very good fit indices but a warning message of latent variables with non positive definite cov matrix
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maryam nasseri
Mar 26, 2019, 7:27:55 AM3/26/19
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HI everyone,
I conducted a CFA/SEM test on a 3-factor model called lex.modelnew (one factor has a single indicator) which gives me the warning that "covariance matrix of latent variables is not positive definite" and I used lavInspect(fit, "cov.lv") with results that I show below; but when I checked goodness-of-fit indices, they all show very good fit.
Then I changed the model to a 2-factor model called lex.model2F (I moved the single indicator variable to its closely theoretically related factor) and the warning disappears but the fit indices show the same or very close results as the 3-factor model (all show very good fit).
-- Since both models' fit indices show very good fit, I was wondering which model to stick to and should I regard or disregard the warning message. The 3-factor model is the exact model taken from the theory/literature on the subject. Also the covariance matrix of latent variables for both models include a large positive value and negative values; what does a negative value here mean?
Below I'm pasting the exact code and results I got; many thanks to anyone who could help:
P.S: Terrence suggested the use of ridge in the sem function below:
lex.modelnew<- 'group1=~ ld + group2=~ mtld + vocd + ndwerz + ndwesz + mattr + hdd + logttr + rttr + uber + lv + nv + vv1 + vv2 + cvv1 + adjv + group3=~ ls1 + ls2 + vs2 + cvs1'
fitnew<- sem(lex.modelnew, sample.cov = shrink.cov, sample.nobs=210, ridge = .01) 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.
lavInspect(fitnew, "cov.lv") group1 group2 group3 group1 0.003 group2 0.207 135.422 group3 0.000 -0.334 0.001
summary(fitnew, ci = TRUE, fit.measures=TRUE, standardized = TRUE)
lavaan 0.6-3 ended normally after 342 iterations
Optimization method NLMINB
Number of free parameters 42
Number of observations 210
Estimator ML
Model Fit Test Statistic 43.786
Degrees of freedom 168
P-value (Chi-square) 1.000
Model test baseline model:
Minimum Function Test Statistic 2206.790
Degrees of freedom 190
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.070
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) 376.739
Loglikelihood unrestricted model (H1) 398.632
Number of free parameters 42
Akaike (AIC) -669.477
Bayesian (BIC) -528.899
Sample-size adjusted Bayesian (BIC) -661.979
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent Confidence Interval 0.000 0.000
P-value RMSEA <= 0.05 1.000
Standardized Root Mean Square Residual:
SRMR 0.023
Parameter Estimates:
Information Expected
Information saturated (h1) model Structured
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
group1 =~
ld 1.000 1.000 1.000 0.057 1.000
group2 =~
mtld 1.000 1.000 1.000 11.637 0.732
vocd 1.881 0.179 10.535 0.000 1.531 2.231 21.887 0.721
ndwerz 0.102 0.010 10.619 0.000 0.083 0.121 1.189 0.727
ndwesz 0.133 0.012 10.698 0.000 0.109 0.157 1.548 0.732
mattr 0.005 0.000 10.702 0.000 0.004 0.005 0.053 0.732
hdd 0.004 0.000 10.645 0.000 0.003 0.005 0.048 0.728
logttr 0.004 0.000 10.732 0.000 0.003 0.004 0.044 0.734
rttr 0.145 0.013 10.745 0.000 0.118 0.171 1.685 0.735
uber 0.133 0.012 10.748 0.000 0.109 0.157 1.548 0.735
lv 0.004 0.000 10.662 0.000 0.003 0.005 0.050 0.729
nv 0.004 0.000 10.539 0.000 0.003 0.005 0.045 0.721
vv1 0.005 0.000 10.558 0.000 0.004 0.006 0.056 0.723
vv2 0.002 0.000 5.332 0.000 0.001 0.002 0.021 0.374
cvv1 0.014 0.001 10.654 0.000 0.012 0.017 0.166 0.729
adjv 0.004 0.000 10.582 0.000 0.003 0.004 0.042 0.724
group3 =~
ls1 1.000 1.000 1.000 0.029 0.485
ls2 -1.636 0.237 -6.904 0.000 -2.101 -1.172 -0.047 -0.720
vs2 -15.573 2.253 -6.911 0.000 -19.990 -11.157 -0.446 -0.721
cvs1 -4.538 0.656 -6.918 0.000 -5.824 -3.253 -0.130 -0.723
Covariances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
group1 ~~
group2 0.207 0.051 4.074 0.000 0.107 0.306 0.314 0.314
group3 -0.000 0.000 -3.306 0.001 -0.001 -0.000 -0.291 -0.291
group2 ~~
group3 -0.334 0.058 -5.756 0.000 -0.447 -0.220 -1.001 -1.001
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.ld 0.000 0.000 0.000 0.000 0.000
.mtld 117.489 12.178 9.648 0.000 93.621 141.358 117.489 0.465
.vocd 441.904 45.635 9.684 0.000 352.462 531.346 441.904 0.480
.ndwerz 1.264 0.131 9.666 0.000 1.008 1.520 1.264 0.472
.ndwesz 2.079 0.215 9.648 0.000 1.657 2.501 2.079 0.465
.mattr 0.002 0.000 9.647 0.000 0.002 0.003 0.002 0.464
.hdd 0.002 0.000 9.660 0.000 0.002 0.002 0.002 0.470
.logttr 0.002 0.000 9.640 0.000 0.001 0.002 0.002 0.461
.rttr 2.421 0.251 9.637 0.000 1.928 2.913 2.421 0.460
.uber 2.042 0.212 9.636 0.000 1.627 2.457 2.042 0.460
.lv 0.002 0.000 9.656 0.000 0.002 0.003 0.002 0.468
.nv 0.002 0.000 9.683 0.000 0.002 0.002 0.002 0.479
.vv1 0.003 0.000 9.679 0.000 0.002 0.003 0.003 0.478
.vv2 0.003 0.000 10.163 0.000 0.002 0.003 0.003 0.860
.cvv1 0.024 0.003 9.658 0.000 0.019 0.029 0.024 0.469
.adjv 0.002 0.000 9.674 0.000 0.001 0.002 0.002 0.475
.ls1 0.003 0.000 10.056 0.000 0.002 0.003 0.003 0.765
.ls2 0.002 0.000 9.301 0.000 0.002 0.002 0.002 0.482
.vs2 0.184 0.020 9.289 0.000 0.145 0.222 0.184 0.480
.cvs1 0.015 0.002 9.277 0.000 0.012 0.019 0.015 0.477
group1 0.003 0.000 10.247 0.000 0.003 0.004 1.000 1.000
group2 135.422 22.239 6.090 0.000 91.835 179.009 1.000 1.000
group3 0.001 0.000 3.643 0.000 0.000 0.001 1.000 1.000
lex.model2F<- 'group1=~ mtld + vocd + ndwerz + ndwesz + mattr + hdd + logttr + rttr + uber + lv + nv + vv1 + vv2 + cvv1 + adjv + ld
group2=~ ls1 + ls2 + vs2 + cvs1'
fit2F<- sem(lex.model2F, sample.cov = shrink.cov, sample.nobs=210, ridge = .01)
summary(fit2F, ci = TRUE, fit.measures=TRUE, standardized = TRUE)
lavaan 0.6-3 ended normally after 329 iterations
Optimization method NLMINB
Number of free parameters 41
Number of observations 210
Estimator ML
Model Fit Test Statistic 44.124
Degrees of freedom 169
P-value (Chi-square) 1.000
Model test baseline model:
Minimum Function Test Statistic 2206.790
Degrees of freedom 190
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.070
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) 376.570
Loglikelihood unrestricted model (H1) 398.632
Number of free parameters 41
Akaike (AIC) -671.140
Bayesian (BIC) -533.908
Sample-size adjusted Bayesian (BIC) -663.820
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent Confidence Interval 0.000 0.000
P-value RMSEA <= 0.05 1.000
Standardized Root Mean Square Residual:
SRMR 0.023
Parameter Estimates:
Information Expected
Information saturated (h1) model Structured
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
group1 =~
mtld 1.000 1.000 1.000 11.638 0.732
vocd 1.881 0.179 10.536 0.000 1.531 2.231 21.890 0.721
ndwerz 0.102 0.010 10.620 0.000 0.083 0.121 1.189 0.727
ndwesz 0.133 0.012 10.699 0.000 0.109 0.157 1.548 0.732
mattr 0.005 0.000 10.703 0.000 0.004 0.005 0.053 0.732
hdd 0.004 0.000 10.646 0.000 0.003 0.005 0.048 0.728
logttr 0.004 0.000 10.732 0.000 0.003 0.004 0.044 0.734
rttr 0.145 0.013 10.745 0.000 0.118 0.171 1.685 0.735
uber 0.133 0.012 10.748 0.000 0.109 0.157 1.548 0.735
lv 0.004 0.000 10.663 0.000 0.003 0.005 0.050 0.729
nv 0.004 0.000 10.537 0.000 0.003 0.005 0.045 0.721
vv1 0.005 0.000 10.563 0.000 0.004 0.006 0.056 0.723
vv2 0.002 0.000 5.329 0.000 0.001 0.002 0.021 0.374
cvv1 0.014 0.001 10.656 0.000 0.012 0.017 0.166 0.729
adjv 0.004 0.000 10.584 0.000 0.003 0.004 0.042 0.724
ld 0.002 0.000 4.402 0.000 0.001 0.002 0.018 0.310
group2 =~
ls1 1.000 1.000 1.000 0.029 0.484
ls2 -1.641 0.238 -6.891 0.000 -2.108 -1.174 -0.047 -0.720
vs2 -15.603 2.263 -6.895 0.000 -20.039 -11.168 -0.446 -0.721
cvs1 -4.547 0.659 -6.902 0.000 -5.839 -3.256 -0.130 -0.723
Covariances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
group1 ~~
group2 -0.333 0.058 -5.746 0.000 -0.446 -0.219 -1.000 -1.000
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.mtld 117.467 12.179 9.645 0.000 93.597 141.336 117.467 0.464
.vocd 441.755 45.631 9.681 0.000 352.320 531.190 441.755 0.480
.ndwerz 1.264 0.131 9.663 0.000 1.007 1.520 1.264 0.472
.ndwesz 2.078 0.215 9.645 0.000 1.656 2.501 2.078 0.465
.mattr 0.002 0.000 9.645 0.000 0.002 0.003 0.002 0.464
.hdd 0.002 0.000 9.657 0.000 0.002 0.002 0.002 0.469
.logttr 0.002 0.000 9.638 0.000 0.001 0.002 0.002 0.461
.rttr 2.421 0.251 9.635 0.000 1.928 2.913 2.421 0.460
.uber 2.042 0.212 9.634 0.000 1.627 2.457 2.042 0.460
.lv 0.002 0.000 9.654 0.000 0.002 0.003 0.002 0.468
.nv 0.002 0.000 9.681 0.000 0.002 0.002 0.002 0.480
.vv1 0.003 0.000 9.675 0.000 0.002 0.003 0.003 0.477
.vv2 0.003 0.000 10.162 0.000 0.002 0.003 0.003 0.860
.cvv1 0.024 0.003 9.655 0.000 0.019 0.029 0.024 0.469
.adjv 0.002 0.000 9.671 0.000 0.001 0.002 0.002 0.475
.ld 0.003 0.000 10.192 0.000 0.002 0.003 0.003 0.904
.ls1 0.003 0.000 10.056 0.000 0.002 0.003 0.003 0.766
.ls2 0.002 0.000 9.292 0.000 0.002 0.002 0.002 0.481
.vs2 0.184 0.020 9.286 0.000 0.145 0.223 0.184 0.480
.cvs1 0.015 0.002 9.273 0.000 0.012 0.019 0.015 0.477
group1 135.445 22.241 6.090 0.000 91.853 179.037 1.000 1.000
group2 0.001 0.000 3.634 0.000 0.000 0.001 1.000 1.000
> lavInspect(fit2F, "cov.lv")
group1 group2
group1 135.445
group2 -0.333 0.001
Thanks to all,Maryam
ya
Mar 26, 2019, 8:36:52 PM3/26/19
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Dear list,
I am having trouble making a two-indicator measurement model identified. The code looks like below, but the output shows that the two indicators still have different loadings. What is the right way to do it? Thank you very much.
> library(lavaan)
> mod='xtyy=~NA*xtyy1+equal(xtyy=~xtyy1)*xtyy2;xtyy~~1*xtyy'
> fit=sem(mod,dat)
Warning message:
In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :
lavaan WARNING:
Could not compute standard errors! The information matrix could
not be inverted. This may be a symptom that the model is not
identified.
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
xtyy =~
xtyy1 0.710 NA 0.710 0.771
xtyy2 (xty1) 0.402 NA 0.402 0.323
Best,
Y.A.
I am having trouble making a two-indicator measurement model identified. The code looks like below, but the output shows that the two indicators still have different loadings. What is the right way to do it? Thank you very much.
> library(lavaan)
> mod='xtyy=~NA*xtyy1+equal(xtyy=~xtyy1)*xtyy2;xtyy~~1*xtyy'
> fit=sem(mod,dat)
Warning message:
In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :
lavaan WARNING:
Could not compute standard errors! The information matrix could
not be inverted. This may be a symptom that the model is not
identified.
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
xtyy =~
xtyy1 0.710 NA 0.710 0.771
xtyy2 (xty1) 0.402 NA 0.402 0.323
Best,
Y.A.
Edward Rigdon
Mar 26, 2019, 9:00:59 PM3/26/19
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Try this:
> mod='xtyy=~a*xtyy1+a*xtyy2
xtyy~~1*xtyy'
If lavaan wants to set a to 1, then try this:xtyy~~1*xtyy'
> mod='xtyy=~NA*xtyy1+a*xtyy1+a*xtyy2
xtyy~~1*xtyy'
xtyy~~1*xtyy'
Yes, you can reference the same variable twice on the same line of code, applying different modifiers each time.
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ya
Mar 27, 2019, 10:01:56 PM3/27/19
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It worked, this is quite convenient. Thank you very much Edward:)
Terrence Jorgensen
Mar 29, 2019, 6:51:53 AM3/29/19
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warning that "covariance matrix of latent variables is not positive definite" and I used lavInspect(fit, "cov.lv") with results that I show below; but when I checked goodness-of-fit indices, they all show very good fit.
Then it might just be sampling error. You can see the problem in the "Std.all" column, where the latent variables are perfectly negatively correlated (with more decimals, you might see it is barely beyond -1, which would be impossible to observe in practice, but these are just estimates).
summary(fit2F, std=TRUE, nd = 5) # more digitsTerrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
maryam nasseri
Mar 29, 2019, 7:07:20 AM3/29/19
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Hi Terrence
Thanks for your reponse. I found out that I made a mistake conducting that test.
cov.shrink() function should be applied to a data matrix; I have by mistake applied it to a covariance matrix and that's thevreason these strange results appeared. I corrected it and applied it to data matrix but model doesn't fit.
This was a L2 regularization method in the corpcor package, and then I used the output of it as the input to sem() function in lavaan so that I don't have to drop variables and loose information.
I'm not sure why the model still doesn't fit. I don't know if it's a case of multicollinearity or just a genuine misfit.
Thanks a lot again for your help
Maryam
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