Some notes on Bayesian time series analysis in psychology

To characterize the dynamics of psychological processes, intensively repeated measurements of certain properties or states within the same person may be used. Often these data are gathered among several individual. One example is measuring a number of emotions, several times a day, for several consecutive weeks. These data are analyzed using time series analysis, to discover patterns over time and/or to predict future behavior. In this these, the psychological empirical data and the related theory, is connected to the statistical models used in time series analysis.

First, I answer the question which estimation method is preferable for relatively short time series, as often encountered in psychological studies, where the data follows a so-called autoregressive model. After comparing several estimation methods, I found that so-called iterative methods, such as maximum likelihood and Bayesian Markov Chain Monte Carlo estimation, are to be preferred.

Second, I answer the question how essential characteristics of time series data can be encompassed in an interpretable model. To this end, I use the Bayesian dynamic model (BDM).The BDM is very flexible, which makes it widely applicable. A first BDM is build for count data of panic attacks, influenced by external variables. A second BDM is build to quantify the characteristics of different emotions. The third application shows a comparison of different BDMs to find the best fitting model.

The clear explanation about the handling of missing data, non-normally distributed data, external variables and other important issues in empirical data, may be used as guideline for future research.