MATH 6643 Summer 2012 Applications of Mixed Models/Snijders and Bosker: Discussion Questions
At the bottom of page 83, Snijders and Bosker outline the process for probing interactions between two level one variables, and how there can be four possibilities for how to model it. If a researcher was to include all four, discuss how each would be interpreted. What might a good selection strategy be if our model had substantially more than two variables?
If we do not have any information about the data set, how to choose a level - two variable to predict the group dependent regression coefficients? After we choose the level - two variable z, how to explain the cross - level interaction term.
A client arrives with a random slope and intercept model using IQ as a predictor. IQ was measured on the traditional scale with a mean of 100 and standard deviation of 15. What should the client keep in mind about the interpretation of the variance of the intercept and covariance of the slope-intercept?
In chapter 5, they talk about hierarchical linear model where fixed effects and random effects are taken into consideration. Discuss a clear simple example in class which shows both effects and give interpretations of each of the coefficients and their use in real life.
In chapter 5, they talked about mostly about the two-level nesting structure. Can we have a bigger example with at least 4 levels that includes the random intercept and slope and how to apply this into R coding?
Exluding fixed effects that are non-significant is common practice in regression analyses, and Snijders and Bosker follow this practice when simplifying the model in Table 5.3 to the model found in Table 5.4. While this practice is used to help make the model more parsimonious it can ignore the joint effect that these variables have on the model as a whole. Discuss alternative criteria that one should explore when determining whether a predictor should be excluded from the model.