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Example
20
Bootstrapping for Model Comparison
Introduction
This example demonstrates the use of the bootstrap for model comparison.
Bootstrap Approach to Model Comparison
The problem addressed by this method is not that of evaluating an individual model
in absolute terms but of choosing among two or more competing models. Bollen and
Stine (1992), Bollen (1982), and Stine (1989) suggested the possibility of using the
bootstrap for model selection in analysis of moment structures. Linhart and Zucchini
(1986) described a general schema for bootstrapping and model selection that is
appropriate for a large class of models, including structural modeling. The Linhart
and Zucchini approach is employed here.
The bootstrap approach to model comparison can be summarized as follows:
Generate several bootstrap samples by sampling with replacement from the
original sample. In other words, the original sample serves as the population for
purposes of bootstrap sampling.
Fit every competing model to every bootstrap sample. After each analysis,
calculate the discrepancy between the implied moments obtained from the
bootstrap sample and the moments of the bootstrap population.
Calculate the average (across bootstrap samples) of the discrepancies for each
model from the previous step.
Choose the model whose average discrepancy is smallest.