summary.faMB {fungible}

Summary Method for an Object of Class faMB

Description

This function summarizes results from a call to faMB.

Usage

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

Arguments

object

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

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, the Residuals Matrix [i.e., Observed - fitted R]) 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.

...

Additional arguments affecting the summary produced.

Details

summary.faMB 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 all within set rotations converged.

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.

• facIndeterminacy (Matrix) Factor Indeterminacy values.

• 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).

• ChiSq (Numeric) Chi-square goodness of fit value. As recommended by Browne (1979), we apply Lawley's (1959) correction when computing the chi-square value when NB = 2.

• DF (Numeric) Degrees of freedom for the estimated model.

• pvalue (Numeric) P-value associated with the above chi-square statistic.

• AIC (Numeric) Akaike's Information Criterion where a lower value indicates better fit.

• BIC (Numeric) Bayesian Information Criterion where a lower value indicates better fit.

• RMSEA (Numeric) The root mean squared error of approximation (Steiger & Lind, 1980).

• Resid (Matrix) The residuals matrix (R - Rhat).

• 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.

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.faMain()

Examples

# These examples reproduce published multiple battery analyses. 

# ----EXAMPLE 1: Browne, M. W. (1979)----
#
# Data originally reported in:
# Thurstone, L. L. & Thurstone, T. G. (1941). Factorial studies 
# of intelligence. Psychometric Monograph (2), Chicago: Univ. 
# Chicago Press.

## Load Thurstone & Thurstone's data used by Browne (1979)
data(Thurstone41)

Example1Output <-  faMB(R             = Thurstone41, 
                        n             = 710,
                        NB            = 2, 
                        NVB           = c(4,5), 
                        numFactors    = 2,
                        rotate        = "oblimin",
                        rotateControl = list(standardize = "Kaiser"))
                        
## Call the summary function
summary(Example1Output)

# ----EXAMPLE 2: Browne, M. W. (1980)----
# Data originally reported in:
# Jackson, D. N. & Singer, J. E. (1967). Judgments, items and 
# personality. Journal of Experimental Research in Personality, 20, 70-79.

## Load Jackson and Singer's dataset
data(Jackson67)

Example2Output <-  faMB(R             = Jackson67, 
                        n             = 480,
                        NB            = 5, 
                        NVB           = rep(4,5), 
                        numFactors    = 4,
                        rotate        = "varimax",
                        rotateControl = list(standardize = "Kaiser"),
                        PrintLevel    = 1)

## Call the summary function
summary(object     = Example2Output,
        Set        = 1,
        PrintLevel = 1)

# ----EXAMPLE 3: Cudeck (1982)----
# Data originally reported by:
# Malmi, R. A., Underwood, B. J., & Carroll, J. B. (1979).
# The interrelationships among some associative learning tasks. 
# Bulletin of the Psychonomic Society, 13(3), 121-123. DOI: 10.3758/BF03335032 

## Load Malmi et al.'s dataset
data(Malmi79)

Example3Output <- faMB(R             = Malmi79, 
                       n             = 97,
                       NB            = 3, 
                       NVB           = c(3, 3, 6), 
                       numFactors    = 2,
                       rotate        = "oblimin",
                       rotateControl = list(standardize = "Kaiser"))

## Call the summary function
summary(object     = Example3Output,
        Set        = 1,
        PrintLevel = 2)
        
# ----Example 4: Cudeck (1982)----
# Data originally reported by: 
# Boruch, R. F., Larkin, J. D., Wolins, L. and MacKinney, A. C. (1970). 
#  Alternative methods of analysis: Multitrait-multimethod data. Educational 
#  and Psychological Measurement, 30,833-853.

## Load Boruch et al.'s dataset
data(Boruch70)

Example4Output <- faMB(R             = Boruch70,
                       n             = 111,
                       NB            = 2,
                       NVB           = c(7,7),
                       numFactors    = 2,
                       rotate        = "oblimin",
                       rotateControl = list(standardize  = "Kaiser",
                                            numberStarts = 100))

## Call the summary function
summary(Example4Output)