faMulti: Multi level (hierarchical) factor analysis

In psych: Procedures for Psychological, Psychometric, and Personality Research

Multi level (hierarchical) factor analysis

Description

Some factor analytic solutions produce correlated factors which may in turn be factored. If the solution has one higher order, the omega function is most appropriate. But, in the case of multi higher order factors, then the faMulti function will do a lower level factoring and then factor the resulting correlation matrix. Multi level factor diagrams are also shown.

Usage

fa.multi(r, nfactors = 3, nfact2 = 1, n.obs = NA, n.iter = 1, rotate = "oblimin", 
 scores = "regression", residuals = FALSE, SMC = TRUE, covar = FALSE, missing = 
 FALSE,impute = "median", min.err = 0.001, max.iter = 50, symmetric = TRUE, warnings 
 =TRUE, fm = "minres", alpha = 0.1, p = 0.05, oblique.scores = FALSE, np.obs = NULL, 
 use ="pairwise", cor = "cor", ...)

fa.multi.diagram(multi.results,sort=TRUE,labels=NULL,flabels=NULL,f2labels=NULL,cut=.2,
	gcut=.2, simple=TRUE,errors=FALSE,
    digits=1,e.size=.1,rsize=.15,side=3,main=NULL,cex=NULL,color.lines=TRUE
    ,marg=c(.5,.5,1.5,.5),adj=2, ...) 

Arguments

The arguments match those of the fa function.

r	A correlation matrix or raw data matrix
nfactors	The desired number of factors for the lower level
nfact2	The desired number of factors for the higher level
n.obs	Number of observations used to find the correlation matrix if using a correlation matrix. Used for finding the goodness of fit statistics. Must be specified if using a correlaton matrix and finding confidence intervals.
np.obs	The pairwise number of observations. Used if using a correlation matrix and asking for a minchi solution.
rotate	"none", "varimax", "quartimax", "bentlerT", "equamax", "varimin", "geominT" and "bifactor" are orthogonal rotations. "promax", "oblimin", "simplimax", "bentlerQ, "geominQ" and "biquartimin" and "cluster" are possible oblique transformations of the solution. The default is to do a oblimin transformation, although versions prior to 2009 defaulted to varimax.
n.iter	Number of bootstrap interations to do in fa or fa.poly
residuals	Should the residual matrix be shown
scores	the default="regression" finds factor scores using regression. Alternatives for estimating factor scores include simple regression ("Thurstone"), correlaton preserving ("tenBerge") as well as "Anderson" and "Bartlett" using the appropriate algorithms (see factor.scores). Although scores="tenBerge" is probably preferred for most solutions, it will lead to problems with some improper correlation matrices.
SMC	Use squared multiple correlations (SMC=TRUE) or use 1 as initial communality estimate. Try using 1 if imaginary eigen values are reported. If SMC is a vector of length the number of variables, then these values are used as starting values in the case of fm='pa'.
covar	if covar is TRUE, factor the covariance matrix, otherwise factor the correlation matrix
missing	if scores are TRUE, and missing=TRUE, then impute missing values using either the median or the mean
impute	"median" or "mean" values are used to replace missing values
min.err	Iterate until the change in communalities is less than min.err
max.iter	Maximum number of iterations for convergence
symmetric	symmetric=TRUE forces symmetry by just looking at the lower off diagonal values
warnings	warnings=TRUE => warn if number of factors is too many
fm	factoring method fm="minres" will do a minimum residual (OLS), fm="wls" will do a weighted least squares (WLS) solution, fm="gls" does a generalized weighted least squares (GLS), fm="pa" will do the principal factor solution, fm="ml" will do a maximum likelihood factor analysis. fm="minchi" will minimize the sample size weighted chi square when treating pairwise correlations with different number of subjects per pair.
alpha	alpha level for the confidence intervals for RMSEA
p	if doing iterations to find confidence intervals, what probability values should be found for the confidence intervals
oblique.scores	When factor scores are found, should they be based on the structure matrix (default) or the pattern matrix (oblique.scores=TRUE).
use	How to treat missing data, use="pairwise" is the default". See cor for other options.
cor	How to find the correlations: "cor" is Pearson", "cov" is covariance, "tet" is tetrachoric, "poly" is polychoric, "mixed" uses mixed cor for a mixture of tetrachorics, polychorics, Pearsons, biserials, and polyserials, Yuleb is Yulebonett, Yuleq and YuleY are the obvious Yule coefficients as appropriate
multi.results	The results from fa.multi
labels	variable labels
flabels	Labels for the factors (not counting g)
f2labels	The labels for the second order factors
size	size of graphics window
digits	Precision of labels
cex	control font size
color.lines	Use black for positive, red for negative
marg	The margins for the figure are set to be wider than normal by default
adj	Adjust the location of the factor loadings to vary as factor mod 4 + 1
main	main figure caption
...	additional parameters, specifically, keys may be passed if using the target rotation, or delta if using geominQ, or whether to normalize if using Varimax. In addition, for fa.multi.diagram, other options to pass into the graphics packages
e.size	the size to draw the ellipses for the factors. This is scaled by the number of variables.
cut	Minimum path coefficient to draw
gcut	Minimum general factor path to draw
simple	draw just one path per item
sort	sort the solution before making the diagram
side	on which side should errors be drawn?
errors	show the error estimates
rsize	size of the rectangles

Details

See fa and omega for a discussion of factor analysis and of the case of one higher order factor.

Value

f1	The standard output from a factor analysis from fa for the raw variables
f2	The standard output from a factor analysis from fa for the correlation matrix of the level 1 solution.

Note

This is clearly an early implementation (Feb 14 2016) which might be improved.

Author(s)

William Revelle

References

Revelle, William. (in prep) An introduction to psychometric theory with applications in R. Springer. Working draft available at https://personality-project.org/r/book/

See Also

fa, omega

Examples

f31 <- fa.multi(Thurstone,3,1) #compare with \code{\link{omega}}
f31
fa.multi.diagram(f31)

psych documentation built on June 27, 2024, 5:07 p.m.