# A MONTE CARLO STUDY OF THE ROBUSTNESS OF CANONICAL CORRELATION UNDER VARYING SAMPLE DATA CONDITIONS

#### Abstract

The present research was done to investigate the behavior of Ordinary Least Square Canonical Correlation using monte carlo methodology under a wide range of data conditions. Specifically, it intended to analyze the effects of crude classification, variable/observation ratio and number of significant eigen values on the consistency of several canonical correlation interpretive criteria.^ Simulated population and sample correlation matrices were generated via a method outlined by Kaiser and Dickman (1962). In this study, four metric transformations, three variable/observation ratios and three target population correlation matrices (each with a unique number of eigenvalues) were chosen. Each of these conditions was crossed with the others thus producing 36 separate alterations. For each of these 36 conditions 50 replications were produced and for each replication three correlation matrices were created, a target population matrix, a sample matrix drawn from that population and a transformed sample. The distance between the canonical solution (loadings, variates, correlations) for the population matrix and the sample matrix were calculated and used as the dependent variables. Thus conditions which consistently produced greater distances between target and sample could be said to yield less reliable results.^ The outcome of the study revealed that variates, loadings and canonical correlations may behave as intuitively expected or anomalously depending on the manipulations. As was to be expected, the effect of subject to variable ratio on the ability of canonical correlation to extract a congruent solution was consistent. As the number of observations per variable increased, there were smaller differences between the target (i.e., population) and sample solutions. On the other hand, the effects of scale variations in the data and the number of significant roots in the population correlation matrix yielded more irregular patterns of results. It can be generally said that as the scale type became more restricted, (i.e., the data scale moved toward a dichotomy) the distances between the population and sample solutions became greater. The effect of the number of eigen roots was dependent, in large part, upon whether we looked at variates or loadings and canonical correlations. ^

#### Subject Area

Quantitative psychology

#### Recommended Citation

CARIFFE, GERARD ALBERT, "A MONTE CARLO STUDY OF THE ROBUSTNESS OF CANONICAL CORRELATION UNDER VARYING SAMPLE DATA CONDITIONS" (1987). *ETD Collection for Fordham University*. AAI8714592.

https://fordham.bepress.com/dissertations/AAI8714592