Estimation of a Unidimensional Factor Model under Full and Partial Measurement Invariance

Estimates a unidimensional factor model based on the normal distribution fitting function under full and partial measurement invariance. Item loadings and item intercepts are successively freed based on the largest modification index and a chosen significance level alpha.

Usage

cfa_meas_inv(dat, group, weights=NULL, alpha=0.01, verbose=FALSE, op=c("~1","=~"))

Arguments

dat

Data frame containing items

group

Vector of group identifiers

weights

Optional vector of sampling weights

alpha

Significance level

verbose

Logical indicating whether progress should be shown

op

Operators (intercepts or loadings) for which estimation should be freed

Value

List with several entries

pars_mi

Model parameters under full invariance

pars_pi

Model parameters under partial invariance

mod_mi

Fitted model under full invariance

mod_pi

Fitted model under partial invariance

...

More output

See also

See also sirt::invariance.alignment

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Factor model under full and partial invariance
#############################################################################

#--- data simulation

set.seed(65)
G <- 3  # number of groups
I <- 5  # number of items
# define lambda and nu parameters
lambda <- matrix(1, nrow=G, ncol=I)
nu <- matrix(0, nrow=G, ncol=I)
err_var <- matrix(1, nrow=G, ncol=I)

# define size of noninvariance
dif <- 1
#- 1st group: N(0,1)
lambda[1,3] <- 1+dif*.4; nu[1,5] <- dif*.5
#- 2nd group: N(0.3,1.5)
gg <- 2 ;
lambda[gg,5] <- 1-.5*dif; nu[gg,1] <- -.5*dif
#- 3nd group: N(.8,1.2)
gg <- 3
lambda[gg,4] <- 1-.7*dif; nu[gg,2] <- -.5*dif
#- define distributions of groups
mu <- c(0,.3,.8)
sigma <- sqrt(c(1,1.5,1.2))
N <- rep(1000,3) # sample sizes per group

#* use simulation function
dat <- sirt::invariance_alignment_simulate(nu, lambda, err_var, mu, sigma, N,
                exact=TRUE)

#--- estimate CFA
mod <- sirt::cfa_meas_inv(dat=dat[,-1], group=dat$group, verbose=TRUE, alpha=0.05)
mod$pars_mi
mod$pars_pi
}