I have a good fitting CFA model and am now conducting some additional analyses by different subgroups (e.g., gender, age, education, ...). Specifically, I'm calculating fit indices for measurement invariance (configural, metric, scalar). Everything looks fine, except for one of my subgroups. I get the following Warning message in Lavaan for a group that has a relatively small sample size:
Warning message:
In lav_object_post_check(object) :
lavaan WARNING: covariance matrix of latent variables
is not positive definite;
use lavInspect(fit, "cov.lv") to investigate.
Model specification and fit:
model <- '
F1 =~ a + b + c + d + e
F2 =~ f + g + h + i + j
F3 =~ k + l + m + n + o
F4 =~ p + q + r + s + t
F5 =~ u + v + w + x + y
Crossload =~ g + j + n + o + q
'
fit.model.group3 <- sem(model, data=MyData.group3, estimator='WLSMV', missing='pairwise', ordered = T)
fit.model.configural.edu <- sem(model, data=MyData.edu, estimator='WLSMV', missing='pairwise', ordered = T, group = "edu")
This grouping variable (edu) has 3 levels (Ns: group1 = 1150, group2 = 215, group3 = 120), and I only get the warning for group3 (the smallest group). I can fix it combining some factors (which were strongly correlated for this group), and then fitting the more parsimonious (4-factor) model. However, as the point of this subgroup analysis is to investigate the same CFA model across the different subgroups, I don't think it's appropriate to change the model specification(?). And so, is it okay to ignore this warning message for the sake of the measurement invariance analysis (the model still converges normally, and I get the necessary metrics)? Note that some of the eigenvalues are negative, and I get the following output from this call:
> det(lavInspect(fit.model.group3, "cov.lv"))
[1] 2.544325e-06
As it's close to zero, could it be a machine precision issue?
Any advice would be very much appreciated. Unfortunately, my technical knowledge is lacking and so I've struggled to follow some of the existing advice elsewhere.
Best wishes, Mary
