统计The Hierarchical Logistic Regression Model for Multilevel Analysis

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The Hierarchical Logistic Regression Model for Multilevel Analysis

文献名称	The Hierarchical Logistic Regression Model for Multilevel Analysis
文献作者	George Y. Wong and William M. Mason
作者所在单位	Assistant Member, Biostatistics Laboratory, Memorial Sloan-Kettering Cancer Center
文献分类	已发表文献
学科一级分类	统计
学科二级分类	统计学
文献摘要	A hierarchical logistic regression model is proposed for study- ing data with group structure and a binary response variable. The group structure is defined by the presence of micro ob- servations embedded within contexts (macro observations), and the specification is at both of these levels. At the first (micro) level, the usual logistic regression model is defined for each context. The same regressors are used in each context, but the micro regression coefficients are free to vary over contexts. At the second level, the micro coefficients are treated as functions of macro regressors. An empirical Bayes estimation procedure is proposed for estimating the micro and macro coefficients. Explicit formulas are provided that are computationally feasible for large-scale data analyses; these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within- and between-macro-equation error variability. The methodology is applied to World Fertility Survey data, with individuals viewed as micro observations and countries as macro observations.
参考文献	Birdsall, N. (ed.) (1985), The Effects of Family Planning Programs on Fertility in the Developing World, Staff Working Paper No. 677, Washington, DC: World Bank. Buse, A. (1982), "The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note," The American Statistician, 36, 153-157. Chamberlain, G. (1980), "Analysis of Covariance With Qualitative Data," Review of Economic Studies, 47, 225-238. Cochrane, S. H. (1983), "Effects of Education and Urbanization on Fertility," in Determinants of Fertility in Developing Countries: A Summary of Knowledge (Vol. 2), eds. R. Bulatao and R. Lee, New York: Academic Press, pp. 587- 626. Dempster, A. P. (1980), "Comment" (on Rubin 1980a), Journal of the Amer- ican Statistical Association, 75, 817. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), "Maximum Likeli- hood From Incomplete Data via the EM Algorithm," Journal of the Royal Statistical Society, Ser. B, 39, 1-38. Dempster, A. P., and Monajemi, A. (1976), "An Algorithmic Approach to Estimating Variances," Research Report S-42, Harvard University, Dept. of Statistics. Dempster, A. P., Rubin, D. B., and Tsutakawa, R. K. (1981), "Estimation in Covariance Components Models," Journal of the American Statistical Association, 76, 341-353. Entwisle, B., Hermalin, A. I., and Mason, W. M. (1982), "Socioeconomic Determinants of Fertility Behavior in Developing Nations: Theory and Initial Results," Committee on Population and Demography Technical Report 17, Washington, DC: National Academy Press. (1984), "A Model for the Comparative Analysis of WFS Contraceptive Use Data," in Survey Analysis for the Guidance of Family Planning Pro- grams, eds. J. Ross and R. McNamara, Liege, Belgium: Ordina Editions, pp. 127-146. Entwisle, B., and Mason, W. M. (1983), "Multilevel Effects of Socioeconomic Development and Family Planning Programs on Children Ever Born," Re- search Report 83- 53, University of Michigan, Population Studies Center. Entwisle, B., Mason, W. M., and Hermalin, A. I. (1984), "The Multilevel Dependence of Contraceptive Use on Socioeconomic Development and Fam- ily Planning Program Strength," Research Report 84-60, University of Mich- igan, Population Studies Center. Wald, A. (1943), "Tests of Statistical Hypotheses Concerning Several Param- eters When the Number of Observations Is Large," Transactions of the American Mathematical Society, 54, 426-482. Wong, G. Y., and Mason, W. M. (1984), "The Hierarchical Logistic Regression Model for Multilevel Analysis," Research Report 84-56, University of Mich- igan, Population Studies Center. Wong, G. Y., Mason, W. M., and Entwisle, B. (1984), "A Generalization of the Hierarchical Normal Linear Model for Multilevel Analysis," paper pre- sented at the Annual Meetings of the American Statistical Association, Phil- adelphia. World Bank (1984), World Development Report 1984, New York: Oxford University Press.
关键字	Fixed effect; Random effect; Mixed model;Maximum likelihood estimation of covariance components;Empirical Bayes estimation procedure
发表所在刊物（或来源）	Journal of the American Statistical Association, Vol. 80, No. 391 (Sep., 1985), pp. 513-524
发表时间	Sep., 1985
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