There and Back: Modeling Inter-Individual Differences in Intra-Individual Variability

This thesis focuses on modeling inter-individual differences in both stable- and developmental processes, where stable processes are characterized by within-person reversible variability over time in the absence of a gross underlying trend (Nesselroade, 1991), and developmental processes are characterized by structural change over time, with intra-individual variability occuring around an (individual's) mean trend or growth curve (Meredith & Tisak, 1990; Bollen & Curran, 2004, 2006).For the modeling of inter-individual differences in stable processes, intensively sampled data, that is, data sampled over a large number of repeated measurements (that are usually close together in time), is required and we focus on a dynamic multilevel model (DMM) that is based on modeling the repeated measures of an individual at level 1 using a time series model, while allowing for individual differences in the model parameters at level 2. Specifically we use a two level first-order autoregressive AR(1) model with random means, random autoregression, and random innovation variance (i.e., the level 1 residual variance). This model is more extensive than the models usually described in the literature, as it also allows for individual differences in error variance. In Chapter 2 of this thesis the estimation and interpretation of the model parameters is considered. In Chapter 3 an expression for the total variance of our DMM is derived, which is subsequently used to study the variance structure of the model in more detail. If intensively sampled data is not available, models focussed more on systematic change trajectories can be used to gain valuable insight in the longitudinal process under study. For this non-intensively sampled data, special attention is given to the the autoregressive latent trajectory (ALT) model that was introduced by Curran and Bollen (2001) (see also Bollen & Curran, 2004), and which combines a latent growth curve (LGC) model (Meredith & Tisak, 1990; Curran & Bollen, 2001; Bollen & Curran, 2004) with an autoregressive model (Jöreskog, 1971, 1979). Chapter 4 of the thesis examines two methods suggested by Curran and Bollen (2001) to deal with the recursion inherent to the ALT model, and paid special attention to the effect of these "start-up" methods on the model parameters. Chapters 5 and 6 of this thesis, are aimed at enabling applied researchers to analyze their own data with either the ALT model, or a number of other models suitable for the study of both stable and developmental processes. Chapter 5 describes a multi-centre randomized trial cost-effectiveness study for the treatment of personality disorders. This study is used as an applied example for researchers, that outlines how the Deviance Information Criterium (DIC) (Spiegelhalter, Best, Carlin, & Linde, 2002) can be used to select the best fitting model, and how this best fitting model should be interpreted. Chapter 6 subsequently provides applied researchers with all the materials needed for analysis of their data. Specifically, it provides instructions and code for the Bayesian estimation of a two level first-order autoregressive model, a linear growth curve model, a quadratic growth curve model, and a autoregressive latent trajectory models.