# 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`. ```r 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 ## Returns 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 ```r ## Not run: ############################################################################# # 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 ## End(Not run) ```

cfa_meas_inv function