REM_CFA {REMLA}

Robust Estimation Maximization Estimates for Confirmatory Factor Analysis

Description

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

Usage

REM_CFA(X, delta = 0.05, model = NA, ctrREM = controlREM())

Arguments

X

data to analyze; should be a data frame or matrix

delta

hyperparameter between 0 and 1 that captures the researcher’s tolerance of incorrectly down-weighting data from the model (default = 0.05).

model

string variable that contains each structural equation in a new line where equalities are denoted by the symbol "~".

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_CFA returns an object of class "REM". The function summary() is used to obtain estimated parameters from the model. An object of class "REM" in Confirmatory Factor Analysis is a list of outputs with four different components: 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

delta

hyperparameter between 0 and 1 that captures the researcher’s tolerance of incorrectly down-weighting data from the model

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

BIC_rem

Bayesian Information Criterion

mu

item intercepts

lambda

factor loadings

psi

unique variances of items

gamma

average weights

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

summary_table

summary of EM and REM estimates, SEs, Z statistics, p-values, and 95% confidence intervals

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

REM_EFA(), summary.REMLA()

Examples

# Creating latent model
library(lavaan)
library(GPArotation)
df <- HolzingerSwineford1939
data = df[,-c(1:6)]

model <- "Visual  =~  x1 + x2 + x3
         Textual =~  x4 + x5 + x6
         Speed   =~  x7 + x8 + x9"

# Modeling Confirmatory Factor Analysis
model_CFA = REM_CFA(X = data, delta = 0.05, model = model)
summary(model_CFA)