Student Seminar Series - July 25, 2006
University of Minnesota
School of Statistics
College of Liberal Arts
Hierarchical
Latent Class Analysis of Siegler's Balance Scale Task
Kentaro
Kato
Tuesday, July 25, 2006
1:30 PM, 170
Ford Hall
Minneapolis, East Bank Campus
Refreshments at 1:00 PM
300 Ford Hall
Abstract
Siegler's balance scale task is intended to measure children's
cognitive
development of the physical concept of torque. Psychological research
identified several cognitive rules that children use to solve balance
scale
problems, and also devised several problem types so that one can
differentiate the cognitive rules by examining patterns of
correct-incorrect
responses to balance scale problems of specific types. In this study, a
dataset from the balance scale task is analyzed by a hierarchical
latent
class model, in which cognitive rules are treated as latent classes,
and
responses to the problems constitute observed categorical variables.
The
probability of a correct response to each problem is assumed to have a
hierarchical structure in which its mean is determined by the cognitive
rule
used and the type of problem. The full Bayesian approach is adopted,
and the
posterior distribution is estimated by Gibbs sampling with data
augmentation
and Metropolis substeps. Several issues encountered in the course of
analysis are discussed, including model identifiability, inequality
constraints, label switching, and model fit. Results from the final
model
partly replicated the finding of previous studies, recovering the most
stable cognitive rules, but latent classes that do not fit the
underlying
psychological theory were also found.