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  • 1. Logistic regression under complex survey designs Archived
    Articles and reports: 12-001-X198900214567
    Description:

    Estimation procedures for obtaining consistent estimators of the parameters of a generalized logistic function and of its asymptotic covariance matrix under complex survey designs are presented. A correction in the Taylor estimator of the covariance matrix is made to produce a positive definite covariance matrix. The correction also reduces the small sample bias. The estimation procedure is first presented for cluster sampling and then extended to more complex situations. A Monte Carlo study is conducted to examine the small sample properties of F-tests constructed from alternative covariance matrices. The maximum likelihood estimation method where the survey design is completely ignored is compared with the usual Taylor’s series expansion method and with the modified Taylor procedure.

    Release date: 1989-12-15
  • 2. Analysis of sample survey data involving categorical response variables: Methods and software Archived
    Articles and reports: 12-001-X198900214569
    Description:

    During the past 10 years or so, rapid progress has been made in the development of statistical methods of analysing survey data that take account of the complexity of survey design. This progress has been particularly evident in the analysis of cross-classified count data. Developments in this area have included weighted least squares estimation of generalized linear models and associated Wald tests of goodness of fit and subhypotheses, corrections to standard chi-squared or likelihood ratio tests under loglinear models or logistic regression models involving a binary response variable, and jackknifed chisquared tests. This paper illustrates the use of various extensions of these methods on data from complex surveys. The method of Scott, Rao and Thomas (1989) for weighted regression involving singular covariance matrices is applied to data from the Canada Health Survey (1978-79). Methods for logistic regression models are extended to Box-Cox models involving power transformations of cell odds ratios, and their use is illustrated on data from the Canadian Labour Force Survey. Methods for testing equality of parameters in two logistic regression models, corresponding to two time points, are applied to data from the Canadian Labour Force Survey. Finally, a general class of polytomous response models is studied, and corrected chi-squared tests are applied to data from the Canada Health Survey (1978-79). Software to implement these methods using the SAS facilities on a main frame computer is briefly described.

    Release date: 1989-12-15
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  • 1. Logistic regression under complex survey designs Archived
    Articles and reports: 12-001-X198900214567
    Description:

    Estimation procedures for obtaining consistent estimators of the parameters of a generalized logistic function and of its asymptotic covariance matrix under complex survey designs are presented. A correction in the Taylor estimator of the covariance matrix is made to produce a positive definite covariance matrix. The correction also reduces the small sample bias. The estimation procedure is first presented for cluster sampling and then extended to more complex situations. A Monte Carlo study is conducted to examine the small sample properties of F-tests constructed from alternative covariance matrices. The maximum likelihood estimation method where the survey design is completely ignored is compared with the usual Taylor’s series expansion method and with the modified Taylor procedure.

    Release date: 1989-12-15
  • 2. Analysis of sample survey data involving categorical response variables: Methods and software Archived
    Articles and reports: 12-001-X198900214569
    Description:

    During the past 10 years or so, rapid progress has been made in the development of statistical methods of analysing survey data that take account of the complexity of survey design. This progress has been particularly evident in the analysis of cross-classified count data. Developments in this area have included weighted least squares estimation of generalized linear models and associated Wald tests of goodness of fit and subhypotheses, corrections to standard chi-squared or likelihood ratio tests under loglinear models or logistic regression models involving a binary response variable, and jackknifed chisquared tests. This paper illustrates the use of various extensions of these methods on data from complex surveys. The method of Scott, Rao and Thomas (1989) for weighted regression involving singular covariance matrices is applied to data from the Canada Health Survey (1978-79). Methods for logistic regression models are extended to Box-Cox models involving power transformations of cell odds ratios, and their use is illustrated on data from the Canadian Labour Force Survey. Methods for testing equality of parameters in two logistic regression models, corresponding to two time points, are applied to data from the Canadian Labour Force Survey. Finally, a general class of polytomous response models is studied, and corrected chi-squared tests are applied to data from the Canada Health Survey (1978-79). Software to implement these methods using the SAS facilities on a main frame computer is briefly described.

    Release date: 1989-12-15
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