The null model

Load the file you downloaded and prepared in the exercises on the previous pages.

Estimate the null model and calculate the intraclass correlation (ICC). How much of the variation in happiness stems from the variation among countries? Is multilevel analysis to be recommended or will an individual level analysis suffice? How do you interpret the intercept?

SPSS
mixed happy with agec agec2 female seced terted missinc medinc highinc copeinc cohab social
/fixed =
/method = ml
/random = intercept | subject(cntry)
/print = solution.

Note that all the explanatory variables are included first to ensure that all models use the same list-wise deletion criterion in SPSS, i.e. that they are estimated on the basis of the same number of respondents.

Table 5.1. Information Criteriaa

Table 5.2. Estimates of Fixed Effectsa

Table 5.3. Estimates of Covariance Parametersa

Table 5.4. Information criteria table for OLS modela

Answers to the questions

Intraclass correlation ICC=0.5855/(3.7717+0.5855)=0.134.

This means that more than 13 per cent of the variation in happiness scores is due to between-country variation.

Is a multilevel analysis necessary? The between-country variation of 13 per cent is far from trivial, and the estimate of the variance in the intercept residuals is about three times larger than its standard error. The definitive answer as regards the statistical significance of the between-country variation is found in the LR test, where the -2LL of the null model is compared to the -2LL for the one-level model:

Chi square=203 026.467 - 196 165.706 = 6860.76, with 1 df, p=0.000. The outcome is highly significant and indicates that a two-level model is necessary.

The intercept in the null model (7.11) is the weighted average of the country mean scores for happiness. It is slightly higher than the overall mean from the one-level model (7.04).

Stata

To estimate the multilevel models with the same number of respondents, we need to create a filter variable to count the number of missing values for the maximum set of variables:

egen nmiss = rowmiss (happy agec agec2 female seced terted missinc medinc highinc copeinc cohab social)

xtmixed happy || cntry: , mle variance, if nmiss==0

Table 5.5. Stata output 1

Answers to the questions

Intraclass correlation ICC=0.5855/(3.7717+0.5855)=0.134.

This means that more than 13 per cent of the variation in happiness scores is due to between-country variation.

Is a multilevel analysis necessary? The between-country variation of 13 per cent is far from trivial, and the estimate of the variance in the intercept residuals is about three times larger than its standard error. The definitive answer as regards the statistical significance of the between-country variation is found in the LR test, where the -2LL of the null model is compared to the -2LL for the one-level model:

The chi square for the LR test comparing the null model with two levels to the one-level equivalent is found at the bottom of the Stata output: 6860.76, df=1, p=0.000. The outcome is highly significant and indicates that a two-level model is necessary.

The intercept in the null model (7.11) is the weighted average of the country mean scores for happiness. It is slightly higher than the overall mean from the one-level model (7.04).

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