S3methodsFAiR: S3 methods for "FA" objects

Description

These methods are technically S4 but are the result of making well-known S3 methods into S4 generic functions and defining methods for objects of FA-class and / or restrictions-class. In any event, they provide somewhat standard post-estimation functions for factor analysis models.

Usage

"deviance"(object)
"df.residual"(object)
"df.residual"(object)
"fitted"(object, reduced = TRUE, standardized = TRUE)
"fitted"(object, reduced = TRUE, standardized = TRUE)
"influence"(model)
"model.matrix"(object, standardized = TRUE)
"pairs"(x, ...)
"residuals"(object, standardized = TRUE)
"rstandard"(model)
"simulate"(object, nsim = 1, seed = NULL, standardized = TRUE, ...)
"weights"(object)

Arguments

object

An object of FA-class or restrictions-class, as appropriate

model

An object of FA-class

reduced

Logical indicating whether communalities should be on the diagonal of the fitted matrix.

standardized

Logical indicating whether the matrix should be calibrated for standardized variables.

nsim

number of simulations

seed

seed to use for random number generation; if NULL the current seed is used

...

additional argument(s) for methods

Value

deviance: returns the value of the discrepancy function
df.residual: returns the degrees of freedom
fitted: returns the model's estimate of the covariance or correlation matrix among manifest variables in common factor space
influence: returns a square matrix that is equal to residuals() * weights()
model.matrix: returns the sample covariance or correlation matrix among outcomes
pairs: returns nothing but plots the estimated reference structure correlations in a nice form
residuals: returns a square matrix that contains the difference between model.matrix() and fitted() and has uniquenesses along the diagonal (based on correlations by default)
rstandard: covariance residuals standardized by the standard deviations of the manifest variables
weights: returns a square matrix with the weights used in the discrepancy function. For Yates' weighted least squares estimator these weights are as defined in equation 188. For maximum likelihood estimation, these weights are proportional to the reciprocal of the crossproduct of the uniquenesses and are only approximately equal to the implied weights that would be used if minimizing the weighted sum of squared residuals. For ease of interpretation they are rescaled so that the mean weight is 1.0.

Details

The code for each of these methods is quite short. There are some other method definitions for objects that inherit from restrictions-class and FA-class but they differ only in implementation and not in their nature or their options.

References

Yates, A. (1987) Multivariate Exploratory Data Analysis: A Perspective on Exploratory Factor Analysis. State University of New York Press.

Examples

Run this code

  ## See the example for Factanal()

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