I have set up a model like this:
model3<-'
# MEASUREMENT
union =~ V24 + V25
loyality =~ V52 + V53 + V54
experience =~ V37 + V38 + V39 + V40
# STRUCTURAL
union ~ loyality
union ~ experience
# CORRELATED RESIDUALS
V37 ~~ V39
V37 ~~ V38
'
From summary i obtain:
> summary(fit3 , standardized=T, fit.measures=T, rsquare=T)
lavaan (0.5-23.1097) converged normally after 77 iterations
Number of observations 21972
Estimator DWLS Robust
Minimum Function Test Statistic 330.153 394.021
Degrees of freedom 22 22
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.847
Shift parameter 4.299
for simple second-order correction (Mplus variant)
Model test baseline model:
Minimum Function Test Statistic 30573.174 22082.251
Degrees of freedom 36 36
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.990 0.983
Tucker-Lewis Index (TLI) 0.983 0.972
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Root Mean Square Error of Approximation:
RMSEA 0.025 0.028
90 Percent Confidence Interval 0.023 0.028 0.025 0.030
P-value RMSEA <= 0.05 1.000 1.000
Robust RMSEA NA
90 Percent Confidence Interval NA NA
Standardized Root Mean Square Residual:
SRMR 0.018 0.018
Parameter Estimates:
Information Expected
Standard Errors Robust.sem
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
union =~
V24 1.000 1.061 0.928
V25 0.777 0.058 13.387 0.000 0.824 0.752
loyality =~
V52 1.000 0.690 0.650
V53 1.167 0.023 51.579 0.000 0.806 0.845
V54 0.936 0.017 55.844 0.000 0.646 0.520
experience =~
V37 1.000 0.349 0.363
V38 2.570 0.071 36.179 0.000 0.897 0.695
V39 0.915 0.033 28.040 0.000 0.319 0.302
V40 2.359 0.100 23.481 0.000 0.824 0.680
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
union ~
loyality 0.039 0.015 2.656 0.008 0.025 0.025
experience 0.346 0.031 11.169 0.000 0.114 0.114
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.V37 ~~
.V39 0.336 0.008 44.158 0.000 0.336 0.372
.V38 0.146 0.012 11.717 0.000 0.146 0.176
loyality ~~
experience -0.034 0.003 -11.799 0.000 -0.142 -0.142
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.V24 2.521 0.008 326.748 0.000 2.521 2.204
.V25 2.411 0.007 326.002 0.000 2.411 2.199
.V52 2.413 0.007 336.811 0.000 2.413 2.272
.V53 2.262 0.006 351.664 0.000 2.262 2.372
.V54 3.211 0.008 382.509 0.000 3.211 2.581
.V37 2.680 0.006 413.404 0.000 2.680 2.789
.V38 3.494 0.009 401.170 0.000 3.494 2.706
.V39 2.857 0.007 400.392 0.000 2.857 2.701
.V40 3.926 0.008 480.422 0.000 3.926 3.241
.union 0.000 0.000 0.000
loyality 0.000 0.000 0.000
experience 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.V24 0.181 0.084 2.152 0.031 0.181 0.139
.V25 0.522 0.051 10.244 0.000 0.522 0.435
.V52 0.651 0.012 53.863 0.000 0.651 0.578
.V53 0.260 0.012 21.187 0.000 0.260 0.286
.V54 1.130 0.013 88.016 0.000 1.130 0.730
.V37 0.801 0.010 81.075 0.000 0.801 0.868
.V38 0.861 0.030 28.782 0.000 0.861 0.517
.V39 1.017 0.010 104.495 0.000 1.017 0.909
.V40 0.789 0.026 29.953 0.000 0.789 0.538
.union 1.112 0.084 13.155 0.000 0.987 0.987
loyality 0.476 0.013 37.173 0.000 1.000 1.000
experience 0.122 0.008 16.093 0.000 1.000 1.000
R-Square:
Estimate
V24 0.861
V25 0.565
V52 0.422
V53 0.714
V54 0.270
V37 0.132
V38 0.483
V39 0.091
V40 0.462
union 0.013
The "funny" thing is that i get an error of negative variance when trying to check:
> measurementInvariance(model3,data=sub1,
+ group="SEX")
Measurement invariance models:
Model 1 : fit.configural
Model 2 : fit.loadings
Model 3 : fit.intercepts
Model 4 : fit.means
Chi Square Difference Test
Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
fit.configural 44 556605 557116 451.90
fit.loadings 50 556754 557218 613.68 161.78 6 < 2.2e-16 ***
fit.intercepts 56 557229 557645 1100.58 486.90 6 < 2.2e-16 ***
fit.means 59 558714 559106 2591.56 1490.98 3 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Fit measures:
cfi rmsea cfi.delta rmsea.delta
fit.configural 0.990 0.029 NA NA
fit.loadings 0.987 0.032 0.004 0.003
fit.intercepts 0.976 0.041 0.011 0.009
fit.means 0.941 0.063 0.035 0.021
Warning messages:
1: In lav_object_post_check(object) :
lavaan WARNING: some estimated ov variances are negative
2: In lav_object_post_check(object) :
lavaan WARNING: some estimated ov variances are negative
3: In lav_object_post_check(object) :
lavaan WARNING: some estimated ov variances are negative
I have been stuck on this for a while now. I have read that under variances in the output, there must be a negative variance (apparently even a single one can cause matrix of residual covariances to be positive definete. My question is:
- Where is that negative variance?! or at least What is causing the error and how i can get remove it?
Secondly, i did get some output from the measurementInvariance just before the error message.
- Is it possible to have the same significance for all Chi Square Difference Tests? or is this merely due to the fact that it is a very small number?
I really will appriciate any help. I am a newbie in lavaan and try to do the best in understanding, but here i need a little push.
Thank you!!