Regression Analysis in Medical Research by Ton J. Cleophas & Aeilko H. Zwinderman

Author:Ton J. Cleophas & Aeilko H. Zwinderman
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

13.3 Canonical Regression

Like Manova, canonical analysis is based on multiple linear regression, used to find the best fit correlation coefficients for your data. However, because it works with Wilks’statistic and beta distributions rather than Pillai’s statistic and normal distributions, it is able to more easily calculate overall correlation coefficients between sets of variables. Yet, it also assesses, how a set of variables, as a whole is related to separate variables. Along this way, an overall canonical model can be further improved by removing unimportant variables. Canonical analysis may be arithmetically equivalent to factor-analysis/partial least squares analysis, but, conceptionally, it is very different. Unlike the latter, the former method does not produce new (latent) variables, but rather makes use of two sets of manifest variables. Also, unlike the latter, it complies with all of the requirements of traditional linear regression, and is, therefore, scientifically rigorous. A canonical analysis should start with a correlation matrix. Variables with large correlation coefficients must be removed from the model. If in canonical models the clusters of predictor and outcome variables have a significant relationship, then this finding can, just like with linear regression, be used for making predictions about individual patients. We will again use SPSS statistical software. The Menu does not offer canonical analysis, but the Syntax program does. Canonical analysis should start with a collinearity matrix. This is because the uncertainty of the canonical weights, being the main outcome of a canonical regression, are severely overestimated in case of collinearity. Variable versus variable correlation coefficients larger than 0.80 means that the models is collinear and that the collinear variables should be removed from the model. In order to assess collinearity, a correlation matrix must be first constructed. We will use the data example from the previous section once more.

Command:

click File… .click New… .click Syntax… .the Syntax Editor dialog box is displayed… .enter the following text: “correlations/variables = “and subsequently enter all of the gene-names… .click Run.

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