Generating Factor Variables for Asymmetry, Non-independence and Skew-symmetry Models in Square Contingency Tables using SAS

In this paper, a SAS program (macro) is written to generate factor and regression variables required for implementing asymmetry, non-independence, non-symmetry + independence models as well as skew-symmetry models in discussed in square a x a contingency tables having nominal or ordinal categories. While several authors have developed similar factor variables for use with GLIM, we have extended this to the non-independence and the non-symmetry+independence models. The former includes both the fixed and variable distance models as well as the quasi-ordinal symmetry model. Further, our implementation of the asymmetry model in terms of the required factor variable is different from those defined for implementation of same in GLIM. Most of the models described in this paper however assume ordinal categories for the contingency table. The SAS macro developed can be applied to any square table of dimension a. We apply the models discussed in this paper to the 5 x 5 Danish mobility data that have been widely analyzed in various literatures.

Comparison of methods in the analysis of dependent ordered catagorical data

Rating scales for outcome variables produce categorical data which are often ordered and measurements from rating scales are not standardized. The purpose of this study is to apply commonly used and novel methods for paired ordered categorical data to two data sets with different properties and to compare the results and the conditions for use of these models. The two applications consist of a data set of inter-rater reliability and a data set from a follow-up evaluation of patients. Standard measures of agreement and measures of association are used. Various loglinear models for paired categorical data using properties of quasi-independence and quasi-symmetry as well as logit models with a marginal modelling approach are used. A nonparametric method for ranking and analyzing paired ordered categorical data is also used. We show that a deeper insight when it comes to disagreement and change patterns may be reached using the nonparametric method and illustrate some problems with standard measures as well as parametric loglinear and logit models. In addition, the merits of the nonparametric method are illustrated.Agreement:ordinal data; ranking; reliability.rating scales

Measure of Departure from Marginal Average Point-Symmetry for Two-Way Contingency Tables

For the analysis of two-way contingency tables with ordered categories, Yamamoto, Tahata, Suzuki, and Tomizawa (2011) considered a measure to represent the degree of departure from marginal point-symmetry. The maximum value of the measure cannot distinguish two kinds of marginal complete asymmetry with respect to the midpoint. A measure is proposed which can distinguish two kinds of marginal asymmetry with respect to the midpoint. It also gives large-sample confidence interval for the proposed measure

An Overview of Methods in the Analysis of Dependent ordered catagorical Data: Assumptions and Implications

Subjective assessments of pain, quality of life, ability etc. measured by rating scales and questionnaires are common in clinical research. The resulting responses are categorical with an ordered structure and the statistical methods must take account of this type of data structure. In this paper we give an overview of methods for analysis of dependent ordered categorical data and a comparison of standard models and measures with nonparametric augmented rank measures proposed by Svensson. We focus on assumptions and issues behind model specifications and data as well as implications of the methods. First we summarise some fundamental models for categorical data and two main approaches for repeated ordinal data; marginal and cluster-specific models. We then describe models and measures for application in agreement studies and finally give a summary of the approach of Svensson. The paper concludes with a summary of important aspects.Dependent ordinal data; GEE; GLMM; Logit; modelling

A review of agreement measure as a subset of association measure between raters

Agreement can be regarded as a special case of association and not the other way round. Virtually in all life or social science researches, subjects are being classified into categories by raters, interviewers or observers and both association and agreement measures can be obtained from the results of this researchers. The distinction between association and agreement for a given data is that, for two responses to be perfectly associated we require that we can predict the category of one response from the category of the other response, while for two response to agree, they must fall into the identical category. Which hence mean, once there is agreement between the two responses, association has already exist, however, strong association may exist between the two responses without any strong agreement. Many approaches have been proposed by various authors for measuring each of these measures. In this work, we present some up till date development on these measures statistics

Extended asymmetry model based on logit transformation and decomposition of symmetry for square contingency tables with ordered categories

The issues of symmetry (or asymmetry) arises naturally for the analysis of square contingency tables. Many existing asymmetry models do not have the constraints on the main diagonal cells. Thus, the observations on the main diagonal cells do not contribute to the likelihood ratio chi-squared test statistics. Herein we propose a model that indicates the asymmetry for the log odds.It can utilize the information in the main diagonal cells. Also, the symmetry model is separated into some models including the proposed model

Exact Approaches for Bias Detection and Avoidance with Small, Sparse, or Correlated Categorical Data

Every day, traditional statistical methodology are used world wide to study a variety of topics and provides insight regarding countless subjects. Each technique is based on a distinct set of assumptions to ensure valid results. Additionally, many statistical approaches rely on large sample behavior and may collapse or degenerate in the presence of small, spare, or correlated data. This dissertation details several advancements to detect these conditions, avoid their consequences, and analyze data in a different way to yield trustworthy results. One of the most commonly used modeling techniques for outcomes with only two possible categorical values (eg. live/die, pass/fail, better/worse, ect.) is logistic regression. While some potential complications with this approach are widely known, many investigators are unaware that their particular data does not meet the foundational assumptions, since they are not easy to verify. We have developed a routine for determining if a researcher should be concerned about potential bias in logistic regression results, so they can take steps to mitigate the bias or use a different procedure altogether to model the data. Correlated data may arise from common situations such as multi-site medical studies, research on family units, or investigations on student achievement within classrooms. In these circumstance the associations between cluster members must be included in any statistical analysis testing the hypothesis of a connection be-tween two variables in order for results to be valid. Previously investigators had to choose between using a method intended for small or sparse data while assuming independence between observations or a method that allowed for correlation between observations, while requiring large samples to be reliable. We present a new method that allows for small, clustered samples to be assessed for a relationship between a two-level predictor (eg. treatment/control) and a categorical outcome (eg. low/medium/high)