SEM message warning: variances are negative

Gouvidé Jean GBAGUIDI

unread,

Feb 13, 2023, 12:54:54 PM2/13/23

to lavaan

Hello, I'm running SEM to assess the causality effect of climatic variables on the incidence of malaria.

I developed two different SEM models:

Mod<-'F1=~Rainfall+Mean_Relative.Humidity
+Max_Relative.Humidity
F2=~Mean_Temperature+Max_Temperature
Malaria_Incidence~F1+F2
F1~~F2
'

Mod2<-'F1=~Rainfall+Mean_Relative.Humidity+Mean_Temperature
Malaria_Incidence~F1
F1~~F1
'

When I run the first model, I got the warning message:

mod.1 <- sem(Mod, data=Mal1,fixed.x = T,estimator = "WLSM")
Warning message:
In lav_object_post_check(object) :
lavaan WARNING: some estimated ov variances are negative.

But I run the second model without any warning and error message.

Summary of Mod1

summary(mod.1, stand=TRUE,fit.measures=TRUE,rsq=TRUE)
lavaan 0.6.14 ended normally after 35 iterations

Estimator DWLS
Optimization method NLMINB
Number of model parameters 14

Number of observations 1193

Model Test User Model:
Standard Scaled
Test Statistic 96.884 554.531
Degrees of freedom 7 7
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.175
Satorra-Bentler correction

Model Test Baseline Model:

Test statistic 8079.332 8079.332
Degrees of freedom 15 15
P-value 0.000 0.000
Scaling correction factor 1.000

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.989 0.932
Tucker-Lewis Index (TLI) 0.976 0.855

Robust Comparative Fit Index (CFI) 0.988
Robust Tucker-Lewis Index (TLI) 0.975

Root Mean Square Error of Approximation:

RMSEA 0.104 0.256
90 Percent confidence interval - lower 0.086 0.214
90 Percent confidence interval - upper 0.123 0.301
P-value H_0: RMSEA <= 0.050 0.000 0.000
P-value H_0: RMSEA >= 0.080 0.985 1.000

Robust RMSEA 0.107
90 Percent confidence interval - lower 0.100
90 Percent confidence interval - upper 0.115
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 1.000

Standardized Root Mean Square Residual:

SRMR 0.060 0.060

Parameter Estimates:

Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured

Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
F1 =~
Rainfall 1.000 0.837 0.837
Men_Rltv.Hmdty 1.134 0.032 35.436 0.000 0.949 0.949
Max_Rltv.Hmdty 1.015 0.033 30.866 0.000 0.849 0.849
F2 =~
Mean_Temperatr 1.000 0.597 0.597
Max_Temperatur 2.129 0.115 18.527 0.000 1.271 1.271

Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv
Malaria_Incidence ~
F1 0.243 0.049 5.009 0.000 0.204
F2 -0.269 0.049 -5.476 0.000 -0.160
Std.all

0.204
-0.160

Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
F1 ~~
F2 -0.313 0.024 -12.926 0.000 -0.627 -0.627

Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Rainfall 0.299 0.021 14.000 0.000 0.299 0.299
.Men_Rltv.Hmdty 0.099 0.009 10.579 0.000 0.099 0.099
.Max_Rltv.Hmdty 0.278 0.014 19.683 0.000 0.278 0.278
.Mean_Temperatr 0.644 0.032 20.381 0.000 0.644 0.644
.Max_Temperatur -0.616 0.065 -9.447 0.000 -0.616 -0.616
.Malaria_Incdnc 0.892 0.087 10.213 0.000 0.892 0.892
F1 0.701 0.034 20.748 0.000 1.000 1.000
F2 0.356 0.030 11.706 0.000 1.000 1.000

R-Square:
Estimate
Rainfall 0.701
Men_Rltv.Hmdty 0.901
Max_Rltv.Hmdty 0.722
Mean_Temperatr 0.356
Max_Temperatur NA
Malaria_Incdnc 0.108

Summary of Mod2:

summary(mod.1, stand=TRUE,fit.measures=TRUE,rsq=TRUE)
lavaan 0.6.14 ended normally after 21 iterations

Estimator DWLS
Optimization method NLMINB
Number of model parameters 8

Number of observations 1193

Model Test User Model:
Standard Scaled
Test Statistic 53.234 96.080
Degrees of freedom 2 2
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.554
Satorra-Bentler correction

Model Test Baseline Model:

Test statistic 1782.303 1782.303
Degrees of freedom 6 6
P-value 0.000 0.000
Scaling correction factor 1.000

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.971 0.947
Tucker-Lewis Index (TLI) 0.913 0.841

Robust Comparative Fit Index (CFI) 0.971
Robust Tucker-Lewis Index (TLI) 0.912

Root Mean Square Error of Approximation:

RMSEA 0.147 0.199
90 Percent confidence interval - lower 0.114 0.155
90 Percent confidence interval - upper 0.182 0.246
P-value H_0: RMSEA <= 0.050 0.000 0.000
P-value H_0: RMSEA >= 0.080 1.000 1.000

Robust RMSEA 0.148
90 Percent confidence interval - lower 0.123
90 Percent confidence interval - upper 0.174
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 1.000

Standardized Root Mean Square Residual:

SRMR 0.061 0.061

Parameter Estimates:

Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured

Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
F1 =~
Rainfall 1.000 0.876 0.876
Men_Rltv.Hmdty 0.963 0.039 24.574 0.000 0.844 0.844
Mean_Temperatr -0.496 0.033 -14.803 0.000 -0.434 -0.434

Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv
Malaria_Incidence ~
F1 0.381 0.035 10.846 0.000 0.334
Std.all

0.334

Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
F1 0.768 0.044 17.307 0.000 1.000 1.000
.Rainfall 0.232 0.032 7.236 0.000 0.232 0.232
.Men_Rltv.Hmdty 0.288 0.029 10.092 0.000 0.288 0.288
.Mean_Temperatr 0.811 0.034 24.071 0.000 0.811 0.811
.Malaria_Incdnc 0.888 0.088 10.119 0.000 0.888 0.888

R-Square:
Estimate
Rainfall 0.768
Men_Rltv.Hmdty 0.712
Mean_Temperatr 0.189
Malaria_Incdnc 0.112

I would like to know if the two models are valid. Could I use the mod one with warning message?

Any comment is welcome to help me.

christop...@gmail.com

unread,

Feb 20, 2023, 3:46:25 PM2/20/23

to lavaan

Seems this post has been unanswered for a week now... You deserve an answer!

- I would like to know if the two models are valid. Could I use the mod one with warning message?

You can look up negative error variance. It is not an admissible solution (variances cannot be negative; how could variation be negative...). Unfortunately, reading output in google groups is not easy unless you use a monospace font (like courier).

Your fist model results in a negative error variance for Max_Temperatur, this item is not included in your second model. A negative error variance might come from an item being a particularly strong indicator of a latent variable, but your point estimate is quite strong (and negative). Other causes of negative error variance include low sample size (not in your case) and using too few indicators of a latent variable (not in your case).

I think you should work further with your models. In addition to the negative error variance, both models have too low fit. I suggest reading on negative error variance (also referred to as Heywood cases) and model fit, and how to develop latent variables.

RMSEA 0.104 0.256 LOW FIT

Gouvidé Jean GBAGUIDI

unread,

Feb 20, 2023, 3:59:55 PM2/20/23

to lav...@googlegroups.com

Thank you so much for the help. I solved this issue of negative variance. and now my model is quite good

> summary(mod.1, stand=TRUE,fit.measures=TRUE,rsq=TRUE)
lavaan 0.6.14 ended normally after 42 iterations

Estimator DWLS
Optimization method NLMINB

Number of model parameters 16

Number of observations 284

Model Test User Model:
Standard Scaled

Test Statistic 7.885 53.822
Degrees of freedom 5 5
P-value (Chi-square) 0.163 0.000
Scaling correction factor 0.152
Shift parameter 1.825
simple second-order correction

Model Test Baseline Model:

Test statistic 2502.829 1271.793

Degrees of freedom 15 15
P-value 0.000 0.000

Scaling correction factor 1.980

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.999 0.961
Tucker-Lewis Index (TLI) 0.997 0.883

Robust Comparative Fit Index (CFI) 0.999
Robust Tucker-Lewis Index (TLI) 0.997

Root Mean Square Error of Approximation:

RMSEA 0.045 0.186
90 Percent confidence interval - lower 0.000 0.143
90 Percent confidence interval - upper 0.102 0.232
P-value H_0: RMSEA <= 0.050 0.482 0.000
P-value H_0: RMSEA >= 0.080 0.183 1.000

Robust RMSEA 0.072
90 Percent confidence interval - lower 0.056
90 Percent confidence interval - upper 0.090
P-value H_0: Robust RMSEA <= 0.050 0.015
P-value H_0: Robust RMSEA >= 0.080 0.255

Standardized Root Mean Square Residual:

SRMR 0.031 0.031

Parameter Estimates:

Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured

Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
F1 =~

Rainfall 0.965 0.046 20.847 0.000 0.965 0.965
Men_Rltv.Hmdty 0.910 0.027 33.655 0.000 0.910 0.910
Max_Rltv.Hmdty 0.693 0.039 17.883 0.000 0.693 0.693
F2 =~
Mean_Temperatr 0.636 0.028 22.682 0.000 0.636 0.636
Max_Temperatur 0.870 0.870 0.870

Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Malaria_Incidence ~
F1 -1.515 1.515 -1.000 0.317 -1.515 -1.515
F2 -2.003 1.515 -1.322 0.186 -2.003 -2.003

Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all

.Mean_Relative.Humidity ~~
.Max_Rltv.Hmdty 0.337 0.035 9.518 0.000 0.337 1.126
.Rainfall ~~
.Men_Rltv.Hmdty -0.102 0.022 -4.562 0.000 -0.102 -0.930
.Mean_Temperature ~~
.Max_Temperatur 0.389 0.043 9.050 0.000 0.389 1.023
F1 ~~
F2 -0.952 0.041 -23.032 0.000 -0.952 -0.952

Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all

.Rainfall 0.070 0.062 1.122 0.262 0.070 0.070
.Men_Rltv.Hmdty 0.172 0.026 6.532 0.000 0.172 0.172
.Max_Rltv.Hmdty 0.520 0.053 9.784 0.000 0.520 0.520
.Mean_Temperatr 0.596 0.050 11.851 0.000 0.596 0.596
.Max_Temperatur 0.243 0.050 4.851 0.000 0.243 0.243
.Malaria_Incdnc 0.468 0.282 1.662 0.097 0.468 0.468
F1 1.000 1.000 1.000
F2 1.000 1.000 1.000

R-Square:
Estimate
Rainfall 0.930
Men_Rltv.Hmdty 0.828
Max_Rltv.Hmdty 0.480
Mean_Temperatr 0.404
Max_Temperatur 0.757
Malaria_Incdnc 0.532

--
You received this message because you are subscribed to a topic in the Google Groups "lavaan" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/lavaan/1B1kc5wiyGI/unsubscribe.
To unsubscribe from this group and all its topics, send an email to lavaan+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/afc5010c-06f1-4669-a9bb-c21921244ec2n%40googlegroups.com.

--

Gouvidé Jean GBAGUIDI
WASCAL PhD-Candidate
Climate Change and Disaster Risks Management
MSc Ecohydrologist

MSc: Natural Sciences

Secretary of Benin Jeunesse Elite NGO

Benin National Focal Point: United International Federation

of Youth for Water and Climate(UN1FY)

Infolines:be...@un1fy.org

E-mail: gouvid...@gmail.com/gbaguid...@yahoo.fr
Phone:(00229)96258002/95036686 (Benin)

(00228)93649692 (Togo-LOME)
Phillipians: 4:13: "I can do all things through him who gives"

Jošt Bartol

unread,

Feb 22, 2023, 2:24:13 AM2/22/23

to lav...@googlegroups.com

Dear Gouvidé,

I checked your solution, and I have noted several issues that you might want to address in in improving your model:

1. As much as I see, you introduced covariances among items measuring F1 and F2. While this might be theoretically appropriate, I observed that correlations among these items (std. covariances) are larger than 1. This indicates problems.

2. I see that the error variances of the two items (Rainfall and Malaria_Incdience) is not statistically significant. While this might not necessarily be a reason for alarm, it is worth checking out. See Brown's 2015 book Confirmatory factor analysis for applied research page 114.

3. The F1 and F2 factors do NOT have a statistically significant influence on Malaria Incidence + this effect is very very different than the effect of your model 1 (which I think is the most reasonable model).

Based on these considerations, I would not trust your proposed solution.

Now, I do not know the conceptual underpinnings for the model and the need for two factors, however, could not the same aim be achieved by running OLS regression analysis with the items in factors F1 and F2 predicting malaria incidence? In this case, you might want to remove redundant items to avoid multicollinearity (e.g., by using principal components analysis to select the items that best represent each of your two factors; see Hair et al., Multivariate data analysis). It seems to me that the reason your model has problems is because the items in each factor are measuring almost the same thing (i.e., in F1 all measure some form of humidity, in F2 all measure some form of temperature).

Hope this helps,

Jošt

V V pon., 20. feb. 2023 ob 21:59 je oseba Gouvidé Jean GBAGUIDI <gouvid...@gmail.com> napisala:

You received this message because you are subscribed to the Google Groups "lavaan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/CAPjjv4jeg5PVOMNTWb4_BNb2SGzWx%3DJ10opK6%3D4i5zYUg3du-Q%40mail.gmail.com.

Gouvidé Jean GBAGUIDI

unread,

Feb 22, 2023, 4:22:29 AM2/22/23

to lav...@googlegroups.com

Thank you for the comment and the suggestion. I will check all the issues to perform the model. My best regards

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/CAL8q69%3DQxFaCMYhmTyKaFnnGRjHR%3Dw1fvJEMLs4bkPsfkfwa7g%40mail.gmail.com.

Reply all

Reply to author

Forward