A predicted value, or fitted value, of the mean corresponding to the vector of covariates is given by
where g is the link function, regardless of whether corresponds to an observation or not. That is, the response variable can be missing and the predicted value is still computed for valid . In the case where does not correspond to a valid observation, is not checked for estimability. You should check the estimability of in this case in order to ensure the uniqueness of the predicted value of the mean. If there is an offset, it is included in the predicted value computation.
Approximate confidence intervals for predicted values of the mean can be computed as follows. The variance of the linear predictor is estimated by
where is the estimated covariance of . The robust estimate of the covariance is used for in the case of models fit with GEEs.
Approximate confidence intervals are computed as
where is the percentile of the standard normal distribution and g is the link function. If either endpoint in the argument is outside the valid range of arguments for the inverse link function, the corresponding confidence interval endpoint is set to missing.