1,720,976 research outputs found
The Aggregate Prediction Index and Non-Symmetrical Correspondence Analysis of Aggregate Data: The 2 X2 Table
No full textFeatures of the polynomial biplots for ordered contingency tables
No full textFor more than 20 years variants of correspondence analysis have arisen that accommodate for the structure of ordered categorical variables using orthogonal polynomials. When the visual display from this analysis is the biplot, projections linking the origin to the standard coordinate of each category is a common feature.
In the case when a column variable, say, consists of ordered categories, the biplot can be constructed so that their standard coordinate is determined using orthogonal polynomials which require a set of a priori scores that reflect the ordered structure of the categories. When the first two polynomials are used to construct the biplot they produce a configuration of standard coordinates that appear to be parabolic in shape.
This paper verifies the exact nature of this parabolic relationship and examines the various features of this configuration of points. Particular emphasis is given to the focus, vertex, intercepts and directrix of this relationship and we also briefly examine the impact of choosing different a priori scores on these features. The R function, parabola.exe(), used to perform these calculates is included as supplementary material to this paper
The prediction index of aggregate data
No full textThe analysis of the association between the two dichotomous variables of a 2 × 2 table arises as an important statistical issue in a number of diverse settings, such as in biomedical, medical, epidemiological, pharmaceutical or environmental research. When only the aggregate (or marginal) information is available, the analyst may determine the likely strength of the association between the variables. In this paper, we propose a new measure, called aggregate prediction index, that assesses the likely statistical significance of the association between the rows and columns of a 2 × 2 table where one variable is treated as a predictor variable and the other is treated as a response variable. Further insight into the predictor’s potential strength can be visually obtained by performing an asymmetric version of correspondence analysis and considering a biplot display of the two variables - this issue shall also be explored in light of the new index
Visualizing departures from symmetry. A study on cardiovascular risk among patients with diabetes.
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A European perception of food using two methods of correspondence analysis
No full textIn a recent issue of this journal, Guerrero et al. (2010) studied an interesting data set involving the analysis
of consumer-driven associations to the word ‘‘Traditional’’, from a food perspective, in six European
countries. As part of their analysis, they demonstrated the sources of association between the words
studied and the country of origin of those interviewed using correspondence analysis. In this paper,
we focus on this association by assuming that the country of origin is a predictor of the words associated
with ‘‘Traditional’’. This analysis is performed using another member of the correspondence analysis
family – non-symmetric correspondence analysis. This paper will also explore the use of both these
correspondence analysis techniques on their data and consider the dendrogram and the semantic differential
plot as alternative approaches to visually summarising the association
Visualising Departures from Symmetry and Bowker’s X2 Statistic
Full text linkSometimes, the same categorical variable is studied over different time periods or across
different cohorts at the same time. One may consider, for example, a study of voting behaviour of
different age groups across different elections, or the study of the same variable exposed to a child
and a parent. For such studies, it is interesting to investigate how similar, or different, the variable is
between the two time points or cohorts and so a study of the departure from symmetry of the variable
is important. In this paper, we present a method of visualising any departures from symmetry using
correspondence analysis. Typically, correspondence analysis uses Pearson’s chi-squared statistic as
the foundation for all of its numerical and visual features. In the case of studying the symmetry of
a variable, Bowker’s chi-squared statistic, presented in 1948, provides a simple numerical means
of assessing symmetry. Therefore, this paper shall discuss how a correspondence analysis can be
performed to study the symmetry (or lack thereof) of a categorical variable when Bowker’s statistic
is considered. The technique presented here provides an extension to the approach developed by
Michael Greenacre in 2000
Simple and multiple correspondence analysis for ordinal-scale variables using orthogonal polynomials
No full textCorrespondence analysis (CA) has gained a reputation for being a very useful statistical technique for determining the nature of association between two or more categorical variables. For simple and multiple CA, the singular value decomposition (SVD) is the primary tool used and allows the user to construct a low-dimensional space to visualize this association. As an alternative to SVD, one may consider the bivariate moment decomposition (BMD), a method of decomposition that involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, a hybrid decomposition (HD) is formed. The aim of this paper is to show the applicability of HD when performing simple and multiple CA.multiple correspondence analysis, ordinal-scale variables, singular value decomposition, bivariate moment decomposition, orthogonal polynomials, hybrid decomposition,
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