Canonical correlation analysis: uses and interpretation by Bruce Thompson

By Bruce Thompson

Contemporary advances in statistical technique and computing device automation are making canonical correlation research to be had to increasingly more researchers. This quantity explains the elemental positive aspects of this subtle procedure in an primarily non-mathematical creation that provides a variety of examples. Thompson discusses the assumptions, common sense, and value trying out strategies required via this research, noting traits in its use and a few lately built extensions.

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The theory is then briefly reviewed and is demonstrated by an example in which canonical variates for discriminating between three groups of psychiatric patients are set up using four dichotomous variables. But canonical analysis involving variables with different levels of scale may inherently violate to some degree the third assumption for the use of the technique. Of course, the more common use of canonical methods with intervally scaled variables also may or may not involve more serious violations of this assumption.

Most computer software packages now include a routine for performing canonical analysis. Canonical correlation analysis is employed to study relationships between two variable sets when each variable set consists of at least two variables. Thus Table 1 presents the data for what is the simplest canonical case, since only two criterion variables, X and Y, and only two predictor variables, A and B, are involved. 06) NOTE: Z-score equivalents of the unstandardized data are presented in parentheses.

300, or the index coefficient for the variable X on the first of the two possible canonical functions. the grasp of some researchers. For example, for this data set the matrix algebra formula for the criterion variable structure coefficients is where R is the symmetric intraset correlation matrix involving the two criterion variables, W is the matrix of the two criterion variables' function coefficients, and S is the matrix of the two criterion variables' structure coefficients. However, structure coefficients (and other canonical coefficients) can be both computed and conceptualized in simpler bivariate terms.

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