R help - Aug 2011 - lavaan: how to analyse residuals of a latent variable

Hi r-help,

I use lavaan:sem() for structural equation modelling with latent
variables. Below is a reproducible example (the code requires a
working installation of lavaan) where the latent variable criminality
is in focus. Besides criminality in general, I am specifically
interested one of the manifest variables that make up the latent
variable criminality, namely fire.setting.

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.

As far as I understand the output of the summary() - of which I have
reproduced a few lines - about half (0.499) of the variation in
fire.setting is included in the latent variable criminality.

                   Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
Latent variables:
  criminality =~
    fire.setting      0.324    0.007   48.223    0.000    0.189    0.499


I would like to analyse the "other half" of fire.setting, so to speak.


my.model <- "
## Measurement model (definitions of the latent variables)
priviledged.parents =~ nr.parents.employed + parental.housing

school.adaption =~ enjoying.school + good.teachers +
                   good.grades.important

school.grades =~ grade.language + grade.english + grade.craft +
                 grade.math + grade.chemistry + grade.arts +
                 grade.sports

criminality =~ vandalism + illegal.grafitti + shop.lifting +
               theft.from.automat + theft.from.school +
               theft.of.bicycle + theft.of.moped + theft.of.car +
               theft.from.car + theft.pick.pocket + burglary +
               buying.stolen.goods + selling.stolen.goods +
               wearing.knife + robbery + fire.setting +
               abuse.unknown.persons + abuse.family.members +
               used.knife + drugs.cannabis + drugs.other +
               drugs.thinner + drugs.steroids + selling.drugs.cannabis
               + selling.drugs.other

## Regressions
priviledged.parents ~ parental.migration + parental.class

school.adaption ~ parental.migration + parental.class + sex.girl +
		  priviledged.parents

school.grades ~ parental.migration + parental.class + sex.girl +
	      	priviledged.parents

criminality ~ parental.migration + parental.class + sex.girl +
	      priviledged.parents + school.adaption + school.grades "

library(lavaan)
con <- url("http://code.cjb.net/temp/lavaan.temp.RData")
print(load(con))
close(con)
my.fit <- sem(my.model, data = my.crim.set)
summary(my.fit, fit.measures = T, standardized = T)

-- 
Hans Ekbrand
Department of Sociology
University of Gothenburg
Sweden
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> 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