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Description:
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This study investigates the performance of the bootstrap when it is applied to structural equation models with ordered categorical variables . The study focuses on the parameter estimates , their standard errors and the coverage rates of the associated bootstrap confidence intervals . Structural equation models are used widely in many disciplines and often the data analyzed involve ordered categorical variables . The performance of the bootstrap has been investigated through simulation , and it is also compared with the Maximum Likelihood estimator applied on both polychoric correlation matrices and Pearson's product moment correlation matrices . The bootstrap samples are generated randomly and transformed , so that they preserve the covariance structure of the model . Then the polychoric correlation matrix is computed and analyzed for each sample .
The study involves three different models , and for each model different sample sizes have been analyzed . One of the models that has been analyzed is one that Muthen and Kaplan used in their research to investigate the performance of the Categorical Variable Methodology (CVM ) estimator , so direct comparisons between the two methods have been made . The bootstrap compares well with the CVM estimator .
The results of this research indicate that the bootstrap pro \ ides correct standard errors that are larger than the standard errors obtained from the Maximum Likelihood estimator when it is applied on the Pearson's product moment correlation matrices . The coverage rates of the bootstrap confidence intervals have also been investigated , using two methods : the percentile method and the bootstrap -t method . The results are not very encouraging , especially for the bootstrap -t method , since the coverage rates are in some cases far away from the prespecified confidence level . The percentile method seems to perform better than the bootstrap -t method with regard to coverage rates , though it presents problems also .
The performance of the bootstrap is affected by the sample size , the complexity of the model and the parameter values . Overall , the bootstrap performs rather adequately and could provide a valid alternative to other estimation methods for structural equation models if the researchers are cautious on its application . |