Introduction to Multilevel Modeling Using HLM 6精编.pdfVIP

Introduction to Multilevel Modeling Using HLM 6 By ATS Statistical Consulting Group Multilevel data structure • Students nested within schools • Children nested within families • Respondents nested within interviewers • Repeated measures nested within individuals – longitudinal data, growth curve modeling In the example of student nested within schools: • Level-1 variables, such as student’s gender and age • Level-2 variables, such as school type and size How would we analyze such multilevel data? • OLS regression • OLS regression with robust standard error • Aggregation • Disaggregation • Ecological fallacy – interpreting analyses on aggregated data at the individual level Ecological Fallacy See figure 3.1, on page 14 from Multilevel Analysis by Snijders and Bosker Hierarchical linear model • Random Intercept model Yij = β0j + rij β0j = γ00 + u0j • Written in mixed model format: Yij = γ00 + u0j + rij • i is for individuals and j is for schools • β0j is the mean of Yij for school j • γ00 is the average of all the β0j’s, therefore the grand • rij and u0j are normally distributed • rij and u0j are independent of each other • Parameters to be estimated include regression coefficients and variance components: γ00, var(rij) and var(u0j) Hierarchical linear model • Random Intercept and random slope model Yij = β0j + β1jX + rij β0j = γ00 + u0j β1j = γ10 + u1j • Written in mixed model format: Yij = γ00 + γ10X + u0j + u1jX+ rij • β0j is the mean of Yij for school j when X is zero • β1j is the slope of X for school j (or the effect of X for school j) • rij, u0j and u1j are normally distributed • u0j a