factanal
which represents the fitted model.
Options include the estimation procedure and the rotation.
factanal(x, factors=1, method="principal", data=NULL, covlist=NULL, scores=T, type="regression", rotation="varimax", na.action, subset, start=<<see below>>, control=NULL, ...)
x
,
data
or
covlist
must be given.
"mle"
(maximum likelihood estimate)
and
"principal"
(principal factor estimate).
If it does not match either of these, then a function with name
paste("factanal.fit", method, sep = ".")
will be used, if present.
x
is a formula, though it may be used
instead of
x
.
cov.wt
and
cov.mve
.
Components must include
center
and
cov
.
A
cor
component will not be used, however, an
n.obs
component will be used
if present.
TRUE
and data are given (via
x
or
data
), then factor
scores will be returned as a component of the result.
"regression"
or
"weighted.ls"
.
rotate
for the list of possibilities (though no name can be used here
that requires additional parameters).
factanal.fit.mle
for details.
factanal.mle.control
for details.
iter.max
and
unique.tol
for either the maximum likelihood
or the principal factor method.
"factanal"
.
See
factanal.object
for details.
Factor analysis essentially assumes a model for the correlation matrix
and produces estimates of the model.
There are several undesirable features of factor analysis modeling.
There is not a clear way of deciding if the
model is appropriate or not, and if so how many factors there should be.
It has also been shown that the estimates need not look like the original
generators of a factor model even when the covariance matrix precisely
fits the model (corresponding to an infinite sample size).
See Seber (1984, pp. 222-235) for a discussion and further references.
Factor scores are estimated with
predict.factanal
, while the estimated
correlation matrix is computed by
fitted.factanal
.
Factor analysis assumes that the data may be successfully
summarized by one or more "factors" which are
unknown linear combinations of the variables known to the data analyst.
For example, suppose we have the answers from 1000 subjects on a
psychological test of 100 questions.
Each question is one of our 100 observed variables, and we may consider
performing factor analysis to find the two factors "aggressiveness"
and "intelligence" that the test was designed to measure.
These factors will each be a linear combination of the 100 questions.
Many books on multivariate statistics have a discussion of factor analysis.
Below is a brief selection.
Harman, H. H. (1976).
Modern Factor Analysis,
3rd Edition.
University of Chicago Press, Chicago.
Johnson, R. A. and Wichern, D. W. (1982).
Applied Multivariate Statistical Analysis.
Prentice-Hall, Englewood Cliffs, New Jersey.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979).
Multivariate Analysis.
Academic Press, London.
Seber, G. A. F. (1984).
Multivariate Observations.
Wiley, New York.
prim9.fa3 <- factanal(prim9, 3) # principal factor solution factanal(prim9, 3, method="mle") # maximum likelihood estimate rotate(prim9.fa3, "promax") biplot(prim9.fa3)