Using covariates in loglinear models with sampling zeros; A cautionary note

When analyzing loglinear models, most computer packages will first construct the contingency table and subsequently fit the required loglinear model. Some computer packages allow the incorporation of covariates, such as age and/or income, into the loglinear model. In the SPSS modules LOGLINEAR and GENLOG this option is implemented by calculating for each pattern of the classifying variables the mean value(s) of the covariate(s), while this covariate vector is subsequently added to the design matrix describing the loglinear model. In this article it is shown that the use of covariates in the case of contingency tables containing sampling zeros will lead to incorrect results for the SPSS modules LOGLINEAR and GENLOG. Parameter estimates, deviances and the number of degrees of freedom may be highly incorrect. This is illustrated in the case of the loglinear uniform association model, using an example from a handbook on categorical data analysis. A second, more complex example is discussed where, as a result of this incorrect handling of covariates, wrong results have been published in the literature. It is concluded that (conditional) multinomial logit models should be used. While SPSS currently does not include such models, it is demonstrated how to obtain correct results for the case that covariates are functions of the classifying variables.