Establishing Measurement Invariance

As discussed in sections 4.3 and 4.3.1 there has been serious doubt whether self-rated health is a reliable indicator for the analysis of health inequalities. To address this problem four questions will be answered in this part.

1. Are answers on items of subjective health in the SOEP comparable across gender in the population?

2. Are these items also comparable between workers in high and regular job status and between private and public sector workers?

3. Are these items comparable across time?

4. Is a latent health variable created by a factor score a good predictor of mortality?

Figure 5.4 reports the results from a confirmatory factor analysis (CFA) where the latent variable health is determining the observed variables self-rated health (SRH), satisfaction with health (SAT) and worries about health (WAH) for the year 2000 in the SOEP. All observed variables are ordinal in their nature. The measurement model and the results are reported with unstandardized coefficients in figure 5.4.

I restricted the model, so that intercepts of indicators are equal across groups. This means that I test for structural invariance between genders. I do not test separately for metric invariance as this is highly complicated when dealing with categorical dependent variables. As structural invariance implies metric invariance, establishing structural invariance is sufficient.

Theχ2statistic with 13 degrees of freedom is 53 and highly significant, indicating a bad model fit. However, as already explained in the methods sections this statistic is very sensitive to the number of observations which is very high in my sample (> 8000). Therefore the other fit indexes should also be scrutinized. CFI is 0.999, TLI 1.000 indicating that model fit is almost as good as the saturated model. RMSEA is 0.021 [CI: 0.015;0.027], and the confidence interval is well within the range of acceptable values. Overall the model fit is still very good, and structural invariance between genders can be established for my sample. This means that in addition to associations with other variables, means of the health variables can be compared between men and women. This will be done in the next section where descriptive evidence on health inequalities between job status is provided. Further restrictions on the model to test for equivalence of error-term variance are possible, but unnecessary for any of my further analyses.

Therefore, I will not conduct them.

The first question of this section can be answered now. The items SRH, SAT, and WAH in the SOEP can be compared across gender in my sample. Any further analyses rely in

their conclusions on these tests. The confirmatory factor analysis addresses the critique that differences in effect sizes might be due to different meanings that these items carry for men and women. Regardless of whether this argument is theoretically sound, it has no empirical relevance for my data set.

Figure5.4.:ConfirmatoryFactorAnalysis-Gender SATSRHWAH

Health Intercept

0.89610.731 Sat1 = -2.207 Sat2 = -1.869 Sat3 = -1.506 Sat4 = -1.221 Sat5 = -0.736 Sat6 = -0.446 Sat7 = -0.005 Sat8 = 0.687 Sat9 = 1.208

SRH1 = -2.131 SRH2 = -1.224 SRH3 = -0.225 SRH4 = 1.141 WAH1 = -1.109 WAH2 = 0.303

F = 1 M = 1.034N = 1 H = 1.013F = 1 M = 1.037 F= 0.880 M=0.819

χ^2 = 52.99 df = 13 CFI = 0.999 TLI = 1.000 RMSEA = 0.021 [0.015;0.027] Note:F=Women;M=Men

Now we can turn to the question whether the health items can be compared over the years under observation. In my study these are the years 1999-2011. As this seems to be of lesser importance in the literature I will just briefly summarize the results of figure 5.5, which presents the unstandardized results and fit statistics of the models. Structural invariance can also be accepted in my sample despite the significant χ² statistic of 824 with 156 degrees of freedom.

The high χ² is mainly due to the sample size of over 100,000 observations. The fit indexes are still very good, only slightly worse than the fit of the structural invariance model for gender.

The CFI is 0.999, TLI 1.000, RMSEA 0.019 [CI: 0.018;0.021].

It is therefore save to conclude, that all health indicators can be compared over time for my sample.

The last measurement invariance test I am going to conduct is between workers in different job status (see figure 5.6). Again I use the year 2000 as a reference. Comparability of subjective health across job status is essential to allow causal interpretation of estimated effects in my regression models. If subjective health turned out not to be invariant it could not be distinguished whether estimated coefficients came from systematic measurement error or an actual causal relationship.

Structural invariance leads to a model with a significant χ² statistic of 82 with 13 degrees of freedom. However, similar to invariance over time and across gender, we can see that all other model fit indicators are very good. CFI and TLI are 0.998 and 0.997 respectively. The estimate of RMSEA is 0.031 [0.025;0.038] with the confidence interval indicating that it is very unlikely that the true parameter is above the critical value of 0.05. Such excellent fit indicators let me conclude that subjective health is comparable across job status.

Key results from this section are: Self-rated health items from the SOEP are comparable across gender, time, and job status. Differences in health effects can be substantively interpreted, because reporting heterogeneity is not an important issue in the data set.

Figure5.5.:ConfirmatoryFactorAnalysis-Time SATSRHWAH

Health Intercept

0.89510.668 Sat1 = -2.283 Sat2 = -1.881 Sat3 = -1.484 Sat4 = -1.185 Sat5 = -0.729 Sat6 = -0.437 Sat7 = 0.042 Sat8 = 0.793 Sat9 = 1.417

SRH1 = -2.181 SRH2 = -1.236 SRH3 = -0.214 SRH4 = 1.242 WAH1 = -1.087 WAH2 = 0.336

1999 = 1 2000 = 0.945 2001 = 0.970 2002 = 0.986 2003 = 0.996 2004 = 1.001 2005 = 1.001 2006 = 1.004 2007 = 1.027 2008 = 1.029 2009 = 0.991 2010 = 0.992 1999 = 1 2000 = 1.011 2001 = 1.031 2002 = 1.067 2003 = 1.083 2004 = 1.047 2005 = 1.090 2006 = 1.056 2007 = 1.079 2008 = 1.071 2009 = 1.036 2010 = 0.994

1999 = 1 2000 = 0.959 2001 = 0.968 2002 = 0.984 2003 = 0.990 2004 = 0.987 2005 = 0.999 2006 = 0.993 2007 = 1.006 2008 = 0.990 2009 = 0.984 2010 = 0.989 1999 = 0.874 2000 = 0.971 2001 = 0.932 2002 = 0.916 2003 = 0.895 2004 = 0.895 2005 = 0.883 2006 = 0.889 2007 = 0.851 2008 = 0.871 2009 = 0.919 2010 = 0.916 2011 = 0.969

χ^2 = 824.39 df = 156 CFI = 0.999 TLI = 1.000 RMSEA = 0.019 [0.018;0.021]

Figure5.6.:ConfirmatoryFactorAnalysis-JobStatus SATSRHWAH

Health Intercept

0.88110.701 Sat1 = -2.309 Sat2 = -1.954 Sat3 = -1.548 Sat4 = -1.237 Sat5 = -0.744 Sat6 = -0.445 Sat7 = 0.014 Sat8 = 0.729 Sat9 = 1.246

SRH1 = -2.274 SRH2 = -1.282 SRH3 = -0.223 SRH4 = 1.198 WAH1 = -1.122 WAH2 = 0.321

N = 1 H = 1.044N = 1 H = 1.078N = 1 H = 1.006 N = 0.879 H = 0.882

χ^2 = 82.13 df = 13 CFI = 0.998 TLI = 0.997 RMSEA = 0.031 [0.025;0.038] Note:N=NormalJob;H=HighStatusJob