Different Nonlinear Regression Models with Incorrectly Observed Covariates

We present quasi-likelihood models for different regression
problems when one of the explanatory variables is measured with
heteroscedastic error. In order to derive models for the observed
data the conditional mean and variance functions of the regression
models are only expressed through functions of the observable
covariates. The latent covariable is treated as a random variable
that follows a normal distribution. Furthermore it is assumed that
enough additional information is provided to estimate the
individual measurement error variances, e.g. through replicated
measurements of the fallible predictor variable. The discussion
includes the polynomial regression model as well as the probit and
logit model for binary data, the Poisson model for count data and
ordinal regression models.