FAiR (version 0.2-0)

Rotate: Choose a Transformation in Exploratory Factor Analysis

Description

This function should be used following Factanal with model = "EFA" to obtain a transformation of the preliminary factors that is optimal with respect to some intersection of criteria.

Usage

Rotate(FAobject, criteria, weights = NULL, seeds = 12345, ...)

Arguments

FAobject

An object of class "FA" produced by Factanal with model = "EFA".

criteria

An optional list whose elements are functions or character strings naming functions to be used in the lexical optimization process. See the details section. It is usually best to leave this argument unspecified and allow

weights

This argument is only relevant if the varphi criterion is used for transformation and should either be NULL or a numeric vector giving the weights to be used If NULL, then a dynamic weighting scheme will be used for the with the varphi crite

seeds

A vector of length one or two to be used as the random number generator seeds corresponding to the unif.seed and int.seed arguments to genoud respectively. If

...

Further arguments that are passed to genoud. Note that several of the default arguments to genoud are silently overridden by Fact

Value

• An object of formal S4 class "FA".

Details

Factor transformation is complicated and is discussed in detail in Goodrich (2008). This help page should really only be used as a reminder for what the various choices are, which are normally indicated by leaving criteria unspecifying and responding to pop-up menus. The vignette provides a step-by-step guide to navigating the pop-up menus and formally defines the criteria to follow; execute vignette("FAiR") to read it.

The basic problem is to choose a transformation of the factors that is optimal with respect to some intersection of criteria. Since the objective function is vector valued, lexical optimization is used via a genetic algorithm; see genoud.

Currently, there are four options for the ultimate criterion in the lexical optimization. These include Thurstone's (1935) criterion ("phi") and a generalization of Thurstone's criterion ("varphi") that may overcome some of the shortcomings with phi. In addition, there is a criterion ("minimaximin") that captures Thurstone's concept of simple structure in another way, and one crition for simple loadings, called the Loading Simplicity Index ("LS") that is advocated in Lorenzo-Seva (2003).

There are also many options for additional criteria that precede the ultimate criterion in the lexical ranking. These criteria can be seen as constraints so that one is searching for the transformation matrix that yields the minimum value of the ultimate criterion subject to the constraints defined by previous criteria. The only required constraint is the constraint that the factor intercorrelation matrix be sufficiently nonsingular.

It is not necessary to provide starting values for the parameters, since there are is a mechanism to generate them automatically. But a matrix of starting values can be passed to through the dots to genoud. This matrix should have rows equal to the pop.size argument in genoud and columns equal the number of factors squared, which corresponds to the nvars argument in genoud. The columns correspond to the cells of the transformation matrix, albeit in a somewhat convoluted order. The order of the parameters is row-major order with respect to the transformation matrix, with the exception that the parameters comprosing the last row of the transformation matrix are moved to the very end. Also, in contrast to some texts, the transformation matrix in Rotate has unit-length columns, rather than unit-length rows.

References

Goodrich, B. (2008) Analytic Transformation of Factors in FAiR. Unwritten manuscript.

Lorenzo-Seva, U. (2003) A factor simplicity index. Psychometrika, 68, 49--60.

Thurstone, L. L. (1935) The Vectors of Mind. Cambridge University Press.

See Also

Factanal

Examples

## See first example for Factanal()