disfa {drclust}

Disjoint Factor Analysis

Description

Performs disjoint factor analysis, i.e., a Factor Analysis with a simple structure. In fact, each factor is defined by a disjoint subset of variables, resulting thus, in a simplified, easier to interpret loading matrix A and factors. Estimation is carried out via Maximum Likelihood.

Usage

disfa(X, Q, Rndstart, verbose, maxiter, tol, constr, prep, print)

Arguments

X

Units x variables numeric data matrix.

Q

Number of factors.

Rndstart

Number of runs to be performed (Defaults is 20).

verbose

Outputs basic summary statistics for each run (1 = enabled; 0 = disabled, default option).

maxiter

Maximum number of iterations allowed (if convergence is not yet reached. Default is 100).

tol

Tolerance threshold (maximum difference between the values of the objective function of two consecutive iterations such that convergence is assumed. Default is 1e-6).

constr

is a vector of length J = nr. of variables, pre-specifying to which cluster some of the variables must be assigned. Each component of the vector can assume integer values from 1 o Q (See example for more details), or 0 if no constraint on the variable is imposed (i.e., it will be assigned based on the plain algorithm).

prep

Pre-processing of the data. 1 performs the z-score transform (default choice); 2 performs the min-max transform; 0 leaves the data un-pre-processed.

print

Prints summary statistics of the performed method (1 = enabled; 0 = disabled, default option).

Value

returns a list of estimates and some descriptive quantities of the final results.

V

Variables x factors membership matrix (binary and row-stochastic). Each row is a dummy variable indicating to which cluster each variable has been assigned.

A

Variables x components loading matrix.

Psi

Specific variance of each observed variable, not accounted for by the common factors (matrix).

discrepancy

Value of the objective function, to be minimized. Difference between the observed and estimated covariance matrices (scalar).

RMSEA

Adjusted Root Mean Squared Error (scalar).

AIC

Aikake Information Criterion (scalar).

BIC

Bayesian Information Criterion (scalar).

GFI

Goodness of Fit Index (scalar).

Author(s)

Ionel Prunila, Maurizio Vichi

References

Vichi M. (2017) "Disjoint factor analysis with cross-loadings" <doi:10.1007/s11634-016-0263-9>

Examples

# Iris data 
# Loading the numeric variables of iris data
iris <- as.matrix(iris[,-5]) 

# No constraint on variables
out <- disfa(iris, Q = 2)

# Constraint: the first two variables must contribute to the same factor.
outc <- disfa(iris, Q = 2, constr = c(1,1,0,0))