Psychological processes are of interest in all areas of psychology, and all such processes occur within individuals over time. Some examples of psychological processes are the regulation of daily mood, the effect of job motivation on job performance and vice versa, or social interactions between a parent and child. In order to study these processes it is necessary to take many repeated measures for each individual. Multilevel autoregressive models are statistical models than can be used to analyze this kind of data - data that consist of many repeated measures, for many individuals. The approach of autoregressive models is summarized well with the saying ``The best predictor of future behavior is past behavior'': In autoregressive models, current observations are used to predict future observations. By extending the autoregressive model to a multilevel autoregressive model, it becomes possible to model the repeated measures for many individuals at the same time, while also modeling the differences between the processes of each individual. Multilevel autoregressive models are increasing in popularity within psychology, however, the methods for analyzing psychological data with these models are still being developed. The aim for this dissertation was to further investigate, explicate, and if possible remedy certain difficulties in fitting and interpreting multilevel autoregressive models in the context of psychological science. Specifically, in Chapter 1 it is discussed why it is important to collect many repeated measures for studying psychological processes, and why it is important to model these processes on an individual level, as well as the similarities and differences between the individuals' processes. In Chapter 2 a difficulty with specifying an Inverse-Wishart prior distribution for the covariance matrix of the random parameters is explored, in the context of fitting the multilevel autoregressive model in a Bayesian framework. In Chapter 3 it is discussed how to standardize the model parameters, such that we can make meaningful comparisons of the strength of the cross-lagged effects in a multivariate model. In Chapters 4 and 5 the consequences of ignoring measurement errors for the estimation of the model parameters are investigated for respectively a single-subject autoregressive model and the multilevel autoregressive model, as well as how to account for measurement errors in these models. The final chapter of this dissertation contains a summary of the work presented in the previous chapters, and a discussion of some limitations of the multilevel autoregressive modeling approach
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