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.
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,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, ...)
A correlation matrix or raw data matrix
The desired number of factors for the lower level
The desired number of factors for the higher level
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.
The pairwise number of observations. Used if using a correlation matrix and asking for a minchi solution.
"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.
Number of bootstrap interations to do in fa or fa.poly
Should the residual matrix be shown
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.
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'.
if covar is TRUE, factor the covariance matrix, otherwise factor the correlation matrix
if scores are TRUE, and missing=TRUE, then impute missing values using either the median or the mean
"median" or "mean" values are used to replace missing values
Iterate until the change in communalities is less than min.err
Maximum number of iterations for convergence
symmetric=TRUE forces symmetry by just looking at the lower off diagonal values
warnings=TRUE => warn if number of factors is too many
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 level for the confidence intervals for RMSEA
if doing iterations to find confidence intervals, what probability values should be found for the confidence intervals
When factor scores are found, should they be based on the structure matrix (default) or the pattern matrix (oblique.scores=TRUE).
How to treat missing data, use="pairwise" is the default". See cor for other options.
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
The results from fa.multi
variable labels
Labels for the factors (not counting g)
size of graphics window
Precision of labels
control font size
Use black for positive, red for negative
The margins for the figure are set to be wider than normal by default
Adjust the location of the factor loadings to vary as factor mod 4 + 1
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
the size to draw the ellipses for the factors. This is scaled by the number of variables.
Minimum path coefficient to draw
Minimum general factor path to draw
draw just one path per item
sort the solution before making the diagram
on which side should errors be drawn?
show the error estimates
size of the rectangles
The standard output from a factor analysis from fa for the raw variables
The standard output from a factor analysis from fa for the correlation matrix of the level 1 solution.
See fa and omega for a discussion of factor analysis and of the case of one higher order factor.
Revelle, William. (in prep) An introduction to psychometric theory with applications in R. Springer. Working draft available at https://personality-project.org/r/book/
# NOT RUN {
f31 <- fa.multi(Thurstone,3,1) #compare with \code{\link{omega}}
f31
fa.multi.diagram(f31)
# }
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