fungible (version 2.4.4)

Ledermann: Ledermann's inequality for factor solution identification

Description

Ledermann's (1937) inequality to determine either (a) how many factor indicators are needed to uniquely estimate a user-specified number of factors or (b) how many factors can be uniquely estimated from a user-specified number of factor indicators. See the Details section for more information

Usage

Ledermann(numFactors = NULL, numVariables = NULL)

Value

• numFactors (Numeric) Given the inputs, the number of factors to be estimated from the numVariables number of factor indicators.

• numVariables (Numeric) Given the inputs, the number of variables needed to estimate numFactorso.

Arguments

numFactors

(Numeric) Determine the number of variables needed to uniquely estimate the [user-specifed] number of factors. Defaults to numFactors = NULL.

numVariables

(Numeric) Determine the number of factors that can be uniquely estimated from the [user-specifed] number of variables Defaults to numVariables = NULL.

Author

Casey Giordano

Details

The user will specified either (a) numFactors or (b) numVariables. When one value is specified, the obtained estimate for the other may be a non-whole number. If estimating the number of required variables, the obtained estimate is rounded up (using ceiling). If estimating the number of factors, the obtained estimate is rounded down (using floor). For example, if numFactors = 2, roughly 4.56 variables are required for an identified solution. However, the function returns an estimate of 5.

For the relevant equations, see Thurstone (1947, p. 293) Equations 10 and 11.

References

Ledermann, W. (1937). On the rank of the reduced correlational matrix in multiple-factor analysis. Psychometrika, 2(2), 85-93.

Thurstone, L. L. (1947). Multiple-factor analysis; a development and expansion of The Vectors of Mind.

See Also

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

Examples

## To estimate 3 factors, how many variables are needed?
Ledermann(numFactors   = 3,
          numVariables = NULL) 
          
## Provided 10 variables are collected, how many factors 
  ## can be estimated?
Ledermann(numFactors   = NULL,
          numVariables = 10)