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The cross-sectional correlation is frequently used to summarize psychological data, and can be considered the basis for many statistical techniques. However, the work of Peter Molenaar on

With the growing popularity of intensive longitudinal research, the modeling techniques and software options for such data are also expanding rapidly. Here we use dynamic multilevel modeling, as it is incorporated in the new dynamic structural equation modeling (DSEM) toolbox in Mplus, to analyze the affective data from the COGITO study. These data consist of two samples of over 100 individuals each who were measured for about 100 days. We use composite scores of positive and negative affect and apply a multilevel vector autoregressive model to allow for individual differences in means, autoregressions, and cross-lagged effects. Then we extend the model to include random residual variances and covariance, and finally we investigate whether prior depression affects later depression scores through the random effects of the daily diary measures. We end with discussing several urgent—but mostly unresolved—issues in the area of dynamic multilevel modeling.

In this article, we show that the underlying dimensions obtained when factor analyzing cross-sectional data actually form a mix of within-person state dimensions and between-person trait dimensions. We propose a factor analytical model that distinguishes between four independent sources of variance: common trait, unique trait, common state, and unique state. We show that by testing whether there is weak factorial invariance across the trait and state factor structures, we can tackle the fundamental question first raised by Cattell; that is, are within-person state dimensions qualitatively the same as between-person trait dimensions? Furthermore, we discuss how this model is related to other trait-state factor models, and we illustrate its use with two empirical data sets. We end by discussing the implications for cross-sectional factor analysis and suggest potential future developments.

Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that have negligible effects on the resulting parameter estimates. However, the conjugate prior distribution for covariance matrices—the Inverse-Wishart distribution—tends to be informative when variances are close to zero. This is problematic for multilevel autoregressive models, because autoregressive parameters are usually small for each individual, so that the variance of these parameters will be small. We performed a simulation study to compare the performance of three Inverse-Wishart prior specifications suggested in the literature, when one or more variances for the random effects in the multilevel autoregressive model are small. Our results show that the prior specification that uses plug-in ML estimates of the variances performs best. We advise to always include a sensitivity analysis for the prior specification for covariance matrices of random parameters, especially in autoregressive models, and to include a data-based prior specification in this analysis. We illustrate such an analysis by means of an empirical application on repeated measures data on worrying and positive affect.

In this article we consider a multilevel first-order autoregressive [AR(1)] model with random intercepts, random autoregression, and random innovation variance (i.e., the level 1 residual variance). Including random innovation variance is an important extension of the multilevel AR(1) model for two reasons. First, between-person differences in innovation variance are important from a substantive point of view, in that they capture differences in sensitivity and/or exposure to unmeasured internal and external factors that influence the process. Second, using simulation methods we show that modeling the innovation variance as fixed across individuals, when it should be modeled as a random effect, leads to biased parameter estimates. Additionally, we use simulation methods to compare maximum likelihood estimation to Bayesian estimation of the multilevel AR(1) model and investigate the trade-off between the number of individuals and the number of time points. We provide an empirical illustration by applying the extended multilevel AR(1) model to daily positive affect ratings from 89 married women over the course of 42 consecutive days.

Outliers are typically regarded as data anomalies that should be discarded. However, dynamic or "innovative" outliers can be appropriately utilized to capture unusual but substantively meaningful shifts in a system's dynamics. We extend De Jong and Penzer's 1998 approach for representing outliers in single-subject state-space models to a group-based framework. The group-based model enables model predictions concerning the group as a whole while individualized change points are incorporated to capture discrete shifts in each individual's trajectory. An illustrative example using cognitive performance data from N = 38 older adults over 60 days is presented. Results indicated that a subset of older adults showed sudden shifts in learning dynamics in several forms, including sudden jumps in level, slope, and linkage between perceived control and actual performance level. The broader implications of incorporating innovative outliers into studies of intraindividual change are discussed.

Results obtained with interindividual techniques in a representative sample of a population are not necessarily generalizable to the individual members of this population. In this article the specific condition is presented that must be satisfied to generalize from the interindividual level to the intraindividual level. A way to investigate whether this condition is satisfied is by means of multivariate time series analysis. More generally, time series analysis can be used to investigate psychological processes situated within individuals. In this article we consider a well established class of multivariate stationary time series models that may be used to study the intraindividual covariance structure. We demonstrate the application of some of these models with an empirical example consisting of state measurements of behavior associated with the Five Factor Model of Personality. We illustrate how one can investigate whether individuals are similar with respect to their intraindividual structure of variation, and whether this structure is similar to the structure of interindividual variation.