summary.faMain {fungible}

Summary Method for an Object of Class faMain

Description

This function summarizes results from a call to faMain.

Usage

## S3 method for class 'faMain'
summary(
  object,
  digits = 2,
  Set = 1,
  HPthreshold = 0.05,
  PrintLevel = 1,
  DiagnosticsLevel = 1,
  itemSort = FALSE,
  ...
)

Arguments

object

(Object of class faMain) The returned object from a call to faMain.

digits

(Integer) Print output with user-specified number of significant digits. Default digits = 2.

Set

The argument Set can be specified as either an integer value (i.e., 1 through the number of unique solution sets) or a character value (i.e., 'UnSpun').

• Integer Summarize the solution from the specified solution set. If Set = 1, the "global minimum" solution is reported. See faMain for more details about finding the "global" and local minima.

• 'UnSpun' Summarize the solution from the rotated output that was produced by rotating from the unrotated (i.e., unspun) factor orientation. All other solutions are rotated from a randomly 'spun' rotation (i.e., by orientating the unrotated factor solution via a random orthonormal matrix) .

HPthreshold

(Numeric) User-defined threshold for declaring that the absolute value of a factor pattern coefficient is in a hyperplane. The hyperplane count is the number of near-zero (as defined by HPthreshold; see Cattell, 1978, p. 105) elements in the factor pattern matrix. Default HPthreshold = .05.

PrintLevel

(Integer) Controls the level of printing. If PrintLevel = 0 then no output is printed. If PrintLevel = 1 then the standard output will be printed. If PrintLevel = 2 more extensive output (e.g., the Factor Structure Matrix) will be printed. Default PrintLevel = 1.

DiagnosticsLevel

(Integer) Controls the amount of diagnostics information that is computed on the rotation local minima. If DiagnosticsLevel = 1 then only the number of local solution sets will be reported. If DiagnosticsLevel = 2 then the program will determine whether all solutions within a solution set are identicial. Default DiagnosticsLevel = 1.

itemSort

(Logical) If TRUE, sort the order of the observed variables to produce a "staircase"-like pattern. Note that this argument cannot handle bifactor models at this time. Defaults to itemSort = FALSE.

...

Additional arguments affecting the summary produced.

Details

summary.faMain provides various criteria for judging the adequacy of the rotated factor solution(s). After reporting the number of solution sets. (i.e., rotated solutions with the same complexity value) the following measures of factor adequacy are reported for each solution set:

• Complexity Value: The rotation complexity value (see faMain for details).

• Hyperplane Count: The number of near-zero loadings (defined by HPthreshold) for all factor patterns in a solution set (if MaxWithinSetRMSD > 0 then Hyperplane Count refers to the first factor pattern in the solution set).

• % Cases (x 100) in Set: The percentage of factor patterns in each solution set.

• RMSD: The root mean squared deviation between the first factor pattern in each solution set with the first factor pattern in the solution set specified by the Set parameter. By default, Set = 1.

• MaxWithinSetRMSD: The maximum root mean squared deviation between all within set solutions and the first element in the solution set. When MaxWithinSetRMSD > 0 then the solution set contains non-identical rotated factor patterns with identical complexity values.

• Converged: A Logical (TRUE/FALSE) that indicates whether the first solution in a solution set has a TRUE convergence status.

Note that the printed factor pattern is not sorted even if itemSort is requested in faMain.

Value

• loadings (Matrix) Factor loadings for the solution associated with the minimum (maximum) rotation complexity value (default) or the user-chosen solution.

• Phi (Matrix) Factor correlation matrix for the solution associated with the minimum (maximum) rotation complexity value (default) or the user-chosen solution.

• FS (Matrix) Factor structure matrix for the solution associated with the minimum (maximum) rotation complexity value (default) or the user-chosen solution.

• Set (Integer) The returned Set number.

• h2 (Matrix) Communalities for the returned factor solution. If Boostrap = TRUE then h2 also returns the bootstrap standard errors and associated confidence bounds from the bootstrap distribution.

• facIndeterminacy (Vector) Factor Indeterminacy values (correlations between the factors and factor scores). If Boostrap = TRUE then facIndeterminacy also returns the bootstrap standard errors and associated confidence bounds from the boostrap distribution.

• SetComplexityValues (Vector) Rotation complexity value for each solution set.

• HP_counts (Vector) Hyperplane count for each solution set.

• MaxWithinSetRMSD (Vector) If DiagnosticsLevel = 2 the the program will compute within set RMSD values. These values represent the root mean squared deviations of each within set solution with the first solution in a set. If the MaxWithinSetRMSD = 0 for a set, then all within set solutions are identical. If MaxWithinSetRMSD > 0 then at least one solution differs from the remaining solutions within a set (i.e., two solutions with different factor loadings produced identical complexity values).

• RMSD (Numeric) The root mean squared deviation between the observed and model-implied correlation matrix.

• RMSAD (Numeric) The root mean squared absolute deviation between the observed and model-implied correlation matrix.

• NumberLocalSolutions (Integer) The number of local solution sets.

• LocalSolutions (List) A list of local solutions (factor loadings, factor correlations, etc).

• rotate Designates which rotation method was applied.

• itemOrder The item order of the (possibly) sorted factor loadings.

Author(s)

• Niels G. Waller ([e-mail])

• Casey Giordano ([e-mail])

References

Cattell, R. (1978). The scientific use of factor analysis in behavioral and life sciences. New York, New York, Plenum.

See Also

Other Factor Analysis Routines: BiFAD(), Box26, GenerateBoxData(), Ledermann(), SLi(), SchmidLeiman(), faAlign(), faEKC(), faIB(), faLocalMin(), faMB(), faMain(), faScores(), faSort(), faStandardize(), faX(), fals(), fapa(), fareg(), fsIndeterminacy(), orderFactors(), print.faMB(), print.faMain(), promaxQ(), summary.faMB()

Examples

## Load Thurstone's Box data from the fungible library
library(fungible)
data(Box26)

## Create a matrix from Thurstone's solution
## Used as a target matrix to sort columns of the estimated solution
ThurstoneSolution <- matrix(c(   .95,  .01,  .01,
                                 .02,  .92,  .01,
                                 .02,  .05,  .91,
                                 .59,  .64, -.03,
                                 .60,  .00,  .62,
                                -.04,  .60,  .58,
                                 .81,  .38,  .01,
                                 .35,  .79,  .01,
                                 .79, -.01,  .41,
                                 .40, -.02,  .79,
                                -.04,  .74,  .40,
                                -.02,  .41,  .74,
                                 .74, -.77,  .06,
                                -.74,  .77, -.06,
                                 .74,  .02, -.73,
                                -.74, -.02,  .73,
                                -.07,  .80, -.76,
                                 .07, -.80,  .76,
                                 .51,  .70, -.03,
                                 .56, -.04,  .69,
                                -.02,  .60,  .58,
                                 .50,  .69, -.03,
                                 .52, -.01,  .68,
                                -.01,  .60,  .55,
                                 .43,  .46,  .45,
                                 .31,  .51,  .46), nrow = 26, ncol = 3,
                                                            byrow=TRUE)
## Example 1: Multiple solution sets.
## Ignore warnings about non-positive definite sample correlation matrix
suppressWarnings(
  fout <- faMain(R             = Box26,
                 numFactors    = 3,
                 facMethod     = 'faregLS',
                 rotate        = 'infomaxQ',
                 targetMatrix  = ThurstoneSolution,
                 rotateControl = 
                   list(numberStarts = 25, ## increase in real problem
                        standardize  = 'none'),
                 Seed          = 123)
)

## Summarize the factor analytic output                                     
summary(object           = fout, 
        digits           = 2,
        Set              = 2, 
        HPthreshold      = .10,
        PrintLevel       = 1,
        DiagnosticsLevel = 2)
          
     
## Example 2: Bootstrap Illustration 
## Step 1: In an initial analysis, confirm that all rotations converge
  ## to a single minimum complexity value.
## Step 2: If Step 1 is satisfied then generate bootstrap samples.

## Load Amazon box data             
data("AmzBoxes")

## Convert box dimensions into Thurstone's indicators
BoxData <- 
  GenerateBoxData(AmzBoxes[, 2:4],          ## Select columns 2, 3, & 4
                  BoxStudy         = 26,    ## 26 indicators
                  Reliability      = 0.75,  ## Add unreliability
                  SampleSize       = 200,   ## Add sampling error
                  ModApproxErrVar  = 0.1,   ## Add model approx error
                  NMinorFac        = 50,    ## Number of minor factors
                  epsTKL           = 0.2,   ## Spread of minor factor influence
                  SeedErrorFactors = 1,     ## Reproducible starting seed
                  SeedMinorFactors = 2,     ## Reproducible starting seed
                  PRINT            = FALSE, ## Suppress some output
                  LB               = FALSE, ## Do not set lower-bounds
                  LBVal            = 1,     ## Lower bound value (ignored)
                  Constant         = 0)     ## Do not add constant to data
                           
## Analyze new box data with added measurement error
fout <- faMain(X             = BoxData$BoxDataE,
               numFactors    = 3,
               facMethod     = 'fapa',
               rotate        = 'infomaxQ',
               targetMatrix  = ThurstoneSolution,
               bootstrapSE   = FALSE,
               rotateControl = 
                 list(numberStarts = 25, ## increase in real problem
                      standardize  = 'CM'),
               Seed          = 1)
               
## Summarize factor analytic output                
sout <- summary(object     = fout, 
                Set        = 1,
                PrintLevel = 1)
                
## Generate bootstrap samples
fout <- faMain(X             = BoxData$BoxDataE,
               numFactors    = 3,
               facMethod     = 'fapa',
               rotate        = 'infomaxQ',
               targetMatrix  = ThurstoneSolution,
               bootstrapSE   = TRUE,
               numBoot       = 25,   ## increase in real problem
               rotateControl = 
                 list(numberStarts = 1,
                      standardize  = 'CM'),
               Seed          = 1)

## Summarize factor analytic output with bootstraps
sout <- summary(object     = fout, 
                Set        = 1,
                PrintLevel = 2)  
                  
 ## To print a specific solution without computing diagnostics and 
   ## summary information, use the print function.
 
   print(fout, 
         Set = 1)