Measurement Invariance warning- not positive definite matrix

joana pipa

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Aug 5, 2018, 1:43:29 PM8/5/18

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Hello everyone,

I am new in testing this models and I am struggling in testing measurement invariance of one instrument. I am validating one instrument and I ran a CFA which fit indexes were quite acceptable. Now I am trying to test the measurement invariance across 3 age groups based on grade levels (3rd 5th and 7th grades). I ran the measurement invariance model and an error appeared in 4 models regarding the first group:

> mi<- measurementInvariance (Mod.CPCQ_2, data= SENSES_var_T1_G2_CPCQ_withoutOutliers, std.lv=TRUE, strict=TRUE, group="S_GRADE_T1")

Measurement invariance models:

Model 1 : fit.configural

Model 2 : fit.loadings

Model 3 : fit.intercepts

Model 4 : fit.residuals

Model 5 : fit.means

Chi Square Difference Test

Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)

fit.configural 426 30029 30904 762.30

fit.loadings 454 30042 30796 831.32 69.018 28 2.55e-05 ***

fit.intercepts 482 30044 30676 889.85 58.533 28 0.0006249 ***

fit.residuals 520 30192 30658 1113.26 223.411 38 < 2.2e-16 ***

fit.means 530 30289 30712 1230.81 117.550 10 < 2.2e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Fit measures:

cfi rmsea cfi.delta rmsea.delta

fit.configural 0.921 0.064 NA NA

fit.loadings 0.912 0.066 0.010 0.002

fit.intercepts 0.904 0.066 0.007 0.001

fit.residuals 0.861 0.077 0.043 0.011

fit.means 0.836 0.083 0.025 0.006

Warning messages:

1: In lav_object_post_check(object) :

lavaan WARNING: covariance matrix of latent variables

is not positive definite in group 1;

use inspect(fit,"cov.lv") to investigate.

2: In lav_object_post_check(object) :

lavaan WARNING: covariance matrix of latent variables

is not positive definite in group 1;

use inspect(fit,"cov.lv") to investigate.

3: In lav_object_post_check(object) :

lavaan WARNING: covariance matrix of latent variables

is not positive definite in group 1;

use inspect(fit,"cov.lv") to investigate.

4: In lav_object_post_check(object) :

lavaan WARNING: covariance matrix of latent variables

is not positive definite in group 1;

use inspect(fit,"cov.lv") to investigate.

When looking to the fit indexes it seems that the invariance holds for the first, second and third model but given the error associated I am wondering if I can trust on these values.

Then I run the inspect function which is bellow but I am not sure how to interpret these values and how they can help me to correct the error of non positive matrix.

Also I ran a CFA to each group separately and for the first group, although the fit indexes were quite good, an warning message regarding the covariance matrix and also the modification indexes appeared (Warning message:In lav_start_check_cov(lavpartable = lavpartable, start = START) : lavaan WARNING: starting values imply a correlation larger than 1; variables involved are: CPCQ_COOPERATION CPCQ_COHESION

Any thoughts about that? Suggestions of readings regarding this matter? I would be very grateful!

Thank you all!

Joana

> inspect(mi$fit.configural,"cov.lv")

> inspect(mi$fit.loadings,"cov.lv")

> inspect(mi$fit.intercepts,"cov.lv")

$`3`

CPCQ_COO CPCQ_CON CPCQ_COH CPCQ_I CPCQ_COM

CPCQ_COOPERATION 0.471

CPCQ_COOPERATION 0.393

CPCQ_COOPERATION 0.380

CPCQ_CONFLICT -0.212 0.536

CPCQ_CONFLICT -0.180 0.477

CPCQ_CONFLICT -0.178 0.478

CPCQ_COHESION 0.538 -0.238 0.559

CPCQ_COHESION 0.425 -0.192 0.434

CPCQ_COHESION 0.411 -0.189 0.415

CPCQ_ISOLATION -0.103 0.322 -0.138 0.377

CPCQ_ISOLATION -0.099 0.328 -0.132 0.438

CPCQ_ISOLATION -0.096 0.321 -0.127 0.419

CPCQ_COMFORT 0.214 -0.059 0.218 -0.031 0.278

CPCQ_COMFORT 0.196 -0.060 0.193 -0.041 0.277

CPCQ_COMFORT 0.189 -0.059 0.187 -0.040 0.265

$`5`

CPCQ_COO CPCQ_CON CPCQ_COH CPCQ_I CPCQ_COM

CPCQ_COOPERATION 0.334

CPCQ_COOPERATION 0.439

CPCQ_COOPERATION 0.428

CPCQ_CONFLICT -0.178 0.329

CPCQ_CONFLICT -0.220 0.370

CPCQ_CONFLICT -0.218 0.371

CPCQ_COHESION 0.373 -0.226 0.548

CPCQ_COHESION 0.433 -0.241 0.550

CPCQ_COHESION 0.424 -0.238 0.536

CPCQ_ISOLATION -0.110 0.187 -0.138 0.450

CPCQ_ISOLATION -0.138 0.206 -0.143 0.487

CPCQ_ISOLATION -0.133 0.201 -0.139 0.467

CPCQ_COMFORT 0.354 -0.189 0.474 -0.177 0.691

CPCQ_COMFORT 0.458 -0.222 0.523 -0.207 0.830

CPCQ_COMFORT 0.444 -0.218 0.509 -0.198 0.801

$`7`

CPCQ_COO CPCQ_CON CPCQ_COH CPCQ_I CPCQ_COM

CPCQ_COOPERATION 0.517

CPCQ_COOPERATION 0.454

CPCQ_COOPERATION 0.442

CPCQ_CONFLICT -0.300 0.347

CPCQ_CONFLICT -0.283 0.349

CPCQ_CONFLICT -0.280 0.350

CPCQ_COHESION 0.433 -0.266 0.466

CPCQ_COHESION 0.428 -0.283 0.515

CPCQ_COHESION 0.420 -0.281 0.506

CPCQ_ISOLATION -0.173 0.150 -0.156 0.426

CPCQ_ISOLATION -0.151 0.140 -0.150 0.378

CPCQ_ISOLATION -0.145 0.136 -0.146 0.361

CPCQ_COMFORT 0.463 -0.297 0.379 -0.246 0.927

CPCQ_COMFORT 0.414 -0.288 0.381 -0.216 0.811

CPCQ_COMFORT 0.402 -0.284 0.374 -0.207 0.782

João Marôco

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Aug 5, 2018, 2:00:49 PM8/5/18

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Joana,

So you are getting negative variances and or correlations greater than one. This happens when you group sizes are small. Can you increase sample size? Otherwise you have to fix correlations /item variances.

Best,

João Marôco
[Sent from my not that smart smartphone with more errors than usual]

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joana pipa

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Aug 5, 2018, 2:15:25 PM8/5/18

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Dear João,

thank you! Unfortunately I cannot increase the sample size. I have 142 observations for group 1, 199 for group 2 and 236 for group 3 and the instrument has 19 itens. And indeed for group 1 the correlations between two factors are greater than 1.

Thank your your suggestions, I will try once more fixing the item variances.

Joana

joana pipa

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Aug 6, 2018, 8:35:59 AM8/6/18

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Dear all,

in trying to overcome the issue that I explained bellow, I am using the std.lv=TRUE function in the model in order to fix the variance, but I get the same warning. Is there another specification of the model that I should use to overcome these issues and report the results?

Thank you all

Joana

Terrence Jorgensen

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Aug 7, 2018, 8:12:04 AM8/7/18

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indeed for group 1 the correlations between two factors are greater than 1.

I will try once more fixing the item variances.

Why? The problem is not the variances, but the covariances/correlations. And you should not use constrained estimation to hide the problem.

http://dx.doi.org/10.1037/1082-989X.13.2.150

Instead, test whether it is a problem at all by looking at the CI for the correlation (when std.lv = TRUE, the factor covariance will be a correlation).

https://doi.org/10.1177/0049124112442138

If the CI includes plausible values (< 1), then sampling error is a plausible explanation for the out-of-bounds estimate (pretty common in small samples), so there is no need to "fix" anything by constraining your estimation (which biases your test statistic).

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

joana pipa

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Aug 8, 2018, 4:52:02 AM8/8/18

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Many thanks!

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