hw11sol

# hw11sol - Stat 511 Homework 11 solution Spring 2011 Due 5pm...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stat 511 Homework 11 solution Spring 2011 Due: 5pm, Tuesday Apr 19 1. The data in school.txt come from an educational study. The full study has 3 treatments, but we will only look at data from one treatment. Treatments were randomly assigned to 8th grade classrooms in 3 schools in each of 4 school districts. Performance on a standardized test was measured for each student in each classroom. There are a total of 24 classrooms and 573 students. We will ignore the multiple levels of vairability and consider a model with a random effect for classroom and a random effect for student. Note that one of these random effects is commonly called “error”. (a) Estimate the variance components (variability between classrooms and variability among students within a classroom) using REML. The appropriate model is Y ij = μ + α i + ǫ ij where 1 ≤ i ≤ 24, 1 ≤ j ≤ n i , α i ∼ (0 , σ 2 α ) the variability among classroom and ǫ ij ∼ (0 , σ 2 ǫ ) the variability among studentswithin a classroom. > temp <- lmer(score~(1|class),data=d) > summary(temp) Linear mixed model fit by REML Formula: score ~ (1 | class) Data: d AIC BIC logLik deviance REMLdev 3592 3605-1793 3589 3586 Random effects: Groups Name Variance Std.Dev. class (Intercept) 63.00 7.9373 Residual 26.03 5.1020 Number of obs: 573, groups: class, 24 (b) Estimate the mean score for this treatment and its standard error. Fixed effects: Estimate Std. Error t value (Intercept) 61.837 1.636 37.79 (c) You have been asked by the teacher of classroom 17 to report that class’s average per- formance on this exam. Report the appropriate value....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

hw11sol - Stat 511 Homework 11 solution Spring 2011 Due 5pm...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online