REM_EFA: Robust Estimation Maximization for Exploratory Factor...

In REMLA: Robust Expectation-Maximization Estimation for Latent Variable Models

Robust Estimation Maximization for Exploratory Factor Analysis

Description

This function uses the robust expectation maximization (REM) algorithm to estimate the parameters of an exploratory factor analysis model as suggested by Nieser & Cochran (2021).

Usage

REM_EFA(X, k_range, delta = 0.05, rotation = "oblimin", ctrREM = controlREM())

Arguments

X	data to analyze; should be a data frame or matrix
k_range	vector of the number of factors to consider
delta	hyperparameter between 0 and 1 that captures the researcher’s tolerance of incorrectly down-weighting data from the model (default = 0.05)
rotation	factor rotation method (default = 'oblimin'); 'varimax' is the only other available option at this time
ctrREM	control parameters (default: (steps = 25, tol = 1e-6, maxiter = 1e3, min_weights = 1e-30, max_ueps = 0.3, chk_gamma = 0.9, n = 2e4))

Value

REM_EFA returns an object of class "REM". The function summary() is used to obtain estimated parameters from the model. An object of class "REM" in Exploratory Factor Analysis is a list of outputs with four different components for each number of factor: the matched call (call), estimates using traditional expectation maximization (EM_output), estimates using robust expectation maximization (REM_output), and a summary table (summary_table). The list contains the following components:

call	match call
model	model frame
k	number of factors
constraints	p x k matrix of zeros and ones denoting the factors (rows) and observed variables (columns)
epsilon	hyperparameter on the likelihood scale
AIC_rem	Akaike information criterion based on REM estimates
BIC_rem	Bayesian information criterion based on REM estimates
mu	item intercepts
lambda	factor loadings
psi	unique variances of items
phi	factor covariance matrix
gamma	average weight
weights	estimated REM weights
ind_lik	likelihood value for each individual
lik_rem	joint log-likelihood evaluated at REM estimates
lik	joint log-likelihood evaluated at EM estimates
mu.se	standard errors of items intercepts
lambda.se	standard errors of factor loadings
psi.se	standard errors of unique variances of items
gamma.se	standard error of gamma
summary_table	summary of EM and REM estimates, SEs, Z statistics, p-values, and 95% confidence intervals

The summary function can be used to obtain estimated parameters from the optimal model based on the BIC from the EM and REM algorithms.

Author(s)

Bryan Ortiz-Torres ([e-mail]); Kenneth Nieser ([e-mail])

References

Nieser, K. J., & Cochran, A. L. (2021). Addressing heterogeneous populations in latent variable settings through robust estimation. Psychological Methods.

See Also

summary.REMLA() for more detailed summaries, oblimin() and varimax() for details on the rotation

Examples

# Modeling Exploratory Factor Analysis
library(lavaan)
library(GPArotation)
df <- HolzingerSwineford1939
data = df[,-c(1:6)]

model_EFA = REM_EFA( X = data, k_range = 1:3, delta = 0.05)
summary(model_EFA)

REMLA documentation built on May 29, 2024, 12:06 p.m.