Warning message: trouble constructing W matrix; used generalized inverse for A11 submatrix

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fotin...@gmail.com

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Aug 10, 2018, 1:57:21 PM8/10/18

to lavaan

Hi,

I am hoping someone can help me (I am desperate!).

I have looked at previous posts but there wasn't much detail as to how to resolve this issue. I am receiving the following:

Warning message:

In muthen1984(Data = X[[g]], ov.names = ov.names[[g]], ov.types = ov.types, :

lavaan WARNING: trouble constructing W matrix; used generalized inverse for A11 submatrix

When I run the following (see below). I am not sure how to fix this warning. I have posted the output below as well. Variances seem fine although the inspect function is showing negatives.

Model.2 <- '

# measurement model

ERa =~ ER1 + ER2 + a4*ER3 + a2*ER4 + a3*ER5

PAa =~ PA1 + PA2 + PAMV1

ERb =~ a4*ER6 + a2*ER7 + a3*ER8

PAb =~ PAMV2 + PAC + PAIB + PAJ + PATB + PAS + PAO + PA3

ERc =~ a4*ER9 + a2*ER10 + a3*ER11

IMD =~ combined_LS + single + income + housing + kessler + job_partner + job_main + academic_partner

#Thresholds

ER3 | c1*t1 + c2*t2; ER9 | c1*t1 + c2*t2; ER6 | c1*t1 + c2*t2

ER4 | d1*t1 + d2*t2; ER10 | d1*t1 + d2*t2; ER7 | d1*t1 + d2*t2

ER5 | e1*t1 + e2*t2; ER11 | e1*t1 + e2*t2; ER8 | e1*t1 + e2*t2

# regressions

# a Path

PAa ~ a * IMD

PAb ~ d * IMD

# b path

ERa ~ b * PAa

ERb ~ e * PAb

ERc ~ g * PAa

#c prime path

ERa ~ cp * IMD

ERb ~ fp * IMD

ERc ~ hp * IMD

#Indirect and total effects

ab := a * b

total := cp + ab

de := d * e

totali := fp + de

ag := a * g

totalii := hp + ag'

> inspect(fit.M2,"cor.lv")

ERa PAa ERb PAb ERc IMD

ERa 1.000

PAa -0.680 1.000

ERb 0.249 -0.169 1.000

PAb -0.004 0.012 -0.306 1.000

ERc 0.298 -0.705 0.249 -0.005 1.000

IMD -0.206 0.564 -0.299 0.021 -0.257 1.000

> summary(fit.M2, fit.measures = TRUE, standardized=TRUE)

lavaan (0.6-1) converged normally after 106 iterations

Number of observations 3770

Estimator DWLS Robust

Model Fit Test Statistic 5895.114 5149.474

Degrees of freedom 412 412

P-value (Chi-square) 0.000 0.000

Scaling correction factor 1.172

Shift parameter 118.804

for simple second-order correction (Mplus variant)

Model test baseline model:

Minimum Function Test Statistic 159854.423 101680.137

Degrees of freedom 435 435

P-value 0.000 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.966 0.953

Tucker-Lewis Index (TLI) 0.964 0.951

Robust Comparative Fit Index (CFI) NA

Robust Tucker-Lewis Index (TLI) NA

Root Mean Square Error of Approximation:

RMSEA 0.059 0.055

90 Percent Confidence Interval 0.058 0.061 0.054 0.057

P-value RMSEA <= 0.05 0.000 0.000

Robust RMSEA NA

90 Percent Confidence Interval NA NA

Standardized Root Mean Square Residual:

SRMR 0.056 0.056

Parameter Estimates:

Information Expected

Information saturated (h1) model Unstructured

Standard Errors Robust.sem

Latent Variables:

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

ERa =~

ER1 0.044 0.009 5.049 0.000 0.063 0.095

ER2 0.062 0.006 10.050 0.000 0.089 0.195

ER3 (a4) 0.643 0.010 61.487 0.000 0.919 0.919

ER4 (a2) 0.664 0.011 61.298 0.000 0.949 0.949

ER5 (a3) 0.643 0.011 60.097 0.000 0.918 0.918

PAa =~

PA1 0.007 0.009 0.798 0.425 0.009 0.015

PA2 0.005 0.011 0.466 0.642 0.006 0.009

PAMV1 0.301 0.044 6.893 0.000 0.365 0.169

ERb =~

ER6 (a4) 0.643 0.010 61.487 0.000 0.710 0.710

ER7 (a2) 0.664 0.011 61.298 0.000 0.733 0.733

ER8 (a3) 0.643 0.011 60.097 0.000 0.710 0.710

PAb =~

PAMV2 0.266 0.017 15.862 0.000 0.266 0.469

PAC 0.014 0.012 1.165 0.244 0.014 0.033

PAIB 0.034 0.012 2.901 0.004 0.034 0.073

PAJ 0.074 0.022 3.306 0.001 0.074 0.082

PATB 0.422 0.027 15.339 0.000 0.422 0.457

PAS 0.214 0.020 10.686 0.000 0.214 0.265

PAO 0.015 0.033 0.446 0.655 0.015 0.011

PA3 -0.279 0.027 -10.182 0.000 -0.279 -0.251

ERc =~

ER9 (a4) 0.643 0.010 61.487 0.000 0.935 0.935

ER10 (a2) 0.664 0.011 61.298 0.000 0.965 0.965

ER11 (a3) 0.643 0.011 60.097 0.000 0.934 0.934

IMD =~

combnd_LS 0.656 0.027 24.135 0.000 0.656 0.540

single 0.129 0.005 25.709 0.000 0.129 0.423

income -1.023 0.036 -28.479 0.000 -1.023 -0.740

housing 0.545 0.022 24.326 0.000 0.545 0.650

kessler 1.156 0.062 18.745 0.000 1.156 0.334

job_prtnr 0.893 0.048 18.509 0.000 0.893 0.555

job_main 0.858 0.050 17.009 0.000 0.858 0.522

acdmc_prt 0.057 0.009 6.036 0.000 0.057 0.114

Regressions:

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

PAa ~

IMD (a) 0.683 0.170 4.029 0.000 0.564 0.564

PAb ~

IMD (d) 0.021 0.027 0.777 0.437 0.021 0.021

ERa ~

PAa (b) -0.976 0.034 -29.110 0.000 -0.828 -0.828

ERb ~

PAb (e) -0.331 0.035 -9.548 0.000 -0.300 -0.300

ERc ~

PAa (g) -0.985 0.034 -29.302 0.000 -0.821 -0.821

ERa ~

IMD (cp) 0.373 0.170 2.194 0.028 0.261 0.261

ERb ~

IMD (fp) -0.323 0.026 -12.322 0.000 -0.293 -0.293

ERc ~

IMD (hp) 0.300 0.170 1.765 0.078 0.206 0.206

Covariances:

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

.ERa ~~

.ERb 0.295 0.033 9.035 0.000 0.295 0.295

.ERc -0.453 0.061 -7.422 0.000 -0.453 -0.453

.ERb ~~

.ERc 0.276 0.033 8.238 0.000 0.276 0.276

Intercepts:

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

.ER1 2.285 0.011 209.408 0.000 2.285 3.413

.ER2 2.761 0.011 244.410 0.000 2.761 6.051

.ER3 0.000 0.000 0.000

.ER4 0.000 0.000 0.000

.ER5 0.000 0.000 0.000

.PA1 1.352 0.016 86.675 0.000 1.352 2.384

.PA2 1.650 0.013 128.718 0.000 1.650 2.431

.PAMV1 6.240 0.038 164.361 0.000 6.240 2.896

.ER6 0.000 0.000 0.000

.ER7 0.000 0.000 0.000

.ER8 0.000 0.000 0.000

.PAMV2 1.277 0.010 126.298 0.000 1.277 2.254

.PAC 0.117 0.019 6.243 0.000 0.117 0.267

.PAIB 0.159 0.017 9.365 0.000 0.159 0.341

.PAJ 0.456 0.027 16.626 0.000 0.456 0.506

.PATB 0.395 0.027 14.729 0.000 0.395 0.427

.PAS 0.276 0.028 9.826 0.000 0.276 0.342

.PAO 0.649 0.038 17.076 0.000 0.649 0.489

.PA3 2.761 0.018 151.439 0.000 2.761 2.486

.ER9 0.000 0.000 0.000

.ER10 0.000 0.000 0.000

.ER11 0.000 0.000 0.000

.combined_LS 2.069 0.024 84.788 0.000 2.069 1.704

.single 1.104 0.000 4233.974 0.000 1.104 3.617

.income 3.269 0.023 139.983 0.000 3.269 2.365

.housing 1.439 0.030 47.753 0.000 1.439 1.714

.kessler 4.029 0.085 47.182 0.000 4.029 1.164

.job_partner 2.624 0.029 90.256 0.000 2.624 1.632

.job_main 2.785 0.030 93.009 0.000 2.785 1.695

.academic_prtnr 1.467 0.008 183.681 0.000 1.467 2.941

.ERa 0.000 0.000 0.000

.PAa 0.000 0.000 0.000

.ERb 0.000 0.000 0.000

.PAb 0.000 0.000 0.000

.ERc 0.000 0.000 0.000

IMD 0.000 0.000 0.000

Thresholds:

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

ER3|t1 (c1) -0.699 0.014 -48.386 0.000 -0.699 -0.699

ER3|t2 (c2) 0.205 0.015 14.000 0.000 0.205 0.205

ER9|t1 (c1) -0.699 0.014 -48.386 0.000 -0.699 -0.699

ER9|t2 (c2) 0.205 0.015 14.000 0.000 0.205 0.205

ER6|t1 (c1) -0.699 0.014 -48.386 0.000 -0.699 -0.699

ER6|t2 (c2) 0.205 0.015 14.000 0.000 0.205 0.205

ER4|t1 (d1) -0.763 0.014 -52.627 0.000 -0.763 -0.763

ER4|t2 (d2) 0.383 0.014 27.418 0.000 0.383 0.383

ER10|t1 (d1) -0.763 0.014 -52.627 0.000 -0.763 -0.763

ER10|t2 (d2) 0.383 0.014 27.418 0.000 0.383 0.383

ER7|t1 (d1) -0.763 0.014 -52.627 0.000 -0.763 -0.763

ER7|t2 (d2) 0.383 0.014 27.418 0.000 0.383 0.383

ER5|t1 (e1) -0.886 0.014 -61.661 0.000 -0.886 -0.886

ER5|t2 (e2) -0.438 0.014 -31.836 0.000 -0.438 -0.438

ER11|t1 (e1) -0.886 0.014 -61.661 0.000 -0.886 -0.886

ER11|t2 (e2) -0.438 0.014 -31.836 0.000 -0.438 -0.438

ER8|t1 (e1) -0.886 0.014 -61.661 0.000 -0.886 -0.886

ER8|t2 (e2) -0.438 0.014 -31.836 0.000 -0.438 -0.438

Variances:

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

.ER1 0.444 0.011 40.867 0.000 0.444 0.991

.ER2 0.200 0.006 33.856 0.000 0.200 0.962

.ER3 0.156 0.156 0.156

.ER4 0.100 0.100 0.100

.ER5 0.157 0.157 0.157

.PA1 0.321 0.010 30.852 0.000 0.321 1.000

.PA2 0.461 0.016 29.558 0.000 0.461 1.000

.PAMV1 4.509 0.104 43.196 0.000 4.509 0.971

.ER6 0.495 0.495 0.495

.ER7 0.462 0.462 0.462

.ER8 0.496 0.496 0.496

.PAMV2 0.250 0.010 26.202 0.000 0.250 0.780

.PAC 0.192 0.003 62.108 0.000 0.192 0.999

.PAIB 0.217 0.004 55.303 0.000 0.217 0.995

.PAJ 0.807 0.014 59.737 0.000 0.807 0.993

.PATB 0.674 0.024 27.528 0.000 0.674 0.791

.PAS 0.604 0.012 48.760 0.000 0.604 0.930

.PAO 1.760 0.024 74.594 0.000 1.760 1.000

.PA3 1.156 0.037 31.611 0.000 1.156 0.937

.ER9 0.126 0.126 0.126

.ER10 0.069 0.069 0.069

.ER11 0.127 0.127 0.127

.combined_LS 1.045 0.035 29.906 0.000 1.045 0.708

.single 0.077 0.001 53.090 0.000 0.077 0.821

.income 0.865 0.038 23.043 0.000 0.865 0.452

.housing 0.407 0.013 30.736 0.000 0.407 0.578

.kessler 10.650 0.229 46.531 0.000 10.650 0.889

.job_partner 1.789 0.074 24.319 0.000 1.789 0.692

.job_main 1.963 0.086 22.825 0.000 1.963 0.727

.academic_prtnr 0.246 0.001 165.428 0.000 0.246 0.987

.ERa 1.000 0.490 0.490

.PAa 1.000 0.682 0.682

.ERb 1.000 0.821 0.821

.PAb 1.000 1.000 1.000

.ERc 1.000 0.474 0.474

IMD 1.000 1.000 1.000

Scales y*:

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

ER3 1.000 1.000 1.000

ER4 1.000 1.000 1.000

ER5 1.000 1.000 1.000

ER6 1.000 1.000 1.000

ER7 1.000 1.000 1.000

ER8 1.000 1.000 1.000

ER9 1.000 1.000 1.000

ER10 1.000 1.000 1.000

ER11 1.000 1.000 1.000

Defined Parameters:

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

ab -0.667 0.169 -3.947 0.000 -0.467 -0.467

total -0.294 0.029 -10.065 0.000 -0.206 -0.206

de -0.007 0.009 -0.777 0.437 -0.006 -0.006

totali -0.330 0.026 -12.900 0.000 -0.299 -0.299

ag -0.673 0.170 -3.957 0.000 -0.463 -0.463

totalii -0.373 0.030 -12.400 0.000 -0.257 -0.257

Chao Xu

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Aug 10, 2018, 10:29:39 PM8/10/18

to lavaan

It seems to me that this issue is due to the singularity of the weight matrix W. W is estimated from the fourth-order moments of the data vector (see various Muthen papers), meaning that the singularity stems from the inherent structure of your data.

The diagnostics can be fairly complex, if not impossible, without working around with your data. What I would suggest is to check your data and see the possibility of some issues (e.g., collinearity, etc.).

Myriam

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Jul 25, 2020, 3:05:57 PM7/25/20

to lavaan

I had the same error message and went to read the Muthen 1984 paper referenced in the error message (A general SEM with dichotomous, ordered categorical, and continuous latent variable indicators).

This is what I gathered (Pp. 119-120. )

W is a positive definite weight matrix used at the third estimation stage. Is part of the weighted least squares fitting function which is miminized by the estimation. Forming this matrix is needed to obtain a limited information generalized least squares estimator.
The A(g) submatrix is a “consistent estimator of the asymptotic covariance matrix of the estimator Theta prime”. Theta (not primed) is the “vector of free and distinct model parameters”

For me the problem came from the fact that I had specified condition.x=FALSE in the lavaan fitting command. I had a dichotomous observed exogenous variable X, so I was using the WLSMV estimator. This requires condition.x=TRUE for models with categorical covariates. So if my understanding is correct, this created a problem in relation to third stage estimation.

You did not list the fitting command you used and your estimator so I am not sure if this applies to you as well. Here is something on the Mplus website that explains why conditioning on X observed covariates is important - if this applies to you (but the post dates back to 2018) or to someone else who might read this post because of the same error message.

https://www.statmodel.com/download/Covariates%20%E2%80%93%20analysis%20conditioned%20on%20covariates.pdf