Ordinal regression

About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.

Assessing the correspondence of one or more vectors to a symmetric matrix using ordinal regression

Abstract: A statistical model for interpreting psychological scaling research, based on the heuristic work of Reynolds (1983), is developed. This new approach has certain advantages over the standard property fitting approach (Chang and Carroll, 1969) currently used to interpret multidimensional scaling spaces (Shepard, 1962; Torgerson, 1965). These advantages are (a) the ability to directly assess the correspondence of a descriptor vector(s) to a symmetric matrix, and (b) to provide a method in which only ordinal properties of such descriptors are required: thus standard rating, ranking, or sorting data collection methods can be used as the basis to interpret the multidimensional space resulting from the distance data.

Ordinal classification for efficient plant stress prediction in hyperspectral data

Abstract: . Detection of crop stress from hyperspectral images is of high importance for breeding and precision crop protection. However, the continuous monitoring of stress in phenotyping facilities by hyperspectral imagers produces huge amounts of uninterpreted data. In order to derive a stress description from the images, interpreting algorithms with high prediction performance are required. Based on a static model, the local stress state of each pixel has to be predicted. Due to the low computational complexity, linear models are preferable. In this paper, we focus on drought-induced stress which is represented by discrete stages of ordinal order. We present and compare five methods which are able to derive stress levels from hyperspectral images: One-vs.-one Support Vector Machine (SVM), one-vs.-all SVM, Support Vector Regression (SVR), Support Vector Ordinal Regression (SVORIM) and Linear Ordinal SVM classification. The methods are applied on two data sets - a real world set of drought stress in single barley plants and a simulated data set. It is shown, that Linear Ordinal SVM is a powerful tool for applications which require high prediction performance under limited resources. It is significantly more efficient than the one-vs.-one SVM and even more efficient than the less accurate one-vs.-all SVM. Compared to the very compact SVORIM model, it represents the senescence process much more accurate.

Robust Estimation for Ordinal Regression

Abstract: Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.

Simple Correspondence Analysis of Nominal-Ordinal Contingency Tables

Abstract: The correspondence analysis of a two-way contingency table is now accepted as a very versatile tool for helping users to understand the structure of the association in their data. In cases where the variables consist of ordered categories, there are a number of approaches that can be employed and these generally involve an adaptation of singular value decomposition. Over the last few years, an alternative decomposition method has been used for cases where the row and column variables of a two-way contingency table have an ordinal structure. A version of this approach is also available for a two-way table where one variable has a nominal structure and the other variable has an ordinal structure. However, such an approach does not take into consideration the presence of the nominal variable. This paper explores an approach to correspondence analysis using an amalgamation of singular value decomposition and bivariate moment decomposition. A benefit of this technique is that it combines the classical technique with the ordinal analysis by determining the structure of the variables in terms of singular values and location, dispersion and higher-order moments.

A latent variable model for mixed continuous and ordinal responses with nonignorable missing responses: Assessing the local influence via covariance structure

Abstract: A joint model for mixed ordinal and continuous responses, with missing values in both variables, and their missing mechanisms is proposed. Full likelihood-based approach that yields maximum likelihood estimates of the model parameters is used. For data with missing responses in both variables some modified Pearson residuals are also proposed. A common way to investigte if perturbations of model components influence key results of the analysis is to compare the results derived from the original and perturbed models using an influence graph. For this, influence of a small perturbation of elements of the covariance structure of the model on likelihood displacement is also studied. The model is illustrated using data from a foreign language achievement study.