canonCommonality {yhat}

Commonality Coefficents for Canonical Correlation

Description

The canonCommonality function produces commonality data for both canonical variables sets. Variables in a given canonical set are used to partition the variance of the canonical variates produced from the other canonical set and vica versa. Commonality data is supplied for the number of canonical functions requested.

Usage

  canonCommonality(A, B, nofns = 1)

Arguments

A

Matrix containing variable set A

B

Matrix containing variable set B

nofns

Number of canonical functions to analyze

Details

The function canonCommonality has two required arguments and one optional argument. The first two arguments contain the two variable sets. The third argument is optional and defnes the number of canonical functions to analyze. Unless specifed, the number of canonical functions defaults to 1.

The function canonCommonality calls a function canonVariate to decompose canonical varites twice: the first time for the variable set identified in the first argument, the second time for the variable set identified in the second argument.

Value

The function canonCommonality returns commonality data for both canonical variable sets. For the number of functions requested, both canonical variates are analyzed. For each canonical variate analyzed, two tables are returned. The first table lists the commonality coefficients and their contribution to the total effect, while the second table lists the unique and common effects for each regressor. The function returns the resulting output ordering the output according to the function's paramaeters.

Author(s)

Kim Nimon <[e-mail]>

References

Nimon, K., Henson, R., & Gates, M. (2010). Revisiting interpretation of canonical correlation analysis: A tutorial and demonstration of canonical commonality analysis. Multivariate Behavioral Research, 45,702-724.

See Also

canonVariate

Examples

  ## Example parallels the R builtin cancor and the 
  ## yacca cca example
     data(LifeCycleSavings)
     pop <- LifeCycleSavings[, 2:3]
     oec <- LifeCycleSavings[, -(2:3)]
  ## Perform Commonality Coefficient Analysis
     canonCommonData<-canonCommonality(pop,oec,1)

  ## Use HS dataset in MBESS 
     if (require("MBESS")){
     data(HS)
     attach(HS)
  ## Create canonical variable sets
     MATH_REASON<-HS[,c("t20_deduction","t22_problem_reasoning")]
     MATH_FUND<-HS[,c("t21_numerical_puzzles","t24_woody_mccall","t10_addition")] 
  ## Perform Commonality Coefficient Analysis
     canonCommonData<-canonCommonality(MATH_FUND,MATH_REASON,1)
     detach(HS)      
     }