Model-Based Clustering for Manifest Variables of Mixed Type

包含分类变量和连续变量混合的数据集在实践中经常出现。分析这些数据集的各种简单方法都是可能的：对所有连续变量进行任意分类，然后使用标准方法对分类数据进行分析，或者对所有分类变量进行任意评分，然后使用标准方法对连续数据进行分析，或者分别分析分类变量和连续变量（分别使用标准方法），然后尝试将两组结果结合起来。对于数据的全面分析，这些选择似乎都不令人满意。第一种方法在连续变量的分类中丢失了信息，第二种方法通过采用数值评分引入了主观性，而第三种方法忽略了分类变量与连续变量之间存在的任何关联。一种更令人满意的一般方法是首先为混合变量指定一个参数模型，然后将模型拟合到手头的数据中，最后使用参数估计进行推断。这里的“参数模型”是指适合于分类变量和连续变量的联合概率分布。这项工作的好处将立即实现的两个领域是生物信息学和感官评估。

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.