Multilevel Factor Analysis and Structural Equation Modeling of Daily Diary Coping Data: Modeling Trait and State Variation

Abstract

This study used multilevel modeling of daily diary data to model within-person (state) and between-person (trait) components of coping variables. This application included the introduction of multilevel factor analysis (MFA) and a comparison of the predictive ability of these trait/state factors. Daily diary data were collected on a large (n = 366) multiethnic sample over the course of 5 days. Intraclass correlation coefficient for the derived factors suggested approximately equal amounts of variability in coping usage at the state and trait levels. MFAs showed that Problem-Focused Coping and Social Support emerged as stable factors at both the within-person and between-person levels. Other factors (Minimization, Emotional Rumination, Avoidance, Distraction) were specific to the within-person or between-person levels but not both. Multilevel structural equation modeling (MSEM) showed that the prediction of daily positive and negative affect differed as a function of outcome and level of coping factor. The Discussion section focuses primarily on a conceptual and methodological understanding of modeling state and trait coping using daily diary data with MFA and MSEM to examine covariation among coping variables and predicting outcomes of interest.

Notes

¹It should be noted that calculation of Cronbach's alpha is tenuous with multilevel data (Hox & Kleiboer, 2007). However, alternative approaches for calculating multilevel reliability (e.g., Sampson & Raudenbush, 1999) require restrictive assumptions of equal item loadings and error variances or are difficult to estimate with two items per construct (Raykov & Marcoulides, 2006). In light of this, we chose to report Cronbach's alpha values.

²As shown in Table 1, the Cronbach's alpha values are low for some coping variables. Cronbach's alpha values will not necessarily be an accurate indicator of reliability with two-item coping variables (see Clark & Watson, 2003).

³Because the distributions of the observed coping variables were relatively normal and the sum of two items per coping variables, these variables were treated as continuous in the factor-analytic models. It should be noted, however, that these variables could also be treated as ordinal (see Goldstein & Browne, 2005).

⁴To account fully for measurement error in the calculation of the ICCs one must use item-level coping variables to create the 14 coping factors. The ICCs reported in Table 1 do not account for this measurement error. We did, in fact, evaluate item-level factor-analytic models for each of the 14 coping strategies. Due to the number of items per strategy (two) and the high correlations among the two items representing each coping strategy, these multilevel models did not converge, thus the ICCs were calculated from multilevel models where the dependent variables were an aggregate of the two items that reflected each of the 14 coping strategies.

⁵Specification of five factors at both or either level of the data structure resulted in models that could not be estimated (i.e., model estimation did not converge).

⁶For information on how to conduct these model comparisons see the Mplus Web site (http://www.statmodel.com/chidiff.shtml).

^aThe 4 Within-4 Between factor model was deemed the best-fitting model.

*p < .05.