Archetypal analysis for ordinal data

Archetypal Analysis of Interval Data

In this paper we present a mathematical model for archetypal analysis of data represented by means of intervals of real numbers. We extend the model for single-valued data proposed in the pioneering work of Cutler and Breiman on this topic. The core problem is a non-convex optimization one, which we solve by means of a sequential quadratic programming method. We show numerical experiments perfo...

Archetypal Analysis of Cellular Flame Data

The application of archetypal analysis to high-dimensional data arising from video-taped images is presented. A hybrid principal components/archetypes technique has been developed to overcome the difficulties of applying archetypes to data sets with points living in a space of dimension higher than about 500. The advantages of the method lie in the creation of patterns typical of the set as a w...

Ordinal longitudinal data analysis

Growth data and longitudinal data in general are often of an ordinal nature. For example, developmental stages may be classified into ordinal categories and behavioral variables repeatedly measured by discrete ordinal scales. Consider the data set presented in Table 15.1. This table contains information on marijuana use taken from five annual waves (1976–80) of the National Youth Survey (Elliot...

Modeling Paired Ordinal Response Data

 About 25 years ago, McCullagh proposed a method for modeling univariate ordinal responses. After publishing this paper, other statisticians gradually extended his method, such that we are now able to use more complicated but efficient methods to analyze correlated multivariate ordinal data, and model the relationship between these responses and host of covariates. In this paper, we aim to...

Ordinal and symbolic data analysis