Fully cross-classified multilevel CFA

Hi there,

We are conducting a study in educational science where raters are assessing teachers.

The data structure is fully cross-classified, meaning that all raters are rating all teachers. In our case all 8 raters are rating the same 46 teachers with the same items. All teachers are rated by all raters.

We would like to conduct a multilevel CFA where the teachers are at level 2 and the raters are at level 1.

This is the syntax (using the cfa function from the lavaan package)

model <- "level:1
f1 =~ item1 + a*item2 + b*item3 + c*item4 + (1|rater)
f2 =~ item5 + d*item6 + e*item7 + (1|rater)
f1 =~ item1 + a*item2 + b*item3 + c*item4
f2 =~ item5 + d*item6 + e*item7
item2 ~~ 0*item2
item5 ~~ 0*item5
item6 ~~ 0*item6
item7 ~~ 0*item7"

multilevel_cfa <-cfa(model, data=dat, std.lv = FALSE, verbose= FALSE,
            cluster = "teacher")

We would like to conduct a fully cross classified multilevel CFA. The rater (1|rater) are the identifiers for the videos.

  1. Is the syntax correct?
  2. At first we got negative variance. Then the variances for the items in question were fixed to zero. Is this approach (fixing variances to zero) acceptable?

Best regards
datatable_screenshot.pdf (221.8 KB)

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