canonical correlation

which of the following best describes the core purpose of canonical correlation analysis?

it measures the relationship between two separate sets of variables.

what is canonical correlation analysis designed to analyze?

how a set of independent variables relates to a set of dependent variables simultaneously

in the context of social science research, what is the generally recommended number of cases required per variable for canonical correlation?

10 cases per variable, assuming a typical reliability of 0.8

how should one conceptualize the canonical variate created during the analysis?

a single SUPER VARIABLE representing a linear combination of the variables in a set

what is a canonical variate?

a composite or linear combination of the variables within set X or set Y that maximizes the correlation between the sets

If you have a data set with 5 variables in Set A and 3 variables in Set B, what is the maximum number of canonical variate pairs you can extract?

3

the number of canonical variate pairs is equal to the number of variables in the

smaller of the two sets

Canonical correlation can be viewed as a general form of which of the following statistical methods/special cases of canonical correlation

, discriminant function analysis, multiple regression

What is unique about the input data required to a canonical correlation analysis in programs like SPSS or R?

You can run the analysis only using a correlation matrix instead of raw data since the analysis is based on the relationships between variables. The correlation matrix contains all the necessary information to compute the results.

In the mathematical process of finding canonical correlations, what does each eigenvalue typically indicate?

The among of shared variance between the sets for that specific variate pair.

The eigenvalue represents ____, which is the proportion of shared variance.

squared canonical correlation

Which mathematical decomposition is performed on the rearranged correlation matrix to find the canonical correlations?

eigenvalue or singular value decomposition

once the correlation matrix is rearranged into the canonical input matrix, ___ ___ is used to find the patterns(eigenvectors)

eigenvalue decomposition

When testing for significance, how is Wilks’ Lambda interpreted in canonical correlation?

It represents the amount of variance NOT shared between the sets of variables.

__ __ is a measure of the ‘leftover’ variance; smaller values indicate a stronger relationship between the sets.

Wilks’ Lambda

Why is it suggested to check for univariate normality for every variable individually?

Because there is no direct way to test for multivariate normality.

When checking assumptions, how would multicollinearity and singularity be addressed?

check for high correlations (above .8 or .9) in set 1 and set 2 separately by running correlations within each set

In the formula for Rao's approximate F-test, what does the value m represent?

a value derived from the sample size and the number of variables in both sets

What happens to the number of variables considered (denoted as pi​ and qi​) as you move from testing the first variate pair to the second variate pair?

the number of variables effectively decreases by one for each subsequent tests, reducing the dimensions/degrees of freedom

If a canonical correlation analysis yields two significant variate pairs, what is the next logical step in the research process?

interpret the loadings to understand which variables contribute most to each significant variance. once significance is established, researchers look at the relationship between variables and their variates (similar to factor loadings) to give the variates meaning.

The 'canonical input matrix' is analogous to which concept in simple regression?

a slow or beta coefficient (b)

what is the primary goal of the ‘art’ side of canonical correlation analysis?

finding subjective meaning and patterns in the sets of variables; interpret which variables are relating and what those relationships mean

what do canonical coefficients (canonical weights) specifically represent in the context of creating a canonical variate?

the weights assigned to individual variables to create a composite (super variable); canonical coefficients are similar to regression slopes in a sense that they determine how much each variable contributes to the resulting variate

if you have 5 variables in the x set and 3 variables in the y set, what is the maximum number of canonical correlations you can obtain?

3

what is the definition of a canonical loading?

the correlation between an individual variable and its own canonical variate. loadings show how strongly each original variable relates to the composite (super variable) create for that set

how is across redundancy calculated for a specific dimension?

by multiplying the within-set redundancy by the squared canonical correlation. this formula accounts for how much variance the variate captures in its own set and then scales it by the strength of the relationship between the two variates

what is across redundancy?

the variance in one set explained by the opposite set

when interpreting canonical correlation results, why might a researcher use canonical variate scores?

to give each person a single value that represents their position on a composite/super variable. variate scores allow researchers to represent complex multi-variate data as a single score for each participant on a latent dimension

In the example provided in the lecture regarding personality and academic scores, why was the third canonical correlation ignored during interpretation?

it was not statistically significant

What is the relationship between 'within redundancy' and canonical loadings?

within redundancy is the average of the squared canonical loadings for a set. squaring each loading gives the variance explained in each variable by the variate; averaging them gives the overall within redundancy

what is a cross-loading?

the correlation between a variable in one set and the canonical variate of the opposite set. cross loadings show how individual variables relate directly to the super variable from the other side of the model.

In newer versions of SPSS, what is the term used for the table that contains redundancy analysis information?

Proportion of Variance Explained