[R] Negative variance with lavaan in a multigroup analysis.

[Raphael Royaute]

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