My question is: how can I analyse the part of the variation in
fire.setting that is not included in the latent variable criminality?
Ideally I would want a new variable that captures just this. Then I
could model regressions with this variable as the dependent variable.

You can add a regression line to your model syntax with 'fire.setting' as the dependent variable:

fire.setting ~ x1 + x2 + x3

were x1-x3 are additional predictors that might influence the variable 'fire.setting'.

Yves Rosseel
http://lavaan.org

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