Ordinal Data

Scrutiny for presage is the era of advance statistics where accuracy matter the most. Commensurate between algorithms with statistical implementation provides better consequence in terms of accurate prediction by using data sets. Prolific usage of algorithms lead towards the simplification of mathematical models, which provide less manual calculations. Presage is the essence of data science and machine learning requisitions that impart control over situations. Implementation of any dogmas require proper feature extraction which helps in the proper model building that assist in precision. This paper is predominantly based on different statistical analysis which includes correlation significance and proper categorical data distribution using feature engineering technique that unravel accuracy of different models of machine learning algorithms.

ABSTRACT Fully nonparametric analysis of covariance with two and three covariates is considered. The approach is based on an extension of the model of Akritas et al. (Biometrika 87(3) (2000) 507). The model allows for possibly nonlinear covariate effect which can have different shape in different factor level combinations. All types of ordinal data are included in the formulation. In particular, the response distributions are not restricted to comply to any parametric or semiparametric model. In this nonparametric model, hypotheses of no main effect no interaction and no simple effect, which adjust for the covariate values, are defined through a decomposition of the conditional distribution functions of the response given to the factor level combination and covariate values. The test statistics are based on averages over the covariate values of certain Nadaraya-Watson regression quantities. Under their respective null hypotheses, such test statistics are shown to have a central [chi]2 distribution. Small sample corrections are also provided. Simulation results and the analysis of two real datasets are also presented.

Deciding on the best statistical method to apply when the response variable is ordinal is essential because the way the categories are ordered in the data is relevant as it could change the results of the analysis. Although the models for continuous variables have similarities to those for ordinal variables, this paper presents the advantages of the use of the ordering information on the outcomes with methods developed for modeling ordinal data such as the ordered stereotype model. The novelty of this article lies in showing the dangers of assigning equally spaced scores to ordered response categories in statistical analysis, which are illustrated with a simulation study and a case study. We propose a new way to use the score parameters, which incorporates the fitted spacing dictated by the data. Additionally , this article uses score parameter estimates in the ordered stereotype model to propose a new measure to calculate continuous medians in the raw data: the adjusted c-median. It benefits the general audience who can easily understand the median as a summary statistic.

We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear extensions of partially ordered sets specified by the data. Our methods refine rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for the exploratory analysis of ordinal data. Convex rank tests correspond to probabilistic conditional independence structures known as semi-graphoids. Submodular rank tests are classified by the faces of the cone of submodular functions, or by Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Graphical tests correspond to both graphical models and to graph associahedra, and they have excellent statistical and algorithmic properties.

Capitalizing on the company's knowledge in the context of decision making is increasingly being recognized in the industrial environment since the process of capitalizing which surfaces tacit knowledge [Nonaka and Takeuchi, 1995], that is often not explicit, has been considered crucial for improving decisions and their resultant outcomes [Prusak, 1997]. As said by [Noh et al., 2000; Eisenhardt, 1989] "tacit knowledge is quite beneficial to a faster decision making process". Thus, companies must invest in engineering methods and tools in order to preserve the knowledge related to the decision making process in the design project. Such knowledge must be used by them to solve similar problems. To minimize these investments, they must identify the so called "crucial knowledge", that is, the most valuable knowledge to be preserved into corporate memory. In addition, as pointed out by Rose Dieng, "identification of crucial knowledge in organization has an infl...

We propose a new approach to inference for ordinal out- comes of dimension k. This is done by means of a mix- ture of multivariate probits model on latent scores. The model can be used for the cell probabilities of any k- dimensional contingency table. Our method achieves two main goals. First, the model allows arbitrarily ac- curate approximation of

The aim of this study was describe functional faunal assemblages occurring in streams with high influence of urbanization in USA and Brazil to answer the question whether similar biological traits of fish assemblages would be found between streams with high influence of urbanization in USA and Brazil. We compiled data on the structure and composition of freshwater fishes in 46 urban streams in the USA and 10 urban streams in Brazil. Data on functional traits was established in accordance with ordinal data on abundance. Cluster analysis was conducted to examine relationships among species composition across all sites sampled and to uncover patterns in functional traits of the fish assemblages by nonmetric multidimensional scaling (NMS). The cluster analysis separated the biogeographic regions in relation to the fish fauna composition. However, the ordination analysis (NMS) did not reveal differences between functional traits in Brazil and USA urban fish assemblages, suggesting functional similarity of very disparate zoogeographic assemblages.

ABSTRACT Latent variable models with observed ordinal variables are particularly useful for analyzing survey data. Typical ordinal variables express attitudinal statements with response alternatives like “strongly disagree”, “disagree”, “strongly agree” or “very dissatisfied”, “dissatisfied”, “satisfied” and “very satisfied”.

The most popular ways to test for independence of two ordinal random variables are by means of Kendall's tau and Spearman's rho. However, such tests are not consistent, only having power for alternatives with "monotonic" association. In this paper, we introduce a natural extension of Kendall's tau, called τ^*, which is non-negative and zero if and only if independence holds, thus leading to a consistent independence test. Furthermore, normalization gives a rank correlation which can be used as a measure of dependence, taking values between zero and one. A comparison with alternative measures of dependence for ordinal random variables is given, and it is shown that, in a well-defined sense, τ ^* is the simplest, similarly to Kendall's tau being the simplest of ordinal measures of monotone association. Simulation studies show our test compares well with the alternatives in terms of average p-values.

The psychometric properties of the Refractive Status and Vision Profile (RSVP) questionnaire were evaluated using Rasch analysis. Ninety-one myopic patients from a refractive surgery clinic and general optometric practice completed the RSVP. Rasch analysis of the RSVP ordinal data was performed to examine for unidimensionality and item reduction. The traditional Likert-scoring system was compared with a Rasch-scored RSVP and a reduced item Rasch-scored RSVP. Rasch analysis of the original RSVP showed poor targeting of item difficulty to patient quality of life, items with a ceiling effect and underutilized response categories. Combining the underutilized response scales and removal of redundant and misfitting items improved the internal consistency and targeting of the RSVP, and the reduced 20-item Rasch scored RSVP showed greater relative precision over standard Likert scoring in discriminating between the two subject groups. A Rasch scaled quality of life questionnaire is recommen...

Population pharmacokinetics (PK)/pharmacodynamics analysis is considered as an important component of drug development process in these days. Owing to different standardization techniques in different laboratories, the drug concentrations in blood are reported in intervals in which they lie. For obvious reason the outcomes are then recorded as multiple discrete indicators with natural ordering. But in view of the reduced amount of information, the modeling of such data becomes intrinsically more difficult than that of continuous data. The primary concern in this study is to analyze a one-compartmental PK model for ordinal data that can be used to describe the change in the concentration of drug over time. A flexible Monte Carlo EM-based two-step estimation method is proposed. Such a method is, in general, capable of analyzing a reasonably wide class of nonlinear mixed models. The modeling strategy is applied to a Phase I study of the drug Divalproex and its metabolite, developed for the treatment of epilepsy. The model's performance is evaluated through simulation. Copyright © 2008 John Wiley & Sons, Ltd.

In the food industry, sensory analysis can be useful to direct marketing decisions concerning not only products, for example product positioning with respect to competitors, but also market segmentation, customer relationship management, advertising strategies and price policies. In this paper we show how interesting information useful for marketing management can be obtained by combining the results from cub models and algorithmic data mining techniques (specifically, variable importance measurements from Random Forest). A case study on sensory evaluation of different varieties of Italian espresso is presented.