Homogeneity analysis, or multiple correspondence analysis, is usually applied to k separate variables. In this paper we apply it to sets of variables by using sums within sets. The resulting technique is called OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consist of three types: nominal, ordinal, and numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of OVERALS. An application to data from an epidemiological survey is presented.

We discuss a variety of methods for quantifying categorical multivariate data. These methods have been proposed in many different countries, by many different authors, under many different names. In the first major section of the paper we analyze the many different methods and show that they all lead to the same equations for analyzing the same data. In the second major section of the paper we introduce the notion of a duality diagram, and use this diagram to synthesize the many superficially different methods into a single method.

We propose a method to reduce many categorical variables to one variable with k categories, or stated otherwise, to classify n objects into k groups. Objects are measured on a set of nominal, ordinal or numerical variables or any mix of these, and they are represented as n points in p-dimensional Euclidean space. Starting from homogeneity analysis, also called multiple correspondence analysis, the essential feature of our approach is that these object points are restricted to lie at only one of k locations. It follows that these k locations must be equal to the centroids of all objects belonging to the same group, which corresponds to a sum of squared distances clustering criterion. The problem is not only to estimate the group allocation, but also to obtain an optimal transformation of the data matrix. An alternating least squares algorithm and an example are given.

This paper aims to investigate the relationship between teacher's personality types, emotional intelligence and burnout and to predict the burnout levels of 147 teachers in the city of Mashhad (Iran). To this end, we have used three inventories: Maslach Burnout Inventory (MBI), NEO Five Factor Inventory (NEO-FFI), and Emotional Quotient Inventory (EQ-I). We used Homogeneity Analysis and Multiple Linear Regression to analyze the data. The results exhibited a significant relationship between personality types and emotional intelligence and the three dimensions of burnout. It was indicated that the best predictors for emotional exhaustion were neuroticism and extroversion, for depersonalization were intrapersonal scale of emotional intelligence and agreeableness, and for personal accomplishment were interpersonal scale and conscientiousness. Finally, the results were discussed in the context of teacher burnout.