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 / Std. Error / p-value
Intercept / γ00
Treatment status / γ01
var(rij) / σ2
var(u0j) / τ00

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.  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).

ii.  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).

iii.  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 / Model B / Model C
b / Std.
Error / b / Std. Error / b / Std. Error
Intercept / γ00
Treatment_statusj / γ01
Genderij / γ10
Genderij*Treatment_statusj / γ11
Gender_Aggj / γ02 / ----- / -----
Gender_Aggj*Treatment_statusj / γ03 / ----- / ----- / ----- / -----
var(rij) / σ2
var(u0j) / τ00

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.