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Bootstrap Procedures for Dynamic Factor Analysis

出版	Ohio State University, 2006
URL	http://books.google.com.hk/books?id=HAXDtAEACAAJ&hl=&source=gbs_api

註釋Abstract: Dynamic factor analysis (DFA), a combination of factor analysis and time series analysis, involves autocorrelation matrices calculated from multivariate time series. Because the distribution of autocorrelation matrices is intractable, obtaining statistical properties of DFA estimators is difficult. The dissertation proposes using the bootstrap to obtain standard error estimates, confidence intervals, and test statistics for DFA models. The dissertation considers two bootstrap procedures for dependent data, namely the parametric bootstrap and the moving block bootstrap. The parametric bootstrap is like a Monte Carlo study in which the population parameters are the parameter estimates obtained from the original sample. The moving block bootstrap breaks down the original time series to blocks, draws samples with replacement from the blocks, and connects the sampled blocks together to form a bootstrap sample. In addition, the dissertation considers DFA with categorical data, which is common in psychological research. Bootstrap confidence intervals and bootstrap tests require quantiles of the distribution of bootstrap replications. The quantiles are often estimated using empirical cumulative distribution functions. The target distribution method is a semiparametric method for estimating distribution functions. This dissertation also investigates whether the target distribution method can be employed to improve the estimation of the quantiles of bootstrap replications. The bootstrap procedures were illustrated using both simulation studies and two published examples. Results of the simulation studies are (1) Both the parametric bootstrap and the moving block bootstrap provided accurate standard error estimates; (2) Actual coverage probabilities of confidence intervals obtained from the two bootstrap procedures were close to their nominal levels; (3) Actual rejection rates of comparing nested models and of testing individual differences were close to their nominal levels, but actual rejection rates of goodness of fit tests were lower than their nominal levels; (4) The parametric bootstrap gave valid inferences when categorical data were analyzed using the polychoric approach; and (5) The empirical CDF and the target distribution smoothed CDF gave similar bootstrap confidence intervals and bootstrap tests at the bootstrap sample size of 1000. The illustrations with the two published examples show that the bootstrap procedure is feasible for a model with 30 indicators.