A Monte Carlo Study of the Stability of Canonical Correlations, Canonical Weights and Canonical Variate-Variable Correlations

Abstract

A Monte Carlo study was run to check the stability of canonical correlations, canonical weights, and canonical variate-variable correlations. Eight data matrices were selected from the literature for the canonical analyses, with the number of variables ranging from 7 to 41. The results showed that the canonical correlations are very stable upon replication. The results also indicated that there is no solid evidence for concluding that the components are superior to the coefficients, a t least not in terms of being more reliable. However, the number of subjects per variable necessary to achieve re1i:tbility in detecting the most important variables, using components or coefficients, was quite large, ranging from 42/1 to 68/1.

Data analytics using canonical correlation analysis and Monte Carlo simulation

“…While there is no simple procedure for estimating sample size sufficiency, some authors have attempted to quantify the increase in sample size required as the number of variables increases. 21,34 In general, the minimum data requirements needed for these techniques depend on the reliability of the data. While relatively large sample sizes are, of course, desirable, and may be necessary in some cases, if there are strong correlations then relatively small Fig.…”

Bias and Precision of the Squared Canonical Correlation Coefficient Under Nonnormal Data Condition

“…According to the authors, large differences demonstrated that sample-specific covariation could affect sample results. Barcikowski and Stevens (1975) also investigated the effect of sampling error on the canonical correlation, but with results that differed from Thorndike and Weiss (1973). They selected 8 correlation matrices from the literature [two of which were from Thorndike and Weiss (1973)] and, using a procedure described by Huberty (1969), generated population matrices with the same properties as the selected datasets.…”

“…The results indicated that the canonical correlations were "very stable under replication" (Barcikowski & Stevens, 1975, p. 362), even in the cases of small sample sizes (e.g., 100-200). Thompson (1990) investigated bias in the canonical correlation that resulted in findings that conflicted with Barcikowski and Stevens (1975). Unlike the studies by Thorndike and Weiss (1973) and Barcikowski and Stevens (1975) that employed real and modeled data, respectively, Thompson used Monte Carlo methods to simulate data such that it met predetermined properties.…”

Typha glauca Godron and its parental plants in Poland: taxonomic characteristics

“…All analyzed variables from the study group were used in the model. To assess the impact of particular variables on the discriminant function, use was made of standardized coefficients (Barcikowski & Stevens, 1975). Seeds were not included in calculations due to the fact that measurements were not taken for particular individuals (see the ''Measurements'' section).…”