corProp: Proportionality Coefficients from Correlations

Description

Abbreviation: prop

In the population, indicators of the same factor or latent variable have parallel correlations with all other variables. Of course, in the presence of sampling error, this parallelism will only be approximate. To assess this parallelism, proportionality coefficients are computed for each pair of variables in the input correlation matrix. Also output is a heat map of the resulting matrix of proportionality coefficients. Each graph is based on a default color theme. The original default is lightbronze, but other color palettes can be generated as well.

Usage

corProp(R=mycor, 
          main=NULL, heat.map=TRUE, bottom=3, right=3, 
          pdf.file=NULL, width=5, height=5)
prop(…)

Arguments

Correlation matrix.

main

Graph title. Set to main="" to turn off.

heat.map

If TRUE, display a heat map of the item correlations with the diagonal ignored.

bottom

Number of lines of bottom margin.

right

Number of lines of right margin.

pdf.file

Name of the pdf file to which graphics are redirected.

width

Width of the pdf file in inches.

height

Height of the pdf file in inches.

…

Parameter values.

Details

Proportionality coefficients indicate the extent of proportionality between two variables. Perfect proportionality of two variables is consistent with both variables being indicators of the same latent variable or factor and indicators of no other factor.

In the current version the diagonal of the input correlation matrix is ignored. To maintain parallelism, the diagonal element of 1.00 would need to be replaced the corresponding communalities, which first requires a factor analysis.

References

Gerbing, D. W. (2014). R Data Analysis without Programming, Chapter 11, NY: Routledge.

Examples

Run this code

# NOT RUN {
# input correlation matrix of perfect two-factor model
# Factor Pattern for each Factor: 0.8, 0.6, 0.4
# Factor-Factor correlation: 0.3
mycor <- matrix(nrow=6, ncol=6, byrow=TRUE,
c(1.000,0.480,0.320,0.192,0.144,0.096,
  0.480,1.000,0.240,0.144,0.108,0.072,
  0.320,0.240,1.000,0.096,0.072,0.048,
  0.192,0.144,0.096,1.000,0.480,0.320,
  0.144,0.108,0.072,0.480,1.000,0.240,
  0.096,0.072,0.048,0.320,0.240,1.000))
colnames(mycor) <- c("X1", "X2", "X3", "X4", "X5", "X6")
rownames(mycor) <- colnames(mycor)

# proportionality coefficients of correlation matrix mycor
# indicators of the same factor have proportional correlations
corProp()

# abbreviated form
prop()

# calculate and store proportionality coefficients in myprop
# order the proportionality coefficients to help identify factors
myprop <- corProp()
corReorder(myprop)
# }