Dissertation Information for Michael Howard Seltzer NAME: - Michael Howard Seltzer
DEGREE:
- Ph.D.
DISCIPLINE:
- Education
SCHOOL:
- University of Chicago (USA) (1991)
ADVISORS: - None COMMITTEE MEMBERS: - None
MPACT Status: Incomplete - Not_Inspected
Title: The use of data augmentation in fitting hierarchical models to educational data
Abstract: The two-state hierarchical linear model (HLM) in which normality is assumed at each stage has become widely used in educational research in the past decade. In the two-stage HLM, first-stage or within-unit parameters, e.g., within-school SES-achievement slopes, are treated as outcomes in a second-stage model. At the second stage, parameters termed fixed effects relate various unit-level characteristics, e.g., differences in school policy and practice, to differences in the magnitude of within-unit parameters, e.g., within-school slopes.
Inferences concerning fixed effects and within-unit parameters are typically based on their conditional posterior distributions where maximum likelihood estimates of the variance components are treated as known values. However, whenever the number of units (e.g., schools) in a study is small, it is important that we try to be fully Bayesian: to account for uncertainty concerning the variance components, we should try to integrate over all unknowns in the model and base inferences on marginal posterior distributions of interest. Also, it is advisable that we conduct sensitivity analyses by re-calculating marginal posteriors of interest under assumptions of heavy-tails in the second-stage model; such analyses would yield, for example, robust estimates for the fixed effects. Unfortunately, the required integrations for implementing this strategy are forbiddingly complex.
The method of Data Augmentation, however, provides a viable means of obtaining the marginal posterior distribution of any parameter in the HLM under multivariate normal (MVN) and multivariate t (MVT) second-stage assumptions. In my thesis, I derive Data Augmentation algorithms for the MVN and MVT cases and illustrate their use through several analyses in which I compare answers obtained via Data Augmentation with results based on standard procedures. These analyses include a synthesis of a set of SAT coaching studies, an exploration of how differences in parent-speech input relate to differences in vocabulary growth among children, and an examination of how differences in the implementation of a pre-algebra curriculum relate to differences in program success.
| |
MPACT Scores for Michael Howard Seltzer A = 0
C = 1
A+C = 1
T = 0
G = 0
W = 0
TD = 0
TA = 0
calculated 2008-01-31 06:14:59
Advisors and Advisees Graph
|