MLM Cluster Level Moderator Exercise
June 16, 2015
Data
The Gambia Data (2009)
Level 1 Variables (pupils)
schoolID – (as ID)
S2Q3_PP – Number of words correct in 60 seconds (in mdm)
Level 2 Variables (head teacher)
schoolID – (as ID)
Q205 – One shift per day=0, Two shifts per day=1 (in mdm)
WSD – Control=0, WSD =1 (in mdm)
WSDxshift – Interaction of WSD and Q205*
*Note that I created the interaction variable in SPSS prior to uploading the data to HLM.
Load the data above into HLM. Use number of words correct in 60 seconds (S2Q3_PP) as the
dependent variable for all analyses.
1. Fit the unconditional 2-level model
a. What is the unconditional ICC.

104.07
 0.19
104.07  443.17
2. Suppose a group of researchers are interested in whether the treatment effect is
moderated by whether a school has 1 or 2 shifts per day.
a. Fit the appropriate model. Is there evidence that number of shifts per day
moderates the treatment effect?
Level-1 Model
S2Q3_PPij = β0j + rij
Level-2 Model
β0j = γ00 + γ01*(Q205j) + γ02*(WSDj) + γ03*(WSDXSHIFj) + u0j
Mixed Model
S2Q3_PPij = γ00 + γ01*Q205j + γ02*WSDj + γ03*WSDXSHIFj + u0j+ rij
No evidence of an interaction.
Final estimation of fixed effects
(with robust standard errors)
Fixed Effect
Coefficient
Standard
error
t-ratio
Approx.
d.f.
p-value
For INTRCPT1, β0
INTRCPT2, γ00
Q205, γ01
WSD, γ02
WSDXSHIF, γ03
35.526064
-2.061806
1.379223
-6.085482
2.372873 14.972
2.698561 -0.764
3.204096 0.430
3.906434 -1.558
170
170
170
170
<0.001
0.446
0.667
0.121
In your own datasets, choose an outcome of interest.
3. Run the unconditional model as a starting point for future analyses. What is the
unconditional ICC?
4. Consider a cluster-level variable that you believe may moderate the treatment effect. Test
the hypothesis.