Multilevel Models for Examining Individual Differences in Within-Person Variation and Covariation Over Time

Abstract

Heterogeneity of variance may be more than a statistical nuisance-it may be of direct interest as a result of individual differences. In studies of short-term fluctuation, individual differences may relate to the magnitude of within-person variation as well as to level of an outcome or its covariation with other processes. Although models for heterogeneous variances have been utilized in group contexts (i.e., dispersion models), they are not usually applied in examinations of intraindividual variation. This work illustrates how an extension of the multilevel model for heterogeneous variances can be used to examine individual differences in level, between-and within-person covariation, and magnitude of within-person variation of daily positive and negative mood in persons with dementia.

On the relation of mean reaction time and intraindividual reaction time variability.

“…In the context of multilevel or mixed models (e.g., Snijders & Bosker, 1999), elegant and efficient methods for overcoming this problem and investigating relations between iM and iSD have been developed (e.g., Hoffman, 2007). These models (sometimes called location-scale models, dispersion models, or models with heterogeneous variances) do not require binning of the data because they model the expected variance at any time point.…”

The calm after the storm

“…Thus, the interpretation for the fixed effect is whether greater relationship length, compared to the mean of the sample, was associated with more or less satisfaction, commitment, and so on, on average over the study period. The repeated statement in SAS PROC MIXED also allows for the inclusion of substantive predictors of the within-person residual variance (for details see Hoffman, 2007) and enabled us to address whether greater relationship length was associated with more or less withinperson variability from day to day in satisfaction, commitment, and so on. Finally, to examine whether there were significant differences between men and women in these associations, we included effect coded sex (1 ¼ male, À1 ¼ female) and the interactions of sex and relationship length in both the fixed effects and the repeated statement.…”

“…Using another version of a two-intercept dyadic model, we examined whether relationship length predicted variability for those constructs that displayed significant heterogeneity of within-person residual variance (Hoffman, 2007). This method involves including relationship length as both a fixed effect (e.g., do individuals in longer relationships report feeling more satisfied committed, etc.…”

“…Note. H is an estimate of heterogeneity in Level 1 residuals, with df indicating the number of individuals contributing minus 1 (see Hoffman, 2007). ***p < .001.…”

“…Here, we followed recommendations by Hoffman (2007) to determine whether there was heterogeneity between people in the within-person residual variances in each construct. This process provides a ''test of the null hypothesis of no individual differences in within-person variation'' (p. 618).…”