mediation model and negative variance

Adeline

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Jul 26, 2023, 4:14:15 AM7/26/23

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Hi,

I am new to lavaan and to SEM. Despite a read quite a lot of things, I probably missed a bunch of things and need some experts' help/advice. So, I ask several questions in this. mesage and I hope it is okay.

I pre-registered a study, planning to run 3 models, from the more simple to the more complex. I have 237 participants.

The first model (with 3 latent variables, and this kind of regression between the variables : SchoolPart ~ EF + CCC) has quite a good fit (RMSEA =.066, CFI = .96) when I added 5 correlations suggested by MI and relevant according to the theory (is it ok to do that?) .

Nevertheless, the X square was significant, but multivariate normality is violated in my data, so I assume that could be a reaosn for the inflation of the model chi square; is that right and can my model still be ok?.

Then, i wanted to run a more complex model, with mediation. I started with my previous improved model (is it ok to do that or was I supposed to remove the added correlations first? ).

Here is the model and its graphical representation is attached (the plot does not include correlations). Is my model in line with the plot (I did not find many example and was not sure I example are usally more simple)?

modSEM2 <- '

#measurment model

EF =~ Brief_Init + Brief_WM + Brief_PlanOrga + Brief_Monit + Brief_Inhib + Brief_Flexi + Brief_EmoCont

CCC =~ CCC_Com + CCC_SocialRelat + CCC_Interests

SchoolPart =~ SchoolAttendanceScore + NbScolPart + ScolInvolv

# regressions

EF ~ p3*Sex + p8*Age

CCC ~ p7*Sex + p5*Age

SchoolPart ~ p4*EF + p6*CCC + p1*Sex + p2*Age + HighestParEduc

# Indirect effects

ind1 := p3*p4 + p7*p6

total1:= p1+ p3*p4 + p7*p6

ind2 := p5*p6 + p8*p4

total2:= p2 + p5*p6 + p8*p4

# correlations

Brief_EmoCont ~~Brief_Inhib + Brief_Flexi

Brief_PlanOrga ~~ Brief_Monit

Brief_Flexi ~~ CCC_Interests

Brief_Init ~~ Brief_Inhib

'

fitSEM2 <- sem (modSEM2, data = DFsem2, estimator = "MLR", fixed.x=FALSE)

summary(fitSEM2, fit.measures = TRUE, standardized = TRUE, modindices = TRUE, rsq = TRUE)

This time, the fit (CFI) is not very good (see below) AND I have a warning message indicating

« Warning message:

In lav_object_post_check(object) :

lavaan WARNING: some estimated ov variances are negative »

(which seems to be for CCC_SocialRelat).

Here is my main question: Where does this negative variance come from (I probably did something wrong…?) and what would you suggest to do ?

Your help and expertise would be greatly appreciated ,

Best,

Adeline

lavaan 0.6.15 ended normally after 204 iterations

Estimator ML

Optimization method NLMINB

Number of model parameters 46

Used Total

Number of observations 214 235

Model Test User Model:

Standard Scaled

Test Statistic 254.788 249.814

Degrees of freedom 90 90

P-value (Chi-square) 0.000 0.000

Scaling correction factor 1.020

Yuan-Bentler correction (Mplus variant)

Model Test Baseline Model:

Test statistic 1528.669 1467.011

Degrees of freedom 117 117

P-value 0.000 0.000

Scaling correction factor 1.042

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.883 0.882

Tucker-Lewis Index (TLI) 0.848 0.846

Robust Comparative Fit Index (CFI) 0.884

Robust Tucker-Lewis Index (TLI) 0.849

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -7517.595 -7517.595

Scaling correction factor 0.987

for the MLR correction

Loglikelihood unrestricted model (H1) NA NA

Scaling correction factor 1.009

for the MLR correction

Akaike (AIC) 15127.191 15127.191

Bayesian (BIC) 15282.026 15282.026

Sample-size adjusted Bayesian (SABIC) 15136.263 15136.263

Root Mean Square Error of Approximation:

RMSEA 0.092 0.091

90 Percent confidence interval - lower 0.079 0.078

90 Percent confidence interval - upper 0.106 0.104

P-value H_0: RMSEA <= 0.050 0.000 0.000

P-value H_0: RMSEA >= 0.080 0.940 0.918

Robust RMSEA 0.092

90 Percent confidence interval - lower 0.079

90 Percent confidence interval - upper 0.106

P-value H_0: Robust RMSEA <= 0.050 0.000

P-value H_0: Robust RMSEA >= 0.080 0.930

Standardized Root Mean Square Residual:

SRMR 0.144 0.144

Parameter Estimates:

Standard errors Sandwich

Information bread Observed

Observed information based on Hessian

Latent Variables:

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

EF =~

Brief_Init 1.000 2.716 0.780

Brief_WM 1.490 0.113 13.187 0.000 4.047 0.846

Brief_PlanOrga 1.699 0.131 12.944 0.000 4.614 0.817

Brief_Monit 0.955 0.082 11.652 0.000 2.593 0.765

Brief_Inhib 1.644 0.121 13.615 0.000 4.465 0.838

Brief_Flexi 0.885 0.083 10.713 0.000 2.403 0.631

Brief_EmoCont 1.212 0.116 10.451 0.000 3.292 0.608

CCC =~

CCC_Com 1.000 4.917 0.292

CCC_SocialRelt 0.952 0.625 1.523 0.128 4.681 1.276

CCC_Interests 0.126 0.033 3.843 0.000 0.622 0.242

SchoolPart =~

SchlAttndncScr 1.000 0.551 0.463

NbScolPart 1.982 0.391 5.075 0.000 1.092 0.786

ScolInvolv 2.180 0.507 4.302 0.000 1.201 0.848

Regressions:

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

EF ~

Sex (p3) 0.970 0.542 1.789 0.074 0.357 0.142

Age (p8) 1.177 0.392 3.000 0.003 0.433 0.216

CCC ~

Sex (p7) 1.512 0.959 1.577 0.115 0.308 0.122

Age (p5) 1.011 0.826 1.224 0.221 0.206 0.103

SchoolPart ~

EF (p4) -0.005 0.020 -0.222 0.825 -0.022 -0.022

CCC (p6) 0.029 0.010 2.880 0.004 0.257 0.257

Sex (p1) 0.027 0.120 0.229 0.819 0.050 0.020

Age (p2) 0.137 0.094 1.448 0.148 0.248 0.124

HghstPrEd 0.004 0.021 0.203 0.839 0.008 0.014

Covariances:

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

.Brief_Flexi ~~

.Brief_EmoCont 5.401 0.945 5.714 0.000 5.401 0.425

.Brief_Inhib ~~

.Brief_EmoCont 5.240 1.028 5.095 0.000 5.240 0.420

.Brief_PlanOrga ~~

.Brief_Monit 2.519 0.617 4.082 0.000 2.519 0.355

.Brief_Flexi ~~

.CCC_Interests -1.948 0.452 -4.312 0.000 -1.948 -0.265

.Brief_Init ~~

.Brief_Inhib -2.052 0.561 -3.658 0.000 -2.052 -0.325

Sex ~~

Age 0.031 0.013 2.352 0.019 0.031 0.156

HighestParEduc 0.001 0.051 0.026 0.979 0.001 0.002

Age ~~

HighestParEduc -0.018 0.063 -0.292 0.770 -0.018 -0.020

Variances:

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

.Brief_Init 4.741 0.659 7.199 0.000 4.741 0.391

.Brief_WM 6.513 0.912 7.139 0.000 6.513 0.285

.Brief_PlanOrga 10.580 1.293 8.182 0.000 10.580 0.332

.Brief_Monit 4.763 0.588 8.105 0.000 4.763 0.415

.Brief_Inhib 8.431 1.154 7.307 0.000 8.431 0.297

.Brief_Flexi 8.732 0.915 9.544 0.000 8.732 0.602

.Brief_EmoCont 18.469 1.625 11.365 0.000 18.469 0.630

.CCC_Com 260.233 25.750 10.106 0.000 260.233 0.915

.CCC_SocialRelt -8.454 12.072 -0.700 0.484 -8.454 -0.628

.CCC_Interests 6.208 0.636 9.765 0.000 6.208 0.941

.SchlAttndncScr 1.112 0.139 7.985 0.000 1.112 0.786

.NbScolPart 0.740 0.157 4.705 0.000 0.740 0.383

.ScolInvolv 0.565 0.194 2.913 0.004 0.565 0.282

.EF 6.812 1.021 6.669 0.000 0.923 0.923

.CCC 23.470 18.917 1.241 0.215 0.971 0.971

.SchoolPart 0.276 0.117 2.358 0.018 0.910 0.910

Sex 0.158 0.016 9.564 0.000 0.158 1.000

Age 0.249 0.002 111.566 0.000 0.249 1.000

HighestParEduc 3.445 0.214 16.069 0.000 3.445 1.000

R-Square:

Estimate

Brief_Init 0.609

Brief_WM 0.715

Brief_PlanOrga 0.668

Brief_Monit 0.585

Brief_Inhib 0.703

Brief_Flexi 0.398

Brief_EmoCont 0.370

CCC_Com 0.085

CCC_SocialRelt NA

CCC_Interests 0.059

SchlAttndncScr 0.214

NbScolPart 0.617

ScolInvolv 0.718

EF 0.077

CCC 0.029

SchoolPart 0.090

Defined Parameters:

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

ind1 0.039 0.039 1.002 0.317 0.071 0.028

total1 0.067 0.122 0.546 0.585 0.121 0.048

ind2 0.024 0.038 0.624 0.532 0.043 0.022

total2 0.160 0.088 1.823 0.068 0.291 0.145

Capture d’écran 2023-07-26 à 10.08.55.png

Prof. Gavin Brown

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Jul 26, 2023, 6:17:15 AM7/26/23

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Adeline

you ask many questions. Allow me to address 1.

you used MI to correlate some of the items within the BRIEF report. It is understandable that MI would indicate this because these items all belong to the one instrument.

# correlations

Brief_EmoCont ~~Brief_Inhib + Brief_Flexi

Brief_PlanOrga ~~ Brief_Monit

Brief_Flexi ~~ CCC_Interests

Brief_Init ~~ Brief_Inhib

'

However, this is a conceptually difficult step, as desirable as its consequences may be.

One of the assumptions in regression is that the residual is independent of all other explanations.

Barker, L. E., & Shaw, K. M. (2015). Best (but oft-forgotten) practices: Checking assumptions concerning regression residuals. The American Journal of Clinical Nutrition, 102(3), 533-539. https://doi.org/10.3945/ajcn.115.113498
What you have done by correlating some of them is claiming that they influence each other. This suggests to me that among the correlated factors it is possible you simply have duplication of information. I'd seriously consider removing some of these items. Furthermore you have correlated a BRIEF item with an item in a completely different scale or construct. It would be more appropriate, IMHO, to correlate the Autism and BRIEF constructs rather than have one item's residual vary with another item's residual.

I know there is a long tradition of correlating residuals, but it simply doesn't make sense to me to do so.

Adeline

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Jul 26, 2023, 9:53:49 AM7/26/23

to lavaan

Dear Prof. Gavin Brown,

Thank you very much for your answer.

To be more precise, the BRIEF is a scale with more tha 80 items and the author found the 8 factors structure. I used these 8 factors. Emotional control imply inhibition so for me it made sense that there is a correlation between these factors, even if inhibition is related more to cognitive inhibition (so the information are different, but related). Who you suggest that I don't use these 8 factors (that are very well known in the litterature) but do my own PCA to use another structure ?

And ok for your second point. Again, it was suggested by MI and make sense regarding the litterature where we can find correlation between flexibility and restrecitive interests, but I can try to correlated the latent variable instead if you think it is better.

Thank you again.

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