The individual level model

Add all candidates and eliminate variables with coefficients that do not attain statistical significance or add variables in groups - demographic, socioeconomic, social support - to find out which group of variables can explain some of the differences between countries.

Follow the latter strategy and add variables in blocks. Eliminate variables that do not appear to have any statistically significant effect on happiness. Create a table with the pseudo R squares for the two levels for each block with the null model as the baseline.

SPSS

Run the commands to see the output.

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

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

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

Run the commands to see the output.

xtmixed happy agec agec2 female || cntry: , mle variance, if nmiss==0

xtmixed happy agec agec2 female seced terted missinc medinc highinc copeinc || cntry: , mle variance, if nmiss==0

xtmixed happy agec agec2 female seced terted missinc medinc highinc copeinc cohab social || cntry: , mle variance, if nmiss==0

Answer
Table 5.6. Explained variance models formed by adding blocks of variables
Null model + Demographic variables + Socioeconomic variables + Social support variables
Individual level variance 3.772 3.701 3.398 3.268
Between-country variance 0.586 0.578 0.345 0.292
Explained individual level variance 0.000 0.019 0.099 0.133
Explained country level variance 0.000 0.013 0.410 0.502

Run the models to see the output and compute the pseudo R squares in the table. We see that the demographic variables, age, age squared and gender, explain very little of the variation at any level. This changes when the socioeconomic variables are added. They explain about 10 per cent of the individual level variance and, more importantly, about 40 per cent of the between-country variation in happiness, which must be the result of compositional effects. The fixed coefficients indicate that the differences among countries in relation to coping on present income are the most important factor in terms of explaining this variation. Adding the two social support indicators increases the explained variances to 13 and 50 per cent for the individual and country level, respectively.

All fixed coefficients are statistically significant and there are no statistical reasons for excluding any explanatory variables from the model.

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