classFA {FAiR}R Documentation

Class "FA" and Classes that Inherit from "FA"

Description

These classes encapsulate estimates from factor analysis models. The "FA.general" and "FA.2ndorder" classes extend class "FA" and have additional slots to contain estimates from a second-order model with one general second-order factor and multiple second-order factors respectively

Objects from the Class

Objects can be created by calls of the form new("FA", ...). However, this use of new("FA", ...) is not recommended. Both Factanal and Rotate call new("FA", ...) internally to create the appropriate object for analysis with the help of the formal methods defined for create_FAobject.

Slots

loadings:
Object of class "array". This array has as many rows as there are outcome variables, as many columns as there are factors, and five shelves. Each shelf is a matrix and contains the primary pattern ('PP'), primary structure ('PS'), reference pattern ('RP'), reference structure ('RS'), and factor contribution ('FC') matrices respectively, which can be extracted via coef() using the appropriate two-letter string for the matrix argument that defaults to 'PP'.
correlations:
Object of class "array". This array has as many rows and columns as there are factors and three shelves. Each shelf is a correlation matrix and contains the correlations among the primary factors ('PF'), among reference factors ('RF'), and between each primary factor and the corresponding reference factor ('PR'), which is a diagonal matrix. There is currently no special accessor function for these three matrices.
trans_mats:
Object of class "array". This array has as many rows and columns as there are factors and two shelves. Both shelves are the identity matrix if semi-exploratory or confirmatory factor analysis was used in the call to Factanal and are the identity matrix prior to the call to Rotate in exploratory factor analysis. Rotate fills these two shelves with the transformation matrix for the primary factors ('primary') and the transformation matrix for the reference factors ('reference'). Both matrices have unit-length columns and the rotated primary pattern matrix is equal to the unrotated primary pattern matrix times the inverse of the transpose of the transformation matrix for the primary factors.
uniquenesses:
Object of class "numeric". This numeric vector has as many elements as there are outcome variables and contains the unique variances (also called specific variances) of the factor analysis model.
restrictions:
Object of class "restrictions". This slot contains information on the restrictions that were placed on the factor analysis model while it was estimated.
vcov:
Object of class "matrix". This matrix is a variance-covariance matrix and thus has as many rows and columns as there are parameters to be estimated. Note that it is calibrated to the sample covariance matrix, rather than the sample correlation matrix.
zstats:
Object of class "list". A list of matrices containing the z-statistic for each estimated parameter under a null hypothesis that the parameter is zero.
scores:
Object of class "matrix". If, in the call to Factanal the user specifies that factor scores should be calculated, this matrix contains the factor scores and has as many rows as there are complete observations and as many columns as there are factors. If factor scores were not requested, then this matrix has one row, one column, and a NA_real_ in its only cell.
manifest:
Object of class "list". This list contains information on the left-hand side of the factor analysis model. It has an element for the sample covariance matrix, the sample correlation matrix, the number of observations in the sample, and possibly a matrix of standardized scores on the outcome variables.
rgenoud:
Object of class "list". This is a list of lists each containing what is returned by genoud, which is called internally by Factanal and Rotate.
model:
Object of class "character". This character string indicates whether a SEFA, EFA, or CFA model was estimated.
method:
Object of class "character". This character string indicates whether maximum-likelihood or weighted least squares was used to estimate the factor analysis model.
call:
Object of class "language". This slot contains the call to Factanal.
seeds:
Object of class "matrix". This matrix has two columns and either one or two rows. The first row contains the unif.seed used by genoud and the int.seed in the call to Factanal. If Rotate is used to transform the factors after they have been extracted via exploratory factor analysis, this matrix has a second row containing the unif.seed and int.seed used in the call to Rotate.

Methods

BIC
signature(object = "FA"): Bayesian Information Criterion
coef
signature(object = "FA"): Extract coefficients. This method has two additional arguments, matrix and level. matrix should be one of "PP" (default) for the primary pattern matrix, "PS" for the primary structure matrix, "RP" for the reference pattern matrix, "RS" for the reference structure matrix, or "FC" for the factor contribution matrix. level should be 1 (default) to extract from level one of the model or 2 to extract from level two of the model (if the model has two levels).
confint
signature(object = "FA"): Extract confidence intervals. Does not work yet.
logLik
signature(object = "FA"): Extract log-likelihood, requires that the model be estimated by maximum likelihood.
plot
signature(x = "FA", y = "ANY"): Plots from nFactors
profile
signature(fitted = "FA"): Plot profile likelihoods for all fixed and zero coefficients in the primary pattern matrix. This method has two additional arguments, param, which is currently ignored and delta which indicates how far on either side of the constrained optimum to plot.
show
signature(object = "FA"): This method displays some information about the restrictions that were imposed on the model and prints a variety of model fit statistics (see note below).
summary
signature(object = "FA"): Gathers the coefficients, intercorrelations, and z-statistics, typically for showing
vcov
signature(object = "FA"): Extracts the variance-covariance matrix

Note

The model comparison statistics printed by the show method are largely resused from the summary.sem function in sem. Most of these statistics are defined in Bollen (1989). The exception is the stochastic information complexity (SIC), which is defined in Preacher, Cai, and MacCallum (2007).

Author(s)

Ben Goodrich http://wiki.r-project.org/rwiki/doku.php?id=packages:cran:fair

References

Bollen, K. A. (1989) Structural Equations With Latent Variables. Wiley.

Preacher, K.J., Cai, L., and MacCallum, R.C. ``Alternatives to traditional model comparison strategies for covariance structure models.'' in Modeling Contextual Effects in Longitudinal Studies, eds. Little, T.D., Bovaird, J.A., and Card, N.A. Psychology Press.

See Also

BIC, coef, profile, confint logLik, plot, show, summary, vcov, and S3methodsFA.

Examples

showClass("FA")

[Package FAiR version 0.2-0 Index]