In this paper, generalized additive mixed models are constructed for the analysis of geographical and temporal variability of disease ratios. In this class of models, spatio–temporal models that use conditionally autoregressive smoothing across the spatial dimension and B-spline smoothing over the temporal dimension are considered. The frequentist analysis of these complex models is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning (DC) method provides a frequentist approach to mixed models and equally computationally convenient. We propose to use DC, which yields to maximum likelihood estimation, to conduct frequentist analysis of spatio–temporal modeling of disease ratios. The advantages of DC approach are that the non-estimable parameters are flagged automatically and prediction (and prediction intervals) of the smoothing incidence ratios over space and time are easily obtained. We illustrate this approach using a real dataset of yearly childhood asthma visits to hospital in the province of Manitoba, Canada, during 2000–2010. The performance of the DC approach is also studied through a simulation study. Copyright © 2013 John Wiley & Sons, Ltd.