fungible (version 2.2.2)

faMAP: Velicer's minimum partial correlation method for determining the number of major components for a principal components analysis or a factor analysis

Description

Uses Velicer's MAP (i.e., matrix of partial correlations) procedure to determine the number of components from a matrix of partial correlations.

Usage

faMAP(R, max.fac = 8, Print = TRUE, Plot = TRUE, ...)

Value

MAP

Minimum partial correlations

MAP4

Minimum partial correlations

fm

average of the squared partial correlations after the first m components are partialed out.

fm4

see Velicer, Eaton, & Fava, 2000.

PlotAvgSq

A saved object of the original MAP plot (based on the average squared partial r's.)

PlotAvg4th

A saved object of the revised MAP plot (based on the average 4th power of the partial r's.)

Arguments

R

input data in the form of a correlation matrix.

max.fac

maximum number of dimensions to extract.

Print

(logical) Print = TRUE will print complete results.

Plot

(logical) Plot = TRUE will plot the MAP values.

...

Arguments to be passed to the plot functions (see par).

Author

Niels Waller

References

Velicer, W. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3):321--327.

Velicer,W. F., Eaton, C. A. , & Fava, J. L. (2000). Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components. In R. D. Goffin & E. Helmes (Eds.). Problems and Solutions in Human Assessment: Honoring Douglas N. Jackson at Seventy (pp. 41-71. Boston, MA: Kluwer Academic.

Examples

	# Harman's data (1967, p 80) 
	# R = matrix(c(
	# 1.000,  .846,  .805,  .859,  .473,  .398,  .301,  .382,
	#  .846, 1.000,  .881,  .826,  .376,  .326,  .277,  .415,
	#  .805,  .881, 1.000,  .801,  .380,  .319,  .237,  .345,
	#  .859,  .826,  .801, 1.000,  .436,  .329,  .327,  .365,
	#  .473,  .376,  .380,  .436, 1.000,  .762,  .730,  .629,
	#  .398,  .326,  .319,  .329,  .762, 1.000,  .583,  .577,
	#  .301,  .277,  .237,  .327,  .730,  .583, 1.000,  .539,
	#  .382,  .415,  .345,  .365,  .629,  .577,  .539, 1.000), 8,8)

	  F <- matrix(c(  .4,  .1,  .0,
	                  .5,  .0,  .1,
	                  .6,  .03, .1,
	                  .4, -.2,  .0,
	                   0,  .6,  .1,
	                  .1,  .7,  .2,
	                  .3,  .7,  .1,
	                   0,  .4,  .1,
	                   0,   0,  .5,
	                  .1, -.2,  .6, 
	                  .1,  .2,  .7,
	                 -.2,  .1,  .7),12,3)
					 
	  R <- F %*% t(F)
	  diag(R) <- 1 
	  
  	faMAP(R, max.fac = 8, Print = TRUE, Plot = TRUE)