MLM Individual Level Moderator Exercise
Day 2
June 15, 2015
Level 1 variables
S1Q3_PP: # of letters correct in 60 seconds
GENDER_PP: individual-level moderator (1=male; 0=female)
schoolID: As ID for student level
Level 2 variables
schoolID: As ID for each school
T_GROUP_PP: school treatment assignment (recode 2 = 0 so that 1=treatment, 0=control)
GENDER_AGG*: proportion of male students in the school
GENDER_AGGxTreat*: proportion of male students in the school interacted with school
treatment assignment
*These two variables were created in SPSS before uploading the data into HLM.
1. Suppose you are interested in understanding if the WSD program was successful in
improving reading outcomes for girls.
Using Optimal Design software, determine if you have enough power to assess what the
Minimum Detectable Effect Size would be under assumptions of 80% power, and
significance of 0.05, with the given ICC of reading outcomes for girls in this sample.
Calculate the MDES under assumptions of (i) R2 = 0.00 and (ii) R2 = 0.50.
i. What is J (i.e., number of clusters)? ___________________
ii. What is n (i.e., the average number of females per school, or sample size per
cluster)?___________
iii. What is ρ for the given outcome for female students? ______________
iv. What is the MDES under assumptions of R2= 0.00? ______________
v. What is the MDES under assumptions of R|W2= 0.50? ______________
2. Estimate the impact of WSD on the reading outcomes of girls by filling out the following
table.
b
Intercept
γ00
Treatment status
γ01
var(rij)
σ2
var(u0j)
τ00
Std. Error
p-value
2. Now, suppose you are interested in understanding if the WSD program affected reading
outcomes differently for males and females (i.e., add a cross-level interaction term
between treatment status and student gender to your main impact model).
(Note: The cross-level interaction term tests the H0, that Bm = Bf).
Using HLM, estimate if gender moderates treatment impacts of WSD. Run the model with three
different specifications:
i.
ii.
iii.
Model A: Include a cross-level interaction term between treatment at Level 2 and
gender at Level 1. (Note this will give you an estimate of the moderated effects that
blends Level 1 and Level 2 effects of gender).
Model B: Add a Level 2 covariate of gender aggregated to the school level (i.e., the
proportion of males in each school). (This will control for the cross-level direct
effects of the proportion of males in a school on reading outcomes).
Model C: Add an interaction term of gender at level 2 with school treatment
assignment. (This will control for the cross-level interaction effect between the
proportion of males in a school with treatment, and will provide a clean estimate of
the interaction term between treatment status at the school level with student gender
at the child level (i.e., γ11).).
Take note of if and how to coefficient estimates change as a result of the addition of variables in
Model B and C. What are the implications of these changes (or lack thereof)?
Model A
Std.
b
Error
Intercept
γ00
Treatment_statusj
γ01
Genderij
γ10
Genderij*Treatment_statusj
γ11
Gender_Aggj
Gender_Aggj*Treatment_st
atusj
var(rij)
var(u0j)
γ02
-----
-----
γ03
σ2
τ00
-----
-----
Model B
Std.
b
Error
-----
-----
Model C
Std.
b
Error
iv.
Using the model of your choice from the table above, estimate the average reading
scores for males and females in the treatment and control conditions.
Treatment
Control
Males
Females
WITH YOUR OWN DATA:
Choose an outcome of interest and a moderator of interest. Determine if you would like to assess
impacts for a particular subgroup, or if you are interested in assessing if the program impacted
particular subgroups in your sample differentially. Depending on your decision, decide what
approach is most appropriate to test your hypothesis. Consider issues of centering your data and
within- and between-level moderating effects.