Hello,
I have a question about HLM. With TIMSS 2019 data, I built a model with students at Level 1 and schools at Level 2. I conducted the analysis with HLM 6.04 program. I used the sample weights variables at both levels (StudentWeights = WGTADJ2 * WGTFAC2 * WGTADJ3 * WGTFAC3 and SchoolWeights = WGTADJ1 * WGTFAC1).
As you know, two important tables are obtained as a result of this analysis [final estimation of fixed effects (with standard errors) and final estimation of variance components]. While the degree of freedom is 179 as a result of the ANOVA model for a country, degree of freedom is 193 in the table giving the variance components (Total number of schools is 194 and there are no predictive variables. There are only IDSCHOOL and IDSTUD).
Do you think this is normal? Because the degrees of freedom in the two separate tables in the data sets of other countries were exactly the same. I looked at the dataset again, there is no missing value in the variables I analyzed, and there is no missing value in the weighting variables.
But you didn't put in your model anything that could tell you if there was a difference in anything. David Booth
David Eugene Booth Yes, you are right. But, I have an outcome variable (mathematics achievement). In the first step, I can state that "about 12% of the overall variance of mathematics achievement can be attributed to differences between schools"
Can't I?
Metehan Güngör You can say that or equivalently the ICC is 0.12, that is pairs of children picked randomly from the same school would be correlated 0.12 for the outcome variable. That is quite typical for school data and represents a large and important correlation (dependency) which should not be ignored.
In terms of testing, it is much more reliable to use a likelihood ratio test where your more complicated model is evaluated against a simpler model, in this case one without the level 2 variance. The difference in the deviance is distributed as chi-square with in this case 1 degree of freedom. See significance testing chapter in
Book Developing multilevel models for analysing contextuality, he...
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