R: Factor Analysis for data (high or low dimensional).

fad {fad}

R Documentation

Factor Analysis for data (high or low dimensional).

Description

Perform fast matrix-free maximum-likelihood factor analysis on a covariance matrix or data matrix, works if number of variables is more than number of observations.

Usage

fad(
  x,
  factors,
  data = NULL,
  covmat = NULL,
  n.obs = NA,
  subset,
  na.action,
  start = NULL,
  scores = c("none", "regression", "Bartlett"),
  rotation = "varimax",
  control = NULL,
  lower = 0.005,
  ...
)

Arguments

`x`	A formula or a numeric matrix or an object that can be coerced to a numeric matrix.
`factors`	The number of factors to be fitted.
`data`	An optional data frame (or similar: see `model.frame`), used only if `x` is a formula. By default the variables are taken from `environment(formula)`.
`covmat`	A covariance matrix, or a covariance list as returned by `cov.wt`. Of course, correlation matrices are covariance matrices.
`n.obs`	The number of observations, used if `covmat` is a covariance matrix.
`subset`	A specification of the cases to be used, if `x` is used as a matrix or formula.
`na.action`	The `na.action` to be used if `x` is used as a formula.
`start`	`NULL` or a matrix of starting values, each column giving an initial set of uniquenesses.
`scores`	Type of scores to produce, if any. The default is none, `"regression"` gives Thompson's scores, `"Bartlett"` given Bartlett's weighted least-squares scores. Partial matching allows these names to be abbreviated. Also note that some of the scores-types are not applicable when `p > n`.
`rotation`	character. `"none"` or the name of a function to be used to rotate the factors: it will be called with first argument the loadings matrix, and should return a list with component `loadings` giving the rotated loadings, or just the rotated loadings. The options included in the package are: `varimax`, `promax`, `quartimax`, `equamax`.
`control`	A list of control values: nstart The number of starting values to be tried if `start = NULL`. Default 1. trace logical. Output tracing information? Default `FALSE`. opt A list of control values to be passed to `optim`'s `control` argument. rotate a list of additional arguments for the rotation function.
`lower`	The lower bound for uniquenesses during optimization. Should be > 0. Default 0.005.
`...`	Components of `control` can also be supplied as named arguments to `fad`.

Value

An object of class "fad" with components

`loadings`	A matrix of loadings on the correlation scale, one column for each factor. The factors are ordered in decreasing order of sums of squares of loadings, and given the sign that will make the sum of the loadings positive. This is of class `"loadings"`
`uniquenesses`	The uniquenesses computed on the correlation scale.
`sd`	The estimated standard deviations.
`criteria`	The results of the optimization: the value of the criterion (a linear function of the negative log-likelihood) and information on the iterations used.
`factors`	The argument `factors`.
`dof`	The number of degrees of freedom of the factor analysis model.
`method`	The method: always `"mle"`.
`rotmat`	The rotation matrix if relevant.
`scores`	If requested, a matrix of scores. `napredict` is applied to handle the treatment of values omitted by the `na.action`.
`n.obs`	The number of observations if available, or `NA`.
`call`	The matched call.
`na.action`	If relevant.
`loglik`, `BIC`	The maximum log-likelihood and the Bayesian Information Criteria.

Examples

set.seed(1234)

## Simulate a 200 x 3 loadings matrix ~i.i.d N(0,1)
L <- matrix(rnorm(200*3),200,3) 

## Simulate the uniquenesses i.i.d U(0.2,0.9)
D <- runif(200,0.2,0.9) 

## Generate a data matrix of size 50 x 200 with rows
## ~i.i.d. N(0,LL'+diag(D))
X <- tcrossprod(matrix(rnorm(50*3),50,3),L) + matrix(rnorm(50*200),50,200) %*% diag(sqrt(D))

## Fit a factor model with 3 factors:
fit = fad(X,3)


## Print the loadings:
print(fit$loadings)