![]() Analogously, column profiles are the relative frequencies of the different countries within each language. In our example, the average row profile shows that, when pooling across countries, English is the dominant primary language while Spanish is the least common. In CA, the average row profile is called the “centroid” of the row variable. The average row profile, presented in the bottom row of Table 2 is the average of the row profiles weighted by the marginal row frequencies, or equivalently, the marginal frequency distribution over the sum of the rows. For example, among the 1,000 fictitious respondents from Switzerland, German is the most common primary language spoken (64.8%) followed by French (22.2%), Italian (9.5%), Spanish (2.0%) and English (1.5%). Row profiles correspond to the relative frequencies of the different languages spoken within each country surveyed. All analyses were conducted using the PROC CORRESP procedure in SAS 9.1.3, Cary, NC, USA.ĬA is based on the analysis of the contingency table through the row and column profiles ( Table 2). For complete MCA results in this frailty study, please see Sourial et al (2009) ( MS Ref 08-216). We also illustrate the use of Multiple Correspondence Analysis (MCA), an extension of CA, using data on several binary variables from a study on frailty in the elderly. In this paper, we describe the use of CA through a simple example of two nominal variables. The value of CA is perhaps most demonstrable in applications to nominal variables for which few alternative analytical methods exist. CA is a versatile technique in part because no underlying distributional assumptions are required, thus accommodating any type of categorical variable whether binary, ordinal or nominal. The primary goal of CA is to illustrate the most important relationships among the variables’ response categories using a graphical representation. This technique preserves the categorical nature of the variables since the analysis is conducted at the level of the response categories themselves rather than at the variable level. One technique that is designed specifically for the analysis of categorical variables and which is not yet widely used in epidemiological research is correspondence analysis (CA). Moreover, the results of the multivariate analysis do not exploit the individual response categories of the categorical variables. These coefficients assume that both variables are dichotomized continuous variables with underlying bivariate normal distribution. An extension to FA has been proposed for binary and ordinal variables by using the tetrachoric and polychoric correlation coefficient, respectively. These techniques were, however, designed for use with continuous variables and utilize the Pearson correlation coefficient as the measure of association. An alternative approach is to employ a multivariate approach to explore these relationships simultaneously.Ĭommonly used exploratory multivariate techniques include principal components analysis (PCA) and factor analysis (FA) which are frequently used in the validation of scales and syndromes, e.g. Moreover, it would not provide us with a global picture of the salient relationships among these variables when taken together. More importantly, such an approach would reveal only that a relationship exists but not which response categories are related. For a large number of categorical variables, however, this pairwise strategy would quickly become cumbersome and render the results difficult to summarize. ![]() One might consider conducting separate chi-square tests one for each pair of variables, or, in the case of binary or ordinal variables, a correlation matrix of the bivariate relationships could be viewed. Researchers are often interested in exploring the relationships among such sets of categorical variables. For example, “Has a doctor ever told you that you have heart disease?”, “How would you rate your health?”, “What is your marital status?”. Much of these data are collected through questionnaires in which many questions have categorical response options, either binary, ordinal or nominal. In epidemiological studies, researchers often collect large amounts of data on study participants. ![]()
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