Analysis

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.

The method of minimum Q^(T) estimation for complex survey designs proposed by Singh (1985) provides asymptotically efficient estimates of model parameters analogous to Neyman’s (1949) min X^2 estimation procedure for simple random samples. The Q^(T) can be viewed as a X^2 type statistic for categorical survey data, and min Q^(T) estimates provide a robust alternative to Weighted Least Squares estimates, which often display unstable behaviour for complex surveys. In this paper, the min Q^(T) method is first described and then illustrated for the problem of estimating parameters of a logit model for survey estimates of unemployment rates which are obtained from the October 1980 Canadian LFS data cross-classified according to age-education covariate categories. It is seen that the trace efficiency of smoothed estimates obtained by Kumar and Rao (1986), who applied the method of pseudo maximum likelihood estimates (pseudo mle) to the same problem can be slightly improved by the min Q^(T) method. Interestingly enough, pseudo mle for individual cells behave much the same way as the efficient min Q^(T) estimates for the particular LFS example.

Goodness of fit tests, tests for independence in a two-way contingency table, log-linear models and logistic regression models are investigated in the context of samples which are obtained from complex survey designs. Suggested approximations to the null distributions are reviewed and some examples from the Canada Health Survey and Canadian Labour Force Survey are given. Software implementation for using these methods is briefly discussed.

Standard chisquared (X^2) or likelihood ratio (G^2) tests for logistic regression analysis, involving a binary response variable, are adjusted to take account of the survey design. The adjustments are based on certain generalized design effects. The adjusted statistics are utilized to analyse some data from the October 1980 Canadian Labour Force Survey (LFS). The Wald statistic, which also takes the survey design into account, is also examined for goodness-of-fit of the model and for testing hypotheses on the parameters of the assumed model. Logistic regression diagnostics to detect any outlying cell proportions in the table and influential points in the factor space are applied to the LFS data, after making necessary adjustments to account for the survey design.

This study considers the suitability of composite estimation techniques for the Canadian Labour Force Survey. The performance of a class of AK composite estimators introduced initially by Gurney and Daly is investigated for several characteristics. While the ordinary composite estimate has a large bias, the AK composite estimate is capable of reducing the bias. Composite estimates having minimum variance and minimum mean square error are compared.

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.

The method of minimum Q^(T) estimation for complex survey designs proposed by Singh (1985) provides asymptotically efficient estimates of model parameters analogous to Neyman’s (1949) min X^2 estimation procedure for simple random samples. The Q^(T) can be viewed as a X^2 type statistic for categorical survey data, and min Q^(T) estimates provide a robust alternative to Weighted Least Squares estimates, which often display unstable behaviour for complex surveys. In this paper, the min Q^(T) method is first described and then illustrated for the problem of estimating parameters of a logit model for survey estimates of unemployment rates which are obtained from the October 1980 Canadian LFS data cross-classified according to age-education covariate categories. It is seen that the trace efficiency of smoothed estimates obtained by Kumar and Rao (1986), who applied the method of pseudo maximum likelihood estimates (pseudo mle) to the same problem can be slightly improved by the min Q^(T) method. Interestingly enough, pseudo mle for individual cells behave much the same way as the efficient min Q^(T) estimates for the particular LFS example.

Goodness of fit tests, tests for independence in a two-way contingency table, log-linear models and logistic regression models are investigated in the context of samples which are obtained from complex survey designs. Suggested approximations to the null distributions are reviewed and some examples from the Canada Health Survey and Canadian Labour Force Survey are given. Software implementation for using these methods is briefly discussed.

Standard chisquared (X^2) or likelihood ratio (G^2) tests for logistic regression analysis, involving a binary response variable, are adjusted to take account of the survey design. The adjustments are based on certain generalized design effects. The adjusted statistics are utilized to analyse some data from the October 1980 Canadian Labour Force Survey (LFS). The Wald statistic, which also takes the survey design into account, is also examined for goodness-of-fit of the model and for testing hypotheses on the parameters of the assumed model. Logistic regression diagnostics to detect any outlying cell proportions in the table and influential points in the factor space are applied to the LFS data, after making necessary adjustments to account for the survey design.

This study considers the suitability of composite estimation techniques for the Canadian Labour Force Survey. The performance of a class of AK composite estimators introduced initially by Gurney and Daly is investigated for several characteristics. While the ordinary composite estimate has a large bias, the AK composite estimate is capable of reducing the bias. Composite estimates having minimum variance and minimum mean square error are compared.