Model-Based Clustering for Manifest Variables of Mixed Type

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Data sets containing mixtures of categorical and continuous variables arise frequently in practice. Various simple approaches to the analysis of such data sets are possible: arbitrary categorization of all the continuous variables followed by analysis using standard methods for categorical data, or arbitrarily scoring all the categorical variables and then using standard methods for continuous data, or analyzing the categorical variables and the continuous variables separately (each by standard methods) and then attempting to combine the two sets of results. None of these options seem satisfactory for comprehensive analysis of the data. The first approach loses information in the categorization of continuous variables, the second introduces subjectivity with the numerical scoring adopted, while the third ignores any associations existing between the categorical and the continuous variables. A much more satisfactory general approach is first to specify a parametric model for mixed variables, then to fit the model to the data at hand and finally to use the parameter estimates for drawing inferences. A 'parametric model' here means a suitable joint probability distribution for categorical variables and continuous variables. Two areas where the benefits of this work will be immediately realized are bioinformatics and sensory evaluation.