Estimating School-Level Factor Scores in a Three-Tier CFA?

CFA
1

Using three-level data (teacher, school, country), I run CFA with lavaan to derive school-level factor scores and test invariance. How can I aggregate teacher scores to schools?

library(lavaan)
library(surveyAdjuvant)

# Define alternative factor model
model_spec <- ' 
  leadership_quality =~ LQ_1 + LQ_2 + LQ_3
  teamwork =~ TW_1 + TW_2 + TW_3
'

# Fit models across groups
default_fit <- cfa(model = model_spec, data = survey_data, group = 'nationID')
metric_fit <- cfa(model = model_spec, data = survey_data, group = 'nationID', group.equal = 'loadings')
scalar_fit <- cfa(model = model_spec, data = survey_data, group = 'nationID', group.equal = c('loadings','intercepts'))

summary(scalar_fit)
2

i would avg teacher scores by school id using aggregate in base r. this simple mean works well but check model fit trends, esp if scool level variance is odd.