A method for estimation of generalized linear models when explanatory variables contain meaurement error

Graduation date: 1990This thesis considers the problem of estimating the linear\ud parameters of generalized linear models (GLM), especially binomial\ud and Poisson regression models, when the explanatory variable is\ud subject to measurement error. In this situation, the dependence of\ud the response variable on the observed explanatory variable cannot\ud typically be modeled as a GLM; in particular, extra variability\ud caused by measurement error cannot be accounted for using the\ud binomial- or Poisson models. One strategy is to use existing methods\ud adapted for extra-variability. The contribution of this thesis is to\ud introduce an estimation method which makes use of Efron's (1986)\ud double exponential family. The proposed method involves the\ud calculation of maximum likelihood estimates from this density when it\ud is used as an approximation to the true density of the response\ud variables given the observed measurements.\ud Efron's family of distributions offers an attractive alternative\ud for approximating the distribution of the response variable given the\ud observed explanatory variable and is closely related to the\ud measurement error in GLM methods suggested by Armstrong (1985) and\ud Prentice (1986). Properties of the proposed method are considered\ud when the double exponential family model is thought to be correct and\ud when it is thought to be an approximation. Special cases and\ud examples are given to illustrate the estimation procedure and how to\ud apply this method. Comparisons are made with other estimation\ud procedures for the measurement error problem, both procedurally and\ud numerically