MLM Refresher Exercise

June 14, 2015

Data

The Gambia Data (2009)

Level 1 Variables (pupils)

schoolID – (as ID)

S1Q3_PP – Number of letters correct in 60 seconds (in mdm)

Gender_PP – Female=0, Male=1 (in mdm)

Level 2 Variables (head teacher)

schoolID – (as ID)

Q205 – One shift per day=0, Two shifts per day=1 (in mdm)

Use number of letters correct in 60 seconds (S1Q3_PP) as the dependent variable for all analyses.

  1. Fit the unconditional 2-level model
  2. What is the unconditional ICC. Show the calculations.
  1. Suppose you hypothesize that there is a gender gap within schools but that the gender gap does not vary randomly across schools.
  2. Fit the appropriate model. What is the estimated gender gap within schools? Is it statistically significant?

Level-1 Model

S1Q3_PPij = β0j + β1j*(GENDER_Pij) + rij

Level-2 Model

β0j = γ00 + u0j
β1j = γ10
GENDER_P has been centered around the group mean.

Mixed Model

S1Q3_PPij = γ00+ γ10*GENDER_Pij +u0j+ rij

Estimated gender gap is 9.01 (p<0.01) points and it is statistically significant. On average, boys are correctly identifying 9 letters more than girls within schools.

  1. Remove gender from the model. Suppose you are interested in whether there is a difference in mean letter recognition for schools with one shift versus two shifts.
  2. Fit the model two ways – with shift uncentered and shift grand mean centered. Is there a statistically significant difference in mean letter recognition for schools with one shift versus two shifts?

Level-1 Model

S1Q3_PPij = β0j + rij

Level-2 Model

β0j = γ00 + γ01*(Q205j) + u0j

Mixed Model

S1Q3_PPij = γ00+ γ01*Q205j +u0j+ rij

Yes – there is a statistically difference in mean number of letters correct for schools with one shift or two. On average, the mean for schools with two shifts is 4.77 points lower than schools with one shift (p<0.05).

  1. What differs across the two models in terms fixed effects and variance components? Explain.

The only difference is the intercept. This is because when shift is entered uncentered, the intercept is the mean for schools with one shift whereas when shift is entered centered, it is the mean across schools adjusted for percent of schools in either shift.

In your own datasets, choose an outcome of interest.

  1. Run the unconditional model as a starting point for future analyses. What is the unconditional ICC?