes. However, despite these differences in assumptions, autoregressive and factor models (i.e. latent growth curve models) can be reformulated as special cases of each other.  

A two-level structural equation model approach for analyzing multivariate longitudinal responses. (023)
Lee Sik-Yum, Song Xinyuan and Hser Yihing
The analysis of longitudinal data to study changes in variables measured repeatedly over time has received considerable attention in many fields. This paper proposes a two-level structural equation model for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables. The first level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that are changed with time. The second level is defined for individuals to assess their characteristics that are invariant with time. The proposed model accommodates fixed covariates, nonlinear terms of the latent variables, and missing data. A maximum likelihood approach is developed for estimation of parameters and model comparison. Results of a simulation study indicate that the performance of the maximum likelihood estimation is satisfactory. The proposed methodology is applied to a longitudinal study concerning cocaine use.

Capabilities of DyFA: A computer program for dynamic factor analysis. (219)
Michael Browne and Guangjian Zhang
Our computer program DyFA is intended for carrying out either exploratory or confirmatory dynamic factor analysis based on autocorrelation matrices. It is a modern development of Cattell's P-Technique that includes parameter estimates for a stationary multivariate-ARMA time series for the latent factors. DyFA has a number of distinctive features. It can handle either continuous input data, converted in the program to product moment autocorrelation matrices, or discrete input data, converted to polychoric autocorrelation matrices. In exploratory dynamic factor analysis target rotation may be applied both to the factor matrix and to the latent autoregressive weight matrices. Consequently the latent cross-weight structure can be investigated. Also the factor correlation matrix can be estimated and decomposed into a part due to random shocks and a part due to the influence of preceding observations. Fit of the model may be decomposed into fit at lag 0, fit at lag 1 and so on. It is also possible to examine predictive fit of the model at lags greater than the maximum lag employed in the analysis. These and several other features of DyFA will be described and illustrated with examples. DyFA is available without charge on the Internet (Google “Michael Browne DyFA”)

DepmixS4: A framework for modelling discrete change. (229)
Ingmar Visser and Maarten Speekenbrink
DepmixS4 is a package developed for the R statistical programming language to fit a broad class of (hidden) Markov mixture models. The basic model fit by DepmixS4 is the hidden Markov model for longitudinal and time series data, and it also includes latent class and mixture models. The data can be multi-variate, and can be modeled with a range of distributions including all the distributions available in the generalized linear model (glm) function from R, the multivariate normal distribution, and the multinomial logistic distribution. Through the S4 interface, adding other measurement models and distributions is straightforward. DepmixS4 includes the possibility of incorporating covariates on the initial or prior probabilities of hidden Markov models and mixture type models, as well as on the transition probabilities of the hidden Markov model. We present the program using a number of illustrative applications, ranging from a latent class model with covariates to the analysis of single case multi variate time series data.