Canonical Correlation Analysis: A Step-by-Step Example in Commonly Available Software

Canonical Correlation Analysis (CCA) can be conceptualized as a multivariate regression involving multiple outcome variables. CCA compares two sets of variables and is the second-most general application of the General Linear Model (GLM) following Structural Equation Modeling. Structural Equation Modeling software have made conducting CCA feasible for researchers in numerous and disparate disciplines. SPSS and AMOS are two commonly used statistical software packages and both can conduct CCAs. AMOS is particularly useful because it enables statistical significance testing of individual canonical correlations. This article provides background knowledge of CCA as part of the GLM and provides step-by-step instructions for conducting a CCA in AMOS. he general linear model (GLM) comprises an overwhelming majority of parametric statistical procedures. Regression is the univariate GLM (Cohen, 1968) and canonical correlation analysis (CCA) is the multivariate GLM (Knapp, 1978). The GLM includes the t-test, ANOVA and other OVA procedures, descriptive discriminate analysis, CCA and structural equation modeling GLM procedures are defined by the fact that they a) create weights applied to measured variables to construct synthetic variables, b) are correlational and c) provide analogues of the r Although univariate methods can be done in both CCA and SEM due to the hierarchical nature of the GLM, typically CCA and SEM focus on multivariate analyses. Multivariate procedures are crucial to the behavioral sciences for several reasons. Arguably the biggest reason is that multivariate methods honor Human behavior is complex and has multiple causes and multiple finalities. Multivariate statistical procedures can aid in bridging the gap between the theoretical and practical world of behavioral sciences. Multivariate methods provide valuable information that univariate methods simply cannot (Thompson, 1985). Another major reason for use of multivariate procedures is that it keeps Type I error to a minimum Experimentwise Type I error rate grows considerably the more statistical tests are conducted on the same dataset (as an example, running multiple post hoc test in ANOVA inflates the experimentwise error rate unless a correction procedure is used to adjust testwise alpha levels). Multivariate methods such as CCA and SEM protect against this inflation. There are three main purposes of this article. The first is to provide the reader with a brief background on CCA. Thompson (1985) pointed out that CCA is becoming more and more popular as an analysis tool in different disciplines. Illustrating that CCA can be done in SEM will also help the reader understand the connection of …