Exercise 3LC1. Linear model, pupil rating of school managers (856 pupils in 94 schools)
This data set (manager.dat) was presented by Hox (2002) and contains the scores ‘responses’ given by each pupil on 6 questions on the nature of school managers/directors, for a collection of schools. The data set also contains information on the director’s gender, the type of the school, the pupil gender and year of the pupil. Hox (2002) presents the results for a 3-level linear model (without any covariates) in Hox (2002, Table 9.5). For details about the book see http://www.geocities.com/joophox/mlbook/leabook.htm
Hox, J., (2002), Multilevel Analysis Techniques and Applications, Lawrence Erlbaum Associates, London
Number of observations = 4981
Number of level-2 cases (‘pupil’) = 856
Number of level-3 cases (‘school ’) = 94
The variables are:
id= pupil identifier across all schools
school =school identifier
pupil = pupil identifier within each school (0,1,…9)
dirsex = gender of school manager (1=F, 2=M)
schtype = school type (1=general (AVO), 2=professional (MBO &T), 3= day/evening)
pupsex = pupil gender (1= F, 2=M)
item= item (1,2,…,6)
class =school year of pupil
scores=response by pupil of the item question.
The first few lines of manager.dat look like:
1. Estimate a linear model (without random effects) for the score with the pupil- and school- level covariates dirsex, schtype and pupsex.
2. Allow for the pupil identifier random effect (id), use mass 24 in a 2-level model. Is this random effect significant?
3. Allow for both the pupil identifier random effect (id) and for the school random effect (school) in a 3-level model with mass 24 for both levels. Are both these random effects significant? Is this model a significant improvement over the model estimated in part 2 of this exercise?
4. Which covariates have a significant effect on the scores? How did your results change when you allowed for pupil-level (level 2) and then school-level (level 3) effects?