SEM - problems with convergence, standardized parameter estimates and negative variances

Pedro Miganda

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Mar 31, 2018, 12:43:05 PM3/31/18

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Dear group,

I've been trying to get the SEM bellow to converge for a while now and today I finally did it (and with a decent fit).

However, when I take a look at the summary, I can see that some of the estimates and standard errors are way off. Also, the model was not able to produce standardized estimates (std.lv and std.all) for some of my parameters.

I double checked the standard errors, scale and correlation structure of all of my variables and I could not find anything obvious that needs fixing, so here I am.

I would really appreciate any help I can get on this. These models (this one and the other ones I'm running) are a good chunk of my thesis and I can't get this one to work.

Model syntax, functions I ran and summary are copied bellow. I am also happy to share my data if it will help figuring out what is happening.

This is the model:

model1 <-

'#latent variables

soil =~ SandLOG + P.totalLOG + Al.cmol. + SB

climate =~ DroughtLOG + mapLOG

fire =~ FireLOG

#Regressions

soil ~ climate

fire ~ climate

Biome ~ climate + soil + fire

#covariances

SB ~~ P.totalLOG

SB ~~ FireLOG

'

In the model above, alll variables are continuous apart from Biome, which is categorical and has two levels.

- Running the following function generates the error message displayed bellow: fit.model1 <- lavaan::sem(model1, data=dat1, fixed.x = F)

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 lv variances are negative

- Getting the summary: summary(fit.savfor.BRA_new, fit.measures=TRUE, standardized=TRUE)

lavaan (0.5-23.1097) converged normally after 408 iterations

Number of observations 66

Estimator ML

Minimum Function Test Statistic 15.508

Degrees of freedom 15

P-value (Chi-square) 0.415

Model test baseline model:

Minimum Function Test Statistic 79.879

Degrees of freedom 28

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.990

Tucker-Lewis Index (TLI) 0.982

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) NA

Loglikelihood unrestricted model (H1) NA

Number of free parameters 21

Akaike (AIC) NA

Bayesian (BIC) NA

Root Mean Square Error of Approximation:

RMSEA 0.023

90 Percent Confidence Interval 0.000 0.120

P-value RMSEA <= 0.05 0.580

Standardized Root Mean Square Residual:

SRMR 0.091

Parameter Estimates:

Information Expected

Standard Errors Standard

Latent Variables:

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

soil =~

SandLOG 1.000 NaN NaN

P.totalLOG 2.350 1.272 1.847 0.065 NaN NaN

Al.cmol. 3.273 1.668 1.962 0.050 NaN NaN

SB 7.947 4.081 1.947 0.052 NaN NaN

climate =~

DroughtLOG 1.000 0.060 0.053

mapLOG 0.219 0.158 1.381 0.167 0.013 0.064

fire =~

FireLOG 1.000 1.074 1.000

Regressions:

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

soil ~

climate 1.371 4.367 0.314 0.754 NaN NaN

fire ~

climate 8.214 16.085 0.511 0.610 0.462 0.462

Biome ~

climate 27.362 100.461 0.272 0.785 1.651 3.403

soil 3.928 9.173 0.428 0.668 NaN NaN

fire -0.973 2.254 -0.432 0.666 -1.044 -2.153

Covariances:

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

.P.totalLOG ~~

.SB 0.966 0.554 1.743 0.081 0.966 0.366

.SB ~~

.FireLOG -0.675 0.380 -1.774 0.076 -0.675 -Inf

Variances:

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

.SandLOG 0.314 0.062 5.037 0.000 0.314 1.107

.P.totalLOG 0.958 0.234 4.098 0.000 0.958 1.212

.Al.cmol. 1.033 0.320 3.227 0.001 1.033 1.461

.SB 7.267 2.029 3.581 0.000 7.267 1.359

.DroughtLOG 1.292 0.225 5.749 0.000 1.292 0.997

.mapLOG 0.042 0.007 5.743 0.000 0.042 0.996

.FireLOG 0.000 0.000 0.000

.Biome -2.280 9.770 -0.233 0.816 -2.280 -9.685

.soil -0.037 0.033 -1.141 0.254 NaN NaN

climate 0.004 0.014 0.251 0.801 1.000 1.000

.fire 0.907 0.848 1.069 0.285 0.787 0.787

I was also given the following warning message:

Warning messages:

1: In sqrt(ETA2) : NaNs produced

2: In sqrt(ETA2) : NaNs produced

3: In sqrt(ETA2) : NaNs produced

Thank you for your time and attention.

Kind regards,

Pedro Miranda

Edward Rigdon

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Mar 31, 2018, 4:12:11 PM3/31/18

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Your second common factor, Climate, has only 2 indicators. Both loadings must be strong for the model to be identified, without additional constraints. The unstandardized loadings are 1.00 (fixed) and 0.22. The p-value on the second loading is not significant at alpha = .05. But it is also not 0 exactly. Your sample size is small. The model is " nearly not identified," as Karl Joreskog used the phrase. Like a satellite in orbit, it spins around and around the black hole if non-identification, never escapinmg but never failing outright. To establish identification, you eitehr need more constraints or more indicators on the second factor.

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kma...@aol.com

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Apr 1, 2018, 9:49:26 AM4/1/18

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Pedro,
To elaborate a little, one option would be to choose an a priori sequence of plausible unique variances and to do a sensitivity analysis by running the model with the unique variances fixed at each level, at least for the problematic factor. A second option might be to use blavaan and encode some of your background knowledge as prior distributions on certain parameters. A third option is to drop the problematic factor and include its indicators as separate variables in the model. You could combine option 1 and 3.

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/

Pedro Miganda

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Apr 2, 2018, 2:51:15 PM4/2/18

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Thank you for this, Edward. I am now adding more indicators and indicators to this model. Will post an update soon.

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Pedro Miganda

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Apr 2, 2018, 2:55:47 PM4/2/18

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Thank you for your input, Keith. I think combining options one and three is going to be quicker, but I will try to use blavaan in the future (I download it, but it is not compatible with R 3.4.4, which is the newest version of R). I'll post an update on this model soon.

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