R help - Jun 2012 - Negative variance with lavaan in a multigroup analysis.

Hi list members,

I saw a couple lavaan posts here so I think I?m sending this to the
correct list.

I am trying to run a multigroup analysis with lavaan in order to
compare behavioural correlations across two populations. I?m following
the method suggested in the paper by Dingemanse et al. (2010) in
Behavioural Ecology.
In one of the groups, lavaan returns negative variance for one path
and I?m unable to obtain the corresponding R-square. As far as I know,
this is not due to measurement error so I?m wondering what else could
be causing this. Since the behavioral variables were standardized at
the population level prior to SEM analysis, lavaan should return 1 for
the variance and all paths coefficients should vary between 0 and 1,
right? Is there anything wrong in my code that may be causing this?

Thanks a lot for your help!

Raphael Royaute
PhD candidate
Dept Natural Resource Sciences
McGill University, Macdonald campus

Below is my code and output (my apologies, this is a pretty lengthy output):
Riskmodel2_cfa <- '# Latent variable
????? ????? SySt =~ Activity+Aggression+Voracity
# Residuals
??????? Boldness~~Boldness'
fit.riskmodel2_multi_Ad_cfa <- cfa(Riskmodel2_cfa, data=Ad_scale,
std.lv=T,std.ov=T,
???????????????????????????????? se=
"boot",test="bootstrap",
???????????????????????????????? bootstrap=5000L,group="Site")
summary(fit.riskmodel2_multi_Ad_cfa,standardized=T, rsquare=T)

lavaan (0.4-14) converged normally after 50 iterations
? Number of observations per group
? 1???????????????????????????????????????????????? 56
? 0????????????????????? ???????????????????????????41

? Estimator???????????????????????????????????????? ML
? Minimum Function Chi-square??????????????????? 6.171
? Degrees of freedom???????????????????????????????? 6
? P-value??????????????????????????????????????? 0.404
? P-value (Bollen-Stine Bootstrap)?????????????? 0.566

Chi-square for each group:
? 1????????????????????????????????????????????? 4.832
? 0????????????????????????????????????????????? 1.339
Parameter estimates:
? Information?????????????????????????????? ??Observed
? Standard Errors??????????????????????????? Bootstrap
? Number of requested bootstrap draws???????????? 5000
? Number of successful bootstrap draws??????????? 3423

Group 1 [1]:
?????????????????? Estimate? Std.err? Z-value? P(>|z|)?? Std.lv? Std.all
Latent variables:
? SySt =~
??? Activity????????? 0.295??? 0.193??? 1.532??? 0.126??? 0.295??? 0.298
??? Aggression??????? 0.962??? 7.533??? 0.128??? 0.898??? 0.962??? 0.971
??? Voracity????????? 0.481??? 1.223??? 0.393??? 0.694??? 0.481??? 0.485

Intercepts:
??? Activity????????? 0.000??? 0.132??? 0.000??? 1.000??? 0.000??? 0.000
??? Aggression??????? 0.000??? 0.131??? 0.000??? 1.000??? 0.000??? 0.000
??? Voracity???????? -0.000??? 0.133?? -0.000??? 1.000?? -0.000?? -0.000
??? Boldness????????? 0.000??? 0.130??? 0.000??? 1.000??? 0.000??? 0.000
??? SySt????????????? 0.000?????????????????????????????? 0.000??? 0.000

Variances:
??? Boldness????????? 0.982??? 0.192????????????????????? 0.982??? 1.000
??? Activity????????? 0.895??? 0.194????????????? ????????0.895??? 0.911
??? Aggression??????? 0.056? 291.974????????????????????? 0.056??? 0.057
??? Voracity????????? 0.751?? 31.367????????????????????? 0.751??? 0.765
??? SySt????????????? 1.000?????????????????????????????? 1.000??? 1.000
Group 2 [0]:
?????????????????? Estimate? Std.err? Z-value? P(>|z|)?? Std.lv? Std.all
Latent variables:
? SySt =~
??? Activity????????? 1.599?? 11.281??? 0.142??? 0.887??? 1.599??? 1.619
??? Aggression??????? 0.162??? 0.219??? 0.740??? 0.459??? 0.162??? 0.164
??? Voracity????????? 0.260??? 0.238??? 1.094??? 0.274??? 0.260??? 0.263

Intercepts:
??? Activity????????? 0.000??? 0.155??? 0.000??? 1.000??? 0.000??? 0.000
??? Aggression?????? -0.000??? 0.154?? -0.000??? 1.000?? -0.000?? -0.000
??? Voracity????????? 0.000??? 0.156??? 0.000??? 1.000??? 0.000??? 0.000
??? Boldness????????? 0.000??? 0.156??? 0.000??? 1.000??? 0.000??? 0.000
??? SySt????????????? 0.000?????????????????????????????? 0.000??? 0.000

Variances:
??? Boldness????????? 0.976??? 0.156???????????????????? ?0.976??? 1.000
??? Activity???????? -1.580? 459.764???????????????????? -1.580?? -1.620
??? Aggression??????? 0.949??? 0.197????????????????????? 0.949??? 0.973
??? Voracity????????? 0.908??? 0.248????????????????????? 0.908??? 0.931
??? SySt???????????? ?1.000?????????????????????????????? 1.000??? 1.000

R-Square Group 1:
??? Activity????????? 0.089
??? Aggression??????? 0.943
??? Voracity????????? 0.235
R-Square Group 0:
??? Activity???????????? NA
??? Aggression??????? 0.027
??? Voracity????????? 0.069