communalities_optimal_solution {FactorAssumptions}

Calculates the Optimal Solution for Communalities in a Dataframe

Description

communalities_optimal_solution() call upon either the principal or fa functions from psych package to iterate over the variables of a dataframe.

Usage

communalities_optimal_solution(
  df,
  nfactors,
  type,
  rotate = "varimax",
  fm = "minres",
  squared = TRUE
)

Arguments

df

a dataframe with only int or num type of variables

nfactors

number of factors to extract in principal components or factor analysis

type

either principal for Principal Components Analysis or fa for Factor Analysis

rotate

rotation to be employed (default is varimax). "none", "varimax", "quartimax", "bentlerT", "equamax", "varimin", "geominT" and "bifactor" are orthogonal rotations. "Promax", "promax", "oblimin", "simplimax", "bentlerQ, "geominQ" and "biquartimin" and "cluster" are possible oblique transformations of the solution. The default is to do a oblimin transformation, although versions prior to 2009 defaulted to varimax. SPSS seems to do a Kaiser normalization before doing Promax, this is done here by the call to "promax" which does the normalization before calling Promax in GPArotation.

fm

Factoring method fm="minres" (default) will do a minimum residual as will fm="uls". Both of these use a first derivative. fm="ols" differs very slightly from "minres" in that it minimizes the entire residual matrix using an OLS procedure but uses the empirical first derivative. This will be slower. fm="wls" will do a weighted least squares (WLS) solution, fm="gls" does a generalized weighted least squares (GLS), fm="pa" will do the principal factor solution, fm="ml" will do a maximum likelihood factor analysis. fm="minchi" will minimize the sample size weighted chi square when treating pairwise correlations with different number of subjects per pair. fm ="minrank" will do a minimum rank factor analysis. "old.min" will do minimal residual the way it was done prior to April, 2017 (see discussion below). fm="alpha" will do alpha factor analysis as described in Kaiser and Coffey (1965)

squared

TRUE if matrix is squared (such as adjacency matrices), FALSE otherwise

Details

If finds any individual communality below the optimal value of 0.5 then removes the lowest communality value variable until no more variable has not-optimal communality values.

Value

A list with

1. df - A dataframe that has reached its optimal solution in terms of KMO values

2. removed - A list of removed variables ordered by the first to last removed during the procedure

3. loadings - A table with the communalities loadings from the variables final iteration

4. results - Results of the final iteration of either the principal or fa functions from psych package

See Also

principal the PCA function from psych and fa the Factor Analysis function from psych

Examples

set.seed(123)
df <- as.data.frame(matrix(rnorm(100*10, 1, .5), ncol=10))
communalities_optimal_solution(df, nfactors = 2,type = "principal", squared = FALSE)