Function performs multiple group analysis to check for measurement invariance

measurement_invariance.R

library(tidyverse)
library(lavaan)

measurement_invariance <- function(model, data, group, fit_measures) {
  
  ## Configural Model
  model1 <- cfa(model = model, data = data, group = group)
  ## Weak/metric invariance
  model2 <- cfa(model = model, data = data, group = group, group.equal=c("loadings"))
  ## Strong/scalar invariance
  model3 <- cfa(model = model, data = data, group = group, group.equal=c("loadings", "intercepts"))
  ## Strict invariance
  model4 <- cfa(model = model, data = data, group = group, group.equal=c("loadings", "intercepts", "residuals"))
  
  table_knitr <- bind_rows(
    fitmeasures(model1, fit.measures = fit_measures),
    fitmeasures(model2, fit.measures = fit_measures),
    fitmeasures(model3, fit.measures = fit_measures),
    fitmeasures(model4, fit.measures = fit_measures)
  )  %>%
    mutate(diff_chisq = chisq - lag(chisq)) %>%
    mutate(diff_df = df - lag(df)) %>%
    mutate(diff_rmsea = rmsea - lag(rmsea)) %>%
    mutate(diff_aic = aic - lag(aic)) 
  
  cat("[Weak/Metric Invariance]:\n\n")
  
  conf <- anova(model1, model2)
  
  print(conf)
  
  if (conf$`Pr(>Chisq)`[2] > 0.1) {
    cat("\nInsignificant Chi Squared change indicates weak/metric invariance!\n")
    
  } else if (conf$`Pr(>Chisq)`[2] <= 0.1) {
    cat("\nWeak/metric invariance could not be established!\n")
    return(table_knitr)
  }
  
  cat("\n\n[Strong/Scalar invariance]:\n\n")
  
  conf <- anova(model2, model3)
  
  print(conf)
  
  if (conf$`Pr(>Chisq)`[2] > 0.1) {
    cat("\nInsignificant Chi Squared change indicates strong/scalar invariance!\n")
    
  } else if (conf$`Pr(>Chisq)`[2] <= 0.1) {
    cat("\nStrong/scalar invariance could not be established!\n")
    return(table_knitr)
  }
  
  cat("\n\n[Strict invariance]:\n\n")
  
  conf <- anova(model3, model4)
  
  print(conf)
  
  if (conf$`Pr(>Chisq)`[2] > 0.1) {
    cat("\nInsignificant Chi Squared change indicates strict invariance!\n")
    
  } else if (conf$`Pr(>Chisq)`[2] <= 0.1) {
    cat("\nStrict invariance could not be established!\n")
    return(table_knitr)
  }
  
  return(table_knitr)
  
  
}

## Example 
HS.model <- ' visual =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

## define which fitmeasures you want
fit_measures <- c("chisq", "df", "pvalue", "cfi", "rmsea", "AIC")


## Check for measurement invariance
measurement_invariance(HS.model, 
                       group = "school", 
                       data = HolzingerSwineford1939, 
                       fit_measures = fit_measures)

Output: