Collections > Electronic Theses and Dissertations > A second-order growth model for longitudinal item response data
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This Dissertation explores the unique issues related to specifying and fitting a second-order growth model to longitudinal item response data. The model examined is a hybrid of the logistic IRT model for binary item responses and the latent growth curve model for repeated measures. Attention centered around parameterization, identification, estimation, and issues related to estimation of the model such as convergence, improper solutions, bias and root mean squared error (RMSE). Two variations on the proposed model: one with correlated errors (model 2) and one without (model 1). In each model two types of estimator were examined: full and limited information estimators. Two sample size conditions were examined, one with N = 750 observations, and another with N = 3000. In addition, two item parameter sets were examined, one having a wide range of difficulty and the other, narrow. Comparing analyses stratified across model, findings indicated greater rates of improper solutions and bias for model 2 versus model 1. Limited information estimators of model 1 performed worse than full information estimators, while the opposite was true for model 2. Bias and convergence issues were greatest when difficulty had a wide range. Lastly, sample size appeared to play a negligible role in bias and RMSE, though it did affect convergence issues and improper solutions. Based on empirical results presented in this simulation the proposed model appears to be a logical statistical framework for modeling longitudinal item responses.