Assignment:
HLM
Data file to use from Bickel's former website: MLAHighSchoolandBeyondSubset.sav (remember his Excel file should be converted to SPSS format!) You may need to create some aggregated variables (i.e., variables for predicting level 2 variability). Use school as the contextual variable. Select "unstructured" in the random dialog box since we are allowing the predictors and intercept terms to correlate with each other. Note that for gender, all 1's are female and all zeros are males.
1. Run an HLM with no predictors.
a. What is the intraclass correlation?
b. Provide an interpretation of the ICC in plain English in no more than 2 sentences. Pretend you are explaining the ICC to a school district leader who does not have any training in HLM.
c. In theory, why does a significant ICC justify using HLM versus OLS?
d. Was the ICC significantly different than zero? Report the F-statistic in the usual fashion. (Hint: the ICC is based on the amount of variance among the schools, and the latter is captured by the intercept).
2. Complete the picture below that depicts 10 students nested in 5 schools. Include labels and all relevant arrows, lines, boxes. Assume that each school had 2 students sampled and they were nested in each school. Show sector as a predictor of the school level variability. Show gender as a predictor of both school and student level variability (use arrows)
3. Include gender as a level 1 predictor.
a. Report the slope value for the gender predictor, along with significance value.
b. Using plain English, interpret the meaning of both the fixed effect and random variance for the gender slope. Pretend you are describing these results to someone who is not trained in using HLM
c. What is the pseudo-R2 for the level 1 gender predictor. (include all hand calculations).
4. Include gender as a level 2 predictor.
a. Report the slope value for the gender predictor, along with significance value.
b. Using plain English, interpret the meaning of both the fixed effect and random variance for the gender slope. Pretend you are describing these results to someone who is not trained in using HLM
c. What is the pseudo-R2 for the level 2 gender predictor. (Include all hand calculations).
5. Include both the level 1 andlevel 2 gender variables as predictors. Also, include a third variable, which is the interaction between gender at level 1 and gender at level 2 (this is a cross-level interaction!).
a. Report the slope value for the cross-level gender1 by gender2 interaction term, along with its significance value.
b. Now, rerun the analysis with everything the same, except use the bootstrap estimation command. In the estimation dialog box, change 1000 maximum iterations to 100 iterations to save computing time. How has the significance value changed when compared to using restricted maximum likelihood for estimating standard errors (the default estimation method)?
c. Using plain English, interpret the meaning of the fixed effect for the gender1Xgender2 slope (based on the significance value when using the nonparametric bootstrap method for estimating p-values). Pretend you are describing these results to someone who is not trained in using HLM.
d. What is the pseudo-R2 for the cross-level gender1Xgender2 interaction term after controlling for the gender1 and gender2 main effects? (Include all hand calculations).