Latent variable models for multivariate longitudinal ordinal responses Silvia Cagnone 1 , Irini Moustaki 2 * and Vassilis Vasdekis 3 1 University of Bologna, Bologna, Italy 2 London School of Economics and Political Science, London, UK 3 Athens University of Economics and Business, Athens, Greece The paper proposes a full information maximum likelihood estimation method for modelling multivariate longitudinal ordinal variables. Two latent variable models are proposed that account for dependencies among items within time and between time. One model fits item-specific random effects which account for the between time points correlations and the second model uses a common factor. The relationships between the time-dependent latent variables are modelled with a non-stationary autoregressive model. The proposed models are fitted to a real data set. 1. Introduction Longitudinal data are collected for studying changes across time. Statistical models that study the evolvement of traits, attitudes, or any latent constructs in time are known as dynamic factor analysis models. Classical factor analysis allows for the measurement of a latent construct or constructs using observed indicators also known as observed variables or items. When fitting a factor model to longitudinal data one needs to account for the interrelationships of the observed variables or indicators within each time point as well as the interrelationships of the same indicator across time in order to measure changes in the latent variables across time. In the classical normal linear factor model the total variance of an item is decomposed into two components: the common factor variance and the specific factor variance that confounds measurement error variance and residual variance. However, when measurements are made across time it is possible to decompose the measurement error from the residual error variance. Marsh and Grayson (1994) and Raffalovich and Bohrnstedt (1987) proposed a class of models for continuous data and Eid (1996) for categorical data, that aim to decompose the total variance into a time-specific, * Correspondence should be addressed to Dr Irini Moustaki, Department of Statistics, London School of Economics, Houghton street, London WC2A 2AE, UK (e-mail: i.moustaki@lse.ac.uk). The British Psychological Society 401 British Journal of Mathematical and Statistical Psychology (2009), 62, 401–415 q 2009 The British Psychological Society www.bpsjournals.co.uk DOI:10.1348/000711008X320134