# faMAP: Velicer's minimum partial correlation method for determining... In fungible: Psychometric Functions from the Waller Lab

 faMAP R Documentation

## 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, ...)
``````

### 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`).

### 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.)

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)

``````

fungible documentation built on March 31, 2023, 5:47 p.m.