Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-042413-141749

Document Typethesis
Author NameWang, Jie
TitleIncorporating survey weights into logistic regression models
DepartmentMathematical Sciences
  • Balgobin Nandram, Advisor
  • Keywords
  • Quasi-likelihood
  • Adjusted weights
  • Multinomial logistic regression
  • Binary logistic regression
  • Sampling weights
  • Date of Presentation/Defense2013-04-22
    Availability unrestricted


    Incorporating survey weights into likelihood-based analysis is a controversial issue because the sampling weights are not simply equal to the reciprocal of selection probabilities but they are adjusted for various characteristics such as age, race, etc. Some adjustments are based on nonresponses as well. This adjustment is accomplished using a combination of probability calculations. When we build a logistic regression model to predict categorical outcomes with survey data, the sampling weights should be considered if the sampling design does not give each individual an equal chance of being selected in the sample. We rescale these weights to sum to an equivalent sample size because the variance is too small with the original weights. These new weights are called the adjusted weights. The old method is to apply quasi-likelihood maximization to make estimation with the adjusted weights. We develop a new method based on the correct likelihood for logistic regression to include the adjusted weights. In the new method, the adjusted weights are further used to adjust for both covariates and intercepts. We explore the differences and similarities between the quasi-likelihood and the correct likelihood methods. We use both binary logistic regression model and multinomial logistic regression model to estimate parameters and apply the methods to body mass index data from the Third National Health and Nutrition Examination Survey. The results show some similarities and differences between the old and new methods in parameter estimates, standard errors and statistical p-values.

  • JieWang.docx

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