Quality & Quantity 34: 137–152, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Estimated Precision for Predictions from
Generalized Linear Models in
TIM FUTING LIAO
Department of Sociology, University of Illinois, 326 Lincoln Hall, 702 S. Wright Street, Urbana, IL
Abstract. In this paper I present a general method for constructing conﬁdence intervals for predic-
tions from the generalized linear model in sociological research. I demonstrate that the method used
for constructing conﬁdence intervals for predictions in classical linear models is indeed a special case
of the method for generalized linear models. I examine four such models – the binary logit, the binary
probit, the ordinal logit, and the Poisson regression model – to construct conﬁdence intervals for
predicted values in the form of probability, odds, Z score, or event count. The estimated conﬁdence
interval for an event prediction, when applied judiciously, can give the researcher useful information
and an estimated measure of precision for the prediction so that interpretation of estimates from the
generalized linear model becomes easier.
Key words: generalized linear models, conﬁdence intervals, predictions, social science methods,
logit analysis, Poisson regression.
Predicted values provide a useful way for interpreting statistical models analyzing
response probabilities in sociological research. The usual logit analysis models
event probability while the Poisson regression models event count. Alternatively,
they can all be seen as members of the family of the generalized linear model
(GLM) because of their similarities in properties such as linearity in the systematic
component of the model (McCullagh and Nelder, 1989; Nelder and Wedderburn,
Despite the popularity of predicted probabilities from logit and probit models in
empirical sociological research, little systematic discussion exists in the literature
about their statistical precision (with the exceptions to be discussed later). In this
paper, I discuss a simple method for constructing approximate conﬁdence intervals
for predictions from the GLM. The method is a natural application of the theory of
the GLM based on some of its known properties.
Although in theory one can mathematically solve for the variance of a prediction
by treating the prediction as a function of the variances and covariances of the