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Categorical Data: Analysis of Two-Way Frequency Tables -- 12. Regression andCorrelation -- 13.
Topics include sampling, experimental design, regression analysis, specification testing, dimension reduction, categorical data analysis, classification and clustering.
The book can be used in senior undergraduate or first-year postgraduate courses on GLMs or categorical data analysis and as a methodology resource for VGAM users.
Categorical data analysis was done using the McNemar test, chi-square test, and Fisher exact test where appropriate.
Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
In categorical data analysis with econometric approach existence of a continuous unobserved or latent variable underlying an observed categorical variable is presumed.
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Unlike normal-theory maximum likelihood (ML) estimation for factor analysis of continuous scores, our use of Muthén's categorical data factor analysis methodology provides asymptotically unbiased, consistent and efficient parameter estimates, as well as a correct chi-square test of fit with dichotomous or ordinal observed variables [ 26].
Unlike Maximum Likelihood (ML) estimation for factor analysis of continuous scores, our use of Muthén's categorical data factor analysis methodology provides asymptotically unbiased, consistent and efficient parameter estimates as well as a correct chi-square test of fit with dichotomous or ordinal observed variables.
For comparisons between groups, we used an independent Student's t-test, Mann–Whitney U test, or one-way analysis of variance for continuous data, as well as a χ or Fisher's exact test for categorical data, where analysis assumptions were met.
Statistical methods including linear and generalized regression; random-effects models; methods for categorical data; survival analysis; and nonparametric methods.
This chapter describes various adjustments that are needed for the traditional chi-square test statistics for goodness of fit, test of independency, and homogeneity for categorical data and analysis when data are obtained from complex survey designs.
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