| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 98 === The sampling design is getting more complex to comply with a variety of social environment and to increase the precision of sampling survey as well. The traditional estimators used with complex survey may lower the accuracy of the statistical analysis. This study explores the methods of regression analysis on survey data obtained under a complex sampling. Three methods of multiple regression analysis proposed by previous studies, namely, ordinary least squares, weighted least squares, and Quasi-Aitken probability weighted least squares are used in this study for comparison analysis. Previous studies show that the ordinary least squares estimator is biased under the data collected under the unequal probability design; while under the equal probability design the weighted least squares estimator is better than ordinary least squares, but under the unequal probability design weighted least squares estimator may have a larger variance.
This study uses the data of "Taiwan Social Change Survey 2007, Phase 5, Wave 3," collected under a stratified unequal probability sampling by the Institute of Sociology Academia Sinica for empirical comparison of those three methods via comparing the estimates of regression coefficients, RMSE, and . The empirical results consist with previous studies. The results show that there is no big difference among the estimated parameters of those three methods. The results also show that the education year of respondents has significant negative relationship with their age but has positive relationship with their parents’ education year.
Keywords: Stratified sampling, Regression analysis, Complex sampling, Least squares, Weighted least squares, Quasi-Aitken weighted least squares.
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