corEFA {lessR}

Exploratory Factor Analysis and Multiple Indicator Measurement Model

Description

Abbreviation: efa

A maximum likelihood exploratory factor analysis of an input correlation matrix, provided by the standard R exploratory factor analysis factanal, which requires the specified number of factors as an input to the analysis. Then constructs the code to run the corresponding multiple indicator measurement model (MIMM) suggested by the exploratory factor analysis loadings in terms of both the lessR corCFA and the cfa function from the lavaan package.

Usage

corEFA(R=mycor, n_factors, rotate=c("promax", "varimax", "none"), 
          min_loading=.2, sort=TRUE, Rmd=NULL, ...)

efa(...)

Arguments

R

Correlation matrix.

n_factors

Number of factors.

rotate

Rotation method, if any. Choices are promax (obique) or varimax (orthogonal.

min_loading

Minimum loading to include in suggested factor for confirmatory analysis and for the display of the loadings for the exploratory analysis. To ignore, set to 0.

sort

Sort the input variables by their highest factor loadings (but only first just list those items with loadings larger than 0.5).

Rmd

File name for the file of R markdown to be written, if specified. The file type is .Rmd, which automatically opens in RStudio, but it is a simple text file that can be edited with any text editor, including RStudio.

...

Parameter values_

Details

Only the loadings from the exploratory factor analysis are provided, with either an oblique (promax), by default, or an orthogonal (varimax) rotation. If more information is desired, run factanal directly.

Also provides the associated multiple indicator measurement model suggested by the exploratory factor analysis. Each MIMM factor is defined by the items that have the highest loading on the corresponding exploratory factor.

For versions of lessR after 3.3, the correlation matrix computed by Correlation is now a list element called R within the returned list. For example, mycor$R from mycor <- cr(d). The function corEFA automatically finds this correlation matrix from just entering the entire list name of the returned list, mycor, or the specific location, mycor$R, or as a stand-alone numerical matrix as done in versions of lessR previous to 3.3.

Value

The output can optionally be returned and saved into an R object, otherwise it simply appears at the console. The components of this object are redesigned in lessR version 3.3 into three different types: pieces of text that form the readable output, a variety of statistics, and R markdown instructions. The readable output are character strings such as tables amenable for viewing and interpretation. The statistics are numerical values amenable for further analysis, such as to be referenced in a subsequent R markdown document. The R~Markdown input is available for entry direct into knitr, such as in RStudio. The motivation of these three types of output is to facilitate R markdown documents, as the name of each piece, preceded by the name of the saved object followed by a dollar sign, can be inserted into the R markdown document (see examples).

READABLE OUTPUT
out_title: Variables in the model, rows of data and retained
out_loadings: Estimated coefficients, hypothesis tests and confidence intervals
out_sum_squares: Fit indices
out_cfa_title: Analysis of variance
out_ice: Correlations among all variables in the model
out_lavaan: Collinearity analysis
out_deleted: R squared adjusted for all (or many) possible subsets

STATISTICS
Rmd: Instructions to run through knitr, such as copy and paste, to obtain output in the form of a web file, pdf document or Word document. Can also obtain these instructions with the Rmd option, which writes them directly to the specified text file. Obtain a less detailed Rmd file by setting explain=FALSE.

Although not typically needed for analysis, if the output is assigned to an object named, for example, fa, then the complete contents of the object can be viewed directly with the unclass function, here as unclass(fa). Invoking the class function on the saved object reveals a class of out_all. The class of each of the text pieces of output is out.

Author(s)

David W. Gerbing (Portland State University; [e-mail])

References

Gerbing, D. W. (2014). R Data Analysis without Programming, Chapter 11, NY: Routledge.

Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.

See Also

Correlation.

Examples

# input correlation matrix of perfect two-factor model
# Factor Pattern for each Factor: 0.8, 0.6, 0.4
# Factor-Factor correlation: 0.3
mycor <- matrix(nrow=6, ncol=6, byrow=TRUE,
c(1.000,0.480,0.320,0.192,0.144,0.096,
  0.480,1.000,0.240,0.144,0.108,0.072,
  0.320,0.240,1.000,0.096,0.072,0.048,
  0.192,0.144,0.096,1.000,0.480,0.320,
  0.144,0.108,0.072,0.480,1.000,0.240,
  0.096,0.072,0.048,0.320,0.240,1.000))
colnames(mycor) <- c("X1", "X2", "X3", "X4", "X5", "X6")
rownames(mycor) <- colnames(mycor) 

# default factor analysis of default correlation matrix mycor
#   with two factors extracted
corEFA(n_factors=2)

# abbreviated form
# use all items to construct the MIMM, regardless of their loadings
#  and show all loadings
# show the initial factor extraction
efa(n_factors=2, min_loading=0, show_initial=TRUE)