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I am working on a dataset with 3 levels:

  1. Teacher
  2. School
  3. Country

Using survey responses from the teachers, the aim is to use Confirmatory Factor Analysis (CFA) with the ultimate goal of having the factor scores at the school level.

A further objective is to test for measurement invariance across countries.

I want to use the lavaan package in R, because it is able to deal with the complex survey design of my data trough the lavaan.survey-extension (sampling design, weights etc.)

I have done some preliminary analysis, where i use country-ID as the group argument in the cfa-function. This gives me the possibility to perform the measurement invariance analysis across countries. The issue is, that my factor scores are given at individual teacher level, and i am interested in the school-level.

Any ideas about how to get these factor scores at the school level?

Here are some examples of the functions i use. I do not think that i data sample is needed, but i will create some if it is requested.

library(lavaan)
library(SEMtools)

#define model
reduced_mod <-' 
 leadership_sup =~ TC3G22D + TC3G22E + TC3G22K
 continous_develop_collab =~ TT3G32A + TT3G32B + TT3G32C + TT3G32D '

#Fit model with different restraints:
fit_no_restraint <- cfa(model = reduced_mod, data = cfa_data, group="countryID")

fit_metric <- cfa(model = reduced_mod, data = cfa_data, group="countryID", group.equal = c("loadings"))

fit_scalar <- cfa(model = reduced_mod, data = cfa_data, group="countryID", group.equal = c("loadings", "intercepts"))

#Compare fit statistics
compareFit(scalar = fit_scalar , metric = fit_metric , config = fit_no_restraint)
Anders
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1 Answers1

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It seems that you want multilevel measurement invariance. You should use the measEq.syntax() from the semTools package:

## ---------------------
## Multilevel Invariance
## ---------------------

## To test invariance across levels in a MLSEM, specify syntax as though
## you are fitting to 2 groups instead of 2 levels.

mlsem <- ' f1 =~ y1 + y2 + y3
           f2 =~ y4 + y5 + y6 '
## metric invariance
syntax.metric <- measEq.syntax(configural.model = mlsem, meanstructure = TRUE,
                               ID.fac = "std.lv", sample.nobs = c(1, 1),
                               group = "cluster", group.equal = "loadings")
## by definition, Level-1 means must be zero, so fix them
syntax.metric <- update(syntax.metric,
                        change.syntax = paste0("y", 1:6, " ~ c(0, NA)*1"))
## save as a character string
mod.metric <- as.character(syntax.metric, groups.as.blocks = TRUE)
## convert from multigroup to multilevel
mod.metric <- gsub(pattern = "group:", replacement = "level:",
                   x = mod.metric, fixed = TRUE)
## fit model to data
fit.metric <- lavaan(mod.metric, data = Demo.twolevel, cluster = "cluster")
summary(fit.metric)

Source

Sinval
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