In a next step, it was analyzed whether the variability of mood in each class can be at least partly explained by influences of other variables. To analyze this question, measures of daily hassles and uplifts in the model were included. The short version of the daily hassles and uplifts scale (Kanner, Coyne, Shaefer, & Lazarus, 1981; Lazarus & Cohen, 1977; Lazarus & Folk-man, 1989) was administered on each occasion of measurement. This scale contains 30 hassles and 30 uplifts, and the participants rated whether a hassle or uplift occurred to them during the last 24 hours (two points scale : yes, no). Item example for hassles and uplifts are : ”I had to wait for someone in vain” (hassle) and ”Someone gave me a helpful advice” (uplift). The per-centage of hassles and the perper-centage of uplifts experienced by an individual were taken as scale values for each occasion of measurement.
It is interesting to investigate whether the differences in the two classes with respect to mood might be due to differential effects of daily events in the two classes. The model depicted in Figure 4.3 tests this hypothesis. The input of the two-class model with covariates is in Appendix B (page 180).
For each occasion, there is a daily hassles and a daily uplifts variable (Xdhakc andXdupkc). To represent the stability in the experiences of daily hassles and uplifts and to save parameters, a latent time-invariant factor was defined for each set of daily events (DHAc and DUPc). These latent variables can be interpreted as a disposition to experience positive and negative daily events.
They can be correlated with all other trait variables. In order to analyze whe-ther the variability in mood was due to variability in daily events, a residual
variable was defined for each occasion of measurement and each type of event (DHAkc and DUPkc). These variables represent influences beyond the dis-positional variables due to occasions and due to measurement error. Because there is only one indicator for each type of event, measurement error cannot be separated from occasion-specific influences (because the daily hassles and uplifts scales do not comprise parallel items, a split of this scale into two halves is not reasonable). The residuals representing both occasion-specific influences and measurement error are modeled as latent factors (DHAkc and DU Pkc) in order to consider these residuals as predictors in the latent regres-sion analysis. Since the residual variablesDHAkcandDU Pkc represents all of the residual part of the daily hassles and daily uplifts observed variables, the error variances of the observed variables (Xdhakc andXdupkc) were set to 0. The regression coefficients of these occasion-specific daily hassles and uplifts resi-duals indicate occasion-specific influences of daily events on occasion-specific mood. They were set equal across time but can differ between classes.
Fig. 4.3: Mixture LST model with covariates. Tc = Trait factor, ISTic = Indicator-Specific Trait,Okc= Occasion-specific factors,Eikc= Measurement Error (for reasons of simplicity, only the first measurement error is labeled), P Uikc= Manifest well-being variable,DHAkc = Latent daily hassles,DU Pkc
= Latent daily uplifts, DHAc = General latent daily hassles, DUPc = Ge-neral latent daily uplifts,Xdhakc = manifest daily hassles variables,Xdupkc = manifest daily hassles variables. The loading structure concerning the mood variables equal the loading structure in Figure 4.2.
Tc
The adjusted likelihood ratio test of Lo et al. (2001) and the bootstrap LRT show that the two-class model with daily hassles and uplifts is superior to a one-class model (p < .01) (see Table 4.3). Additionally, the mean assi-gnment probabilities are very high (Class 1 : .92, Class 2 : .97) suggesting that the two classes can clearly be separated. The additional parameters of this model are presented in Table 4.5. The other parameters are not presen-ted because they are very similar to the estimapresen-ted parameters of the model without covariates. The two classes do not differ much with respect to the mean values and the variances of the daily uplifts, the differences with res-pect to daily hassles are stronger. Individuals in the second class experience more hassles and the variance of the general hassles factor is smaller in this class. However, the mean differences are not very strong and not significantly different from 0. The time-invariant daily hassles and uplifts factors are si-gnificantly correlated with the trait mood factors only in the second class showing that individuals experiencing more uplifts and less hassles are in ge-neral more happy. Most interestingly, the regression coefficients differ between the two classes showing that negative events have a significant influence on occasion-specific mood only in the second more variable class but not in the first more stable class. Positive events, however, have significant influences in both classes. Hence, members of the first class seem to use positive events to enhance their well-being but seem to be more resilient with respect to the negative effect of daily hassles. The differences between the two classes with respect to the regression coefficients might partly be due to the smaller va-riances of the residuals of the daily hassles in the second class (between 46.97 and 65.08) compared to the first class (between 19.41 and 27.50). Because the occasion-specific variances of the hassles are smaller in the second class, the correlations are smaller and this result can partly explain the smaller regression coefficients. However, the variances differ also significantly from 0 in the second class showing that there are differences that could be related to momentary mood. Moreover, the smaller mean value in the first class could also indicate that people of this class are able to avoid daily hassles or to forget them. Hence, the differences between the classes might not only reflect differences in the reactivity to negative events or resilience but also more general differences in mood regulation.
The analyses reported here show that mixture LST models can and do offer interesting insights into structural differences between subgroups.
Tab. 4.5: Relations Between Daily Hassles and Uplifts and Latent Person-and Occasion-Specific Variables for Each Class.
Common hassles/uplifts factor
Mixture structural equation models are relatively new developments and there are few applications available (but see for example, Dolan et al., 2004;
Jedidi et al., 1997a; Schmittmann et al., in press). Hence, currently there is not much knowledge about the conditions under which the parameters of spe-cific mixture structural equation models, for example mixture LST models, can be appropriately estimated. Moreover, there is only limited information concerning the adjusted likelihood ratio test of Lo et al. (2001) because this is a rather new test. For these reasons, three simulation studies were conducted to find out whether the parameters of the mixture LST models can be ap-propriately estimated and whether the aLRT can be validly used to compare the number of classes in the application. These simulation studies also aimed at determining the minimum sample size and number of occasions necessary to get valid results that can be used for planning future studies.
Based on the empirical results of the applications, three simulation stu-dies were conducted to find out whether the parameters and the aLRT of the mixture LST models without and with covariates were appropriately estima-ted. The first simulation study focused on the mixture LST model separating more variable from less variable individuals. The second simulation study was based on the extended mixture LST model analyzing the influence of daily hassles and uplifts on momentary mood. The third simulation study was ai-med specifically at estimating type I error for the aLRT given the conditions of the application (four occasions of measurement, N = 500). This last si-mulation study is smaller than the first two because it is not the main goal