Lavaan and MPLUS different test statistics

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mplus2lavaan

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Leoni

未読、

2020/06/03 12:11:522020/06/03

To: lavaan

Dear Group,

I am fitting a multilevel CFA on two groups to test for invariance of factor loadings on the Within Person Model.

I specified two factors with 3 and 4 indicators at Level 1 and a saturated model at Level 2.

I used effect coding to set the metric of the latent variables and indicated the estimation method as MLR in the command.

I fit the same model in MPLUS where MLR is the default for a two-level analysis. In Mplus I get a warning that the dataset contains cases with missing values on all variables, which lavaan does not give me.

I compared the output between lavaan and MPLUS. All of the test statistics differ. At level 1 the parameter estimates are the same in lavaan and in mplus. At level 2 the means are the same in lavaan as in mplus but the variances and covariances do not match.

Why is this the case? I tried all different model specifications and changing estimators in the lavaan code but I cannot get the Test Statistics to align between the two programs?
How are the model specifications between lavaan and MPLUS different? Or is the problem the estimatior?

Has anyone had experience with comparing lavaan and MPLUS output for Multilevel, Multigroup CFA?

Thank you very much!!

Yves Rosseel

未読、

2020/06/03 14:24:342020/06/03

To: lav...@googlegroups.com

On 6/3/20 6:11 PM, Leoni wrote:
> I fit the same model in MPLUS where MLR is the default for a two-level
> analysis. In Mplus I get a warning that the dataset contains cases with
> missing values on all variables, which lavaan does not give me.

Did you use missing = "ml"? (Mplus does this by default, lavaan not).

If this doesn't solve it, can you show us the lavaan output and the
Mplus output?

Yves.

Leoni

未読、

2020/06/04 3:42:002020/06/04

To: lavaan

Thank you so much for your help Yves! Unfortunately assing the missing command did not make a difference

twolevel <- '

group: 1

level: 1

f1 =~ relaxed + happy + euphoric

f2 =~ depressed + stressed + anxious + anger

level: 2

relaxed ~~ relaxed + happy + euphoric + depressed + stressed + anxious + anger

happy ~~ happy + euphoric + depressed + stressed + anxious + anger

euphoric ~~ euphoric + depressed + stressed + anxious + anger

depressed ~~ depressed + stressed + anxious + anger

stressed ~~ stressed + anxious + anger

anxious ~~ anxious + anger

anger ~~ anger

group: 2

level: 1

f1 =~ relaxed + happy + euphoric

f2 =~ depressed + stressed + anxious + anger

level: 2

relaxed ~~ relaxed + happy + euphoric + depressed + stressed + anxious + anger

happy ~~ happy + euphoric + depressed + stressed + anxious + anger

euphoric ~~ euphoric + depressed + stressed + anxious + anger

depressed ~~ depressed + stressed + anxious + anger

stressed ~~ stressed + anxious + anger

anxious ~~ anxious + anger

anger ~~ anger

results <- cfa(twolevel, data = data, group = "HC", cluster = 'PID', estimator = "MLR", missing = "ML", effect.coding = TRUE)

The data is non-normal that's why I was using MLR (which is the Yuan Bentler scaled statistic right) also there is little variance on the items in group two. Should I look at the scaled statistic or the robust standard error statistic in lavaan to match it with MPLUS?

UNIVARIATE SAMPLE STATISTICS

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS FOR G1

Variable/ Mean/ Skewness/ Minimum/ % with Percentiles

Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median

RELAXED 36.996 0.349 0.000 3.49% 14.000 28.000 35.000

4619.000 538.437 -0.564 100.000 0.91% 44.000 57.000

HAPPY 31.387 0.566 0.000 6.41% 9.000 21.000 27.000

4619.000 551.156 -0.497 100.000 0.48% 35.000 53.000

EUPHORIC 19.249 1.460 0.000 14.96% 2.000 8.000 11.000

4619.000 451.769 1.621 100.000 0.35% 16.000 35.000

DEPR 46.568 0.030 0.000 3.85% 17.000 39.000 49.000

4619.000 783.234 -0.983 100.000 3.18% 55.000 73.000

STRESS 46.752 0.039 0.000 2.62% 20.000 39.000 48.000

4619.000 723.872 -0.898 100.000 2.90% 55.000 72.000

ANXIOUS 36.450 0.437 0.000 5.76% 9.000 23.000 32.000

4619.000 744.584 -0.905 100.000 1.43% 43.000 63.000

ANGER 26.471 1.141 0.000 11.63% 4.000 12.000 17.000

4619.000 692.231 0.438 100.000 2.36% 24.000 50.000

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS FOR G2

Variable/ Mean/ Skewness/ Minimum/ % with Percentiles

Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median

RELAXED 56.542 -0.464 0.000 0.97% 39.000 52.000 58.000

2576.000 455.401 -0.174 100.000 1.05% 64.000 75.000

HAPPY 50.985 -0.473 0.000 1.16% 32.000 49.000 53.000

2576.000 477.775 -0.379 100.000 0.19% 59.000 71.000

EUPHORIC 25.417 0.627 0.000 13.08% 3.000 9.000 16.000

2576.000 567.208 -0.861 99.000 0.04% 29.000 50.000

DEPR 5.890 3.716 0.000 28.03% 0.000 2.000 4.000

2576.000 69.029 22.211 100.000 0.04% 5.000 9.000

STRESS 17.847 1.397 0.000 13.12% 2.000 7.000 9.000

2576.000 385.101 1.237 98.000 0.04% 14.000 33.000

ANXIOUS 6.154 3.875 0.000 27.52% 0.000 2.000 4.000

2576.000 94.272 19.440 84.000 0.08% 5.000 9.000

ANGER 6.524 3.488 0.000 26.75% 0.000 2.000 4.000

2576.000 97.546 15.292 83.000 0.04% 6.000 9.000

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE

TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE

FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING

VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE

CONDITION NUMBER IS -0.791D-19. PROBLEM INVOLVING THE FOLLOWING PARAMETER:

Parameter 95, Group G2, %BETWEEN%: ANXIOUS WITH DEPR

Here is the lavaan output

lavaan 0.6-6 ended normally after 803 iterations

Estimator ML

Optimization method NLMINB

Number of free parameters 104

Number of equality constraints 4

Number of observations per group: Used Total

0 4619 5460

1 2576 2800

Number of clusters [PID]:

0 78

1 40

Model Test User Model:

Standard Robust

Test Statistic 1004.143 204.885

Degrees of freedom 26 26

P-value (Chi-square) 0.000 0.000

Scaling correction factor 4.901

Yuan-Bentler correction (Mplus variant)

Test statistic for each group:

0 701.196 143.072

1 302.947 61.813

Model Test Baseline Model:

Test statistic 12537.945 6089.715

Degrees of freedom 84 84

P-value 0.000 0.000

Scaling correction factor 2.059

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.921 0.970

Tucker-Lewis Index (TLI) 0.746 0.904

Robust Comparative Fit Index (CFI) 0.929

Robust Tucker-Lewis Index (TLI) 0.771

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -206597.021 -206597.021

Scaling correction factor 4.683

for the MLR correction

Loglikelihood unrestricted model (H1) -206094.950 -206094.950

Scaling correction factor 4.876

for the MLR correction

Akaike (AIC) 413394.043 413394.043

Bayesian (BIC) 414082.157 414082.157

Sample-size adjusted Bayesian (BIC) 413764.379 413764.379

Root Mean Square Error of Approximation:

RMSEA 0.102 0.044

90 Percent confidence interval - lower 0.097 0.041

90 Percent confidence interval - upper 0.108 0.046

P-value RMSEA <= 0.05 0.000 1.000

Robust RMSEA 0.097

90 Percent confidence interval - lower 0.085

90 Percent confidence interval - upper 0.109

Standardized Root Mean Square Residual (corr metric):

SRMR (within covariance matrix) 0.072 0.072

SRMR (between covariance matrix) 0.087 0.087

Parameter Estimates:

Standard errors Sandwich

Information bread Observed

Observed information based on Hessian

Group 1 [0]:

Level 1 [within]:

Latent Variables:

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

f1 =~

relaxed 1.069 0.053 20.176 0.000 13.823 0.696

happy 1.173 0.036 32.148 0.000 15.157 0.803

euphoric 0.758 0.059 12.930 0.000 9.801 0.641

f2 =~

depressed 0.993 0.039 25.732 0.000 12.734 0.705

stressed 1.143 0.038 30.021 0.000 14.651 0.699

anxious 0.975 0.047 20.778 0.000 12.494 0.641

anger 0.889 0.045 19.569 0.000 11.400 0.587

Covariances:

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

f1 ~~

f2 -119.626 18.094 -6.611 0.000 -0.722 -0.722

Intercepts:

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

.relaxed 0.000 0.000 0.000

.happy 0.000 0.000 0.000

.euphoric 0.000 0.000 0.000

.depressed 0.000 0.000 0.000

.stressed 0.000 0.000 0.000

.anxious 0.000 0.000 0.000

.anger 0.000 0.000 0.000

f1 0.000 0.000 0.000

f2 0.000 0.000 0.000

Variances:

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

.relaxed 202.900 17.561 11.554 0.000 202.900 0.515

.happy 126.161 15.760 8.005 0.000 126.161 0.354

.euphoric 137.933 13.437 10.265 0.000 137.933 0.589

.depressed 164.391 12.958 12.687 0.000 164.391 0.503

.stressed 224.582 18.955 11.848 0.000 224.582 0.511

.anxious 224.269 19.891 11.275 0.000 224.269 0.590

.anger 247.230 21.273 11.622 0.000 247.230 0.655

f1 167.112 24.664 6.775 0.000 1.000 1.000

f2 164.344 17.482 9.401 0.000 1.000 1.000

Level 2 [PID]:

Covariances:

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

.relaxed ~~

.happy 183.183 71.113 2.576 0.010 183.183 0.844

.euphoric 177.380 79.849 2.221 0.026 177.380 0.749

.depressed -85.146 30.383 -2.802 0.005 -85.146 -0.347

.stressed -59.927 25.013 -2.396 0.017 -59.927 -0.307

.anxious -46.632 26.254 -1.776 0.076 -46.632 -0.204

.anger -5.903 25.569 -0.231 0.817 -5.903 -0.026

.happy ~~

.euphoric 214.853 85.880 2.502 0.012 214.853 0.809

.depressed -101.042 33.847 -2.985 0.003 -101.042 -0.367

.stressed -50.513 23.396 -2.159 0.031 -50.513 -0.231

.anxious -19.262 27.359 -0.704 0.481 -19.262 -0.075

.anger -3.349 30.510 -0.110 0.913 -3.349 -0.013

.euphoric ~~

.depressed -51.806 34.071 -1.521 0.128 -51.806 -0.172

.stressed -17.512 25.753 -0.680 0.497 -17.512 -0.073

.anxious 4.367 29.637 0.147 0.883 4.367 0.016

.anger 35.535 34.488 1.030 0.303 35.535 0.129

.depressed ~~

.stressed 181.122 27.687 6.542 0.000 181.122 0.732

.anxious 148.201 30.799 4.812 0.000 148.201 0.512

.anger 74.111 26.855 2.760 0.006 74.111 0.259

.stressed ~~

.anxious 158.462 23.172 6.839 0.000 158.462 0.689

.anger 64.895 17.345 3.741 0.000 64.895 0.286

.anxious ~~

.anger 126.549 29.914 4.230 0.000 126.549 0.476

Intercepts:

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

.relaxed 37.093 1.397 26.550 0.000 37.093 2.667

.happy 31.653 1.600 19.786 0.000 31.653 2.028

.euphoric 19.473 1.671 11.654 0.000 19.473 1.144

.depressed 46.157 2.445 18.875 0.000 46.157 2.615

.stressed 46.546 1.946 23.917 0.000 46.546 3.321

.anxious 36.176 2.196 16.475 0.000 36.176 2.204

.anger 26.263 1.986 13.227 0.000 26.263 1.622

Variances:

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

.relaxed 193.449 68.370 2.829 0.005 193.449 1.000

.happy 243.499 76.769 3.172 0.002 243.499 1.000

.euphoric 289.701 95.532 3.033 0.002 289.701 1.000

.depressed 311.473 31.858 9.777 0.000 311.473 1.000

.stressed 196.482 24.620 7.981 0.000 196.482 1.000

.anxious 269.494 26.147 10.307 0.000 269.494 1.000

.anger 262.297 65.434 4.009 0.000 262.297 1.000

Group 2 [1]:

Level 1 [within]:

Latent Variables:

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

f1 =~

relaxed 1.317 0.158 8.352 0.000 12.850 0.678

happy 1.095 0.100 11.001 0.000 10.686 0.625

euphoric 0.588 0.088 6.701 0.000 5.732 0.399

f2 =~

depressed 0.439 0.119 3.699 0.000 2.295 0.348

stressed 2.041 0.307 6.636 0.000 10.661 0.669

anxious 0.606 0.130 4.674 0.000 3.165 0.428

anger 0.914 0.130 7.019 0.000 4.777 0.537

Covariances:

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

f1 ~~

f2 -34.900 6.411 -5.444 0.000 -0.685 -0.685

Intercepts:

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

.relaxed 0.000 0.000 0.000

.happy 0.000 0.000 0.000

.euphoric 0.000 0.000 0.000

.depressed 0.000 0.000 0.000

.stressed 0.000 0.000 0.000

.anxious 0.000 0.000 0.000

.anger 0.000 0.000 0.000

f1 0.000 0.000 0.000

f2 0.000 0.000 0.000

Variances:

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

.relaxed 193.606 31.926 6.064 0.000 193.606 0.540

.happy 178.251 28.080 6.348 0.000 178.251 0.610

.euphoric 173.283 26.934 6.434 0.000 173.283 0.841

.depressed 38.194 7.228 5.284 0.000 38.194 0.879

.stressed 140.026 25.278 5.539 0.000 140.026 0.552

.anxious 44.588 12.118 3.680 0.000 44.588 0.817

.anger 56.348 11.235 5.016 0.000 56.348 0.712

f1 95.172 14.247 6.680 0.000 1.000 1.000

f2 27.298 5.478 4.983 0.000 1.000 1.000

Level 2 [PID]:

Covariances:

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

.relaxed ~~

.happy 68.983 35.983 1.917 0.055 68.983 0.561

.euphoric 27.250 29.095 0.937 0.349 27.250 0.159

.depressed -15.374 1951.805 -0.008 0.994 -15.374 -0.121

.stressed -60.246 193.316 -0.312 0.755 -60.246 -0.540

.anxious -15.328 2352.072 -0.007 0.995 -15.328 -0.100

.anger -5.536 1556.384 -0.004 0.997 -5.536 -0.055

.happy ~~

.euphoric 42.500 60.541 0.702 0.483 42.500 0.186

.depressed -19.014 1406.841 -0.014 0.989 -19.014 -0.112

.stressed -11.599 109.474 -0.106 0.916 -11.599 -0.078

.anxious 3.535 1705.408 0.002 0.998 3.535 0.017

.anger 4.606 1139.787 0.004 0.997 4.606 0.034

.euphoric ~~

.depressed 23.487 239.438 0.098 0.922 23.487 0.100

.stressed 31.003 42.216 0.734 0.463 31.003 0.150

.anxious 2.256 273.280 0.008 0.993 2.256 0.008

.anger 8.979 188.400 0.048 0.962 8.979 0.048

.depressed ~~

.stressed 37.847 2173.835 0.017 0.986 37.847 0.246

.anxious 199.126 1123.980 0.177 0.859 199.126 0.945

.anger 132.981 46.396 2.866 0.004 132.981 0.951

.stressed ~~

.anxious 43.338 2616.937 0.017 0.987 43.338 0.234

.anger 27.316 1664.291 0.016 0.987 27.316 0.222

.anxious ~~

.anger 164.389 48.754 3.372 0.001 164.389 0.976

Intercepts:

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

.relaxed 56.300 1.644 34.250 0.000 56.300 5.861

.happy 50.834 2.217 22.931 0.000 50.834 3.972

.euphoric 25.385 3.094 8.204 0.000 25.385 1.424

.depressed 6.074 0.887 6.845 0.000 6.074 0.459

.stressed 18.197 1.964 9.266 0.000 18.197 1.566

.anxious 6.287 1.084 5.800 0.000 6.287 0.395

.anger 6.613 0.781 8.468 0.000 6.613 0.626

Variances:

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

.relaxed 92.257 20.874 4.420 0.000 92.257 1.000

.happy 163.771 76.693 2.135 0.033 163.771 1.000

.euphoric 317.867 84.888 3.745 0.000 317.867 1.000

.depressed 174.980 941.596 0.186 0.853 174.980 1.000

.stressed 135.112 408.318 0.331 0.741 135.112 1.000

.anxious 253.984 1329.789 0.191 0.849 253.984 1.000

.anger 111.689 544.016 0.205 0.837 111.689 1.000

This is the MPLUS Output:

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters 100

Loglikelihood

H0 Value -206555.230

H0 Scaling Correction Factor 5.6264

for MLR

H1 Value -206094.950

H1 Scaling Correction Factor 4.8763

for MLR

Information Criteria

Akaike (AIC) 413310.460

Bayesian (BIC) 413998.575

Sample-Size Adjusted BIC 413680.797

(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value 462.303*

Degrees of Freedom 26

P-Value 0.0000

Scaling Correction Factor 1.9912

for MLR

Chi-Square Contribution From Each Group

G1 339.956

G2 122.347

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used

for chi-square difference testing in the regular way. MLM, MLR and WLSM

chi-square difference testing is described on the Mplus website. MLMV, WLSMV,

and ULSMV difference testing is done using the DIFFTEST option.

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.068

CFI/TLI

CFI 0.923

TLI 0.751

Chi-Square Test of Model Fit for the Baseline Model

Value 5736.973

Degrees of Freedom 84

P-Value 0.0000

SRMR (Standardized Root Mean Square Residual)

Value for Within 0.049

Value for Between 0.001

MODEL RESULTS

Two-Tailed

Estimate S.E. Est./S.E. P-Value

Group G1

Within Level

FW1 BY

RELAXED 1.069 0.054 19.869 0.000

HAPPY 1.173 0.037 31.668 0.000

EUPHORIC 0.758 0.060 12.738 0.000

FW2 BY

DEPR 0.993 0.039 25.354 0.000

STRESS 1.143 0.039 29.587 0.000

ANXIOUS 0.975 0.048 20.475 0.000

ANGER 0.889 0.046 19.284 0.000

FW2 WITH

FW1 -119.437 18.317 -6.521 0.000

Variances

FW1 166.839 24.962 6.684 0.000

FW2 164.222 17.708 9.274 0.000

Residual Variances

RELAXED 202.918 17.822 11.386 0.000

HAPPY 126.180 15.998 7.887 0.000

EUPHORIC 137.944 13.637 10.115 0.000

DEPR 164.406 13.151 12.502 0.000

STRESS 224.569 19.232 11.677 0.000

ANXIOUS 224.263 20.184 11.111 0.000

ANGER 247.221 21.585 11.454 0.000

Between Level

RELAXED WITH

HAPPY 139.316 24.588 5.666 0.000

EUPHORIC 115.834 25.422 4.556 0.000

DEPR -139.878 36.749 -3.806 0.000

STRESS -98.271 30.750 -3.196 0.001

ANXIOUS -82.996 31.896 -2.602 0.009

ANGER -30.181 23.441 -1.288 0.198

HAPPY WITH

EUPHORIC 157.016 30.493 5.149 0.000

DEPR -158.841 38.750 -4.099 0.000

STRESS -86.356 28.814 -2.997 0.003

ANXIOUS -65.562 33.715 -1.945 0.052

ANGER -21.147 30.242 -0.699 0.484

EUPHORIC WITH

DEPR -83.479 37.108 -2.250 0.024

STRESS -26.632 28.113 -0.947 0.343

ANXIOUS -14.368 31.757 -0.452 0.651

ANGER 29.231 31.789 0.920 0.358

DEPR WITH

STRESS 309.895 55.844 5.549 0.000

ANXIOUS 301.188 56.026 5.376 0.000

ANGER 176.704 49.444 3.574 0.000

STRESS WITH

ANXIOUS 269.815 45.628 5.913 0.000

ANGER 143.655 33.815 4.248 0.000

ANXIOUS WITH

ANGER 207.094 47.085 4.398 0.000

Means

RELAXED 37.094 1.418 26.162 0.000

HAPPY 31.656 1.624 19.492 0.000

EUPHORIC 19.475 1.696 11.485 0.000

DEPR 46.152 2.482 18.594 0.000

STRESS 46.543 1.976 23.555 0.000

ANXIOUS 36.171 2.229 16.228 0.000

ANGER 26.260 2.015 13.033 0.000

Variances

RELAXED 150.020 25.422 5.901 0.000

HAPPY 199.688 28.325 7.050 0.000

EUPHORIC 220.247 33.950 6.487 0.000

DEPR 475.004 65.052 7.302 0.000

STRESS 297.040 49.065 6.054 0.000

ANXIOUS 380.927 47.721 7.982 0.000

ANGER 310.559 79.794 3.892 0.000

Group G2

Within Level

FW1 BY

RELAXED 1.316 0.153 8.615 0.000

HAPPY 1.095 0.096 11.365 0.000

EUPHORIC 0.589 0.085 6.921 0.000

FW2 BY

DEPR 0.439 0.116 3.805 0.000

STRESS 2.041 0.299 6.824 0.000

ANXIOUS 0.606 0.126 4.806 0.000

ANGER 0.914 0.127 7.216 0.000

FW2 WITH

FW1 -35.150 6.296 -5.583 0.000

Variances

FW1 96.203 14.069 6.838 0.000

FW2 27.375 5.350 5.117 0.000

Residual Variances

RELAXED 193.419 31.107 6.218 0.000

HAPPY 177.940 27.334 6.510 0.000

EUPHORIC 173.160 26.176 6.615 0.000

DEPR 38.194 7.028 5.434 0.000

STRESS 140.009 24.579 5.696 0.000

ANXIOUS 44.584 11.800 3.778 0.000

ANGER 56.351 10.929 5.156 0.000

Between Level

RELAXED WITH

HAPPY 80.059 25.070 3.193 0.001

EUPHORIC 48.679 31.650 1.538 0.124

DEPR -14.958 9.947 -1.504 0.133

STRESS -61.758 24.159 -2.556 0.011

ANXIOUS -14.314 13.901 -1.030 0.303

ANGER -7.391 7.446 -0.993 0.321

HAPPY WITH

EUPHORIC 131.251 40.228 3.263 0.001

DEPR -18.035 13.626 -1.324 0.186

STRESS -17.786 23.204 -0.767 0.443

ANXIOUS 1.135 7.815 0.145 0.885

ANGER 0.872 7.279 0.120 0.905

EUPHORIC WITH

DEPR 15.430 16.221 0.951 0.341

STRESS 57.405 36.128 1.589 0.112

ANXIOUS 12.330 17.462 0.706 0.480

ANGER 13.161 13.629 0.966 0.334

DEPR WITH

STRESS 26.753 17.818 1.502 0.133

ANXIOUS 23.289 7.158 3.254 0.001

ANGER 17.103 5.535 3.090 0.002

STRESS WITH

ANXIOUS 26.590 16.109 1.651 0.099

ANGER 19.770 9.183 2.153 0.031

ANXIOUS WITH

ANGER 24.147 9.619 2.510 0.012

Means

RELAXED 56.296 1.595 35.301 0.000

HAPPY 50.829 2.152 23.620 0.000

EUPHORIC 25.385 3.011 8.431 0.000

DEPR 6.075 0.848 7.160 0.000

STRESS 18.202 1.903 9.565 0.000

ANXIOUS 6.289 1.025 6.137 0.000

ANGER 6.616 0.712 9.292 0.000

Variances

RELAXED 96.312 20.017 4.812 0.000

HAPPY 180.597 43.711 4.132 0.000

EUPHORIC 359.496 52.770 6.813 0.000

DEPR 28.016 8.678 3.228 0.001

STRESS 140.681 42.570 3.305 0.001

ANXIOUS 41.096 21.945 1.873 0.061

ANGER 19.065 5.508 3.461 0.001

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix -0.791E-19

(ratio of smallest to largest eigenvalue)

Yves Rosseel

未読、

2020/06/05 3:12:262020/06/05

To: lav...@googlegroups.com

Hello Leoni,

I would like to investigate this further. Would you be able to send me
your data (or a snippet of the data) togehter with the Rscript and the
Mplus scripts?

In the meantime, I would suggest the following:

First extract the saturated (h1) values for the between level (per group):

lavInspect(results, "h1")[[2]]$cov

for the first group, and

lavInspect(results, "h1")[[4]]$cov

for the second group.

Then, use these values as starting values for the level: 2
variances/covariances, eg

relaxed ~~ start(150.020)*relaxed +
start(139.316)*happy +
start(115.834)*euphoric +
start(-139.878)*depressed +
start(-98.271)*stressed +
start(-82.996)*anxious +
start(-30.181)*anger

and so on...

Yves.

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Lan Nguyen

未読、

2023/11/21 14:25:502023/11/21

To: lavaan

I also have the same problem when running a two-level model using MLR estimator in both lavaan and Mplus.

All the test statistics, estimated coefficients, standard errors and p-value are so different. The Chi-square test in lavaan is higher than in M'plus, which indicated better goodness of fit. However, the SRMR within level in lavaan is much higher than in Mplus (0.092 vs 0.010). Lavaan's estimated coefficients are different but not much, but lavaan's SEs are much higher than what I found in Mplus, which leads to more insignificant effects.

Also I received the message from lavaan which I did not see in Mplus:

3: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING: The variance-covariance matrix of the estimated parameters (vcov) does not appear to be positive definite! The smallest eigenvalue (= -1.516512e-18) is smaller than zero. This may be a symptom that the model is not identified.

Could you please help me know why is it the case? Which one should be trusted?

Following is my lavaan's code and results

model_1<- '
level: 1
diet_ind ~ crop_indi + ploti + mktparti + inctrli
crop_indi ~ ploti
mktparti ~ crop_indi + inctrli
inctrli ~ ploti
veg_inc ~ mktparti + inctrli
diet_ind ~~ 0*veg_inc

level: 2
crop_indi ~ sa + crop_com
diet_ind ~ crop_indi + crop_com + diet_com
crop_com ~ sa
diet_com ~ crop_com + sa
diet_com ~~ 0*crop_com
diet_ind ~~ 0* crop_indi '
fit <- sem(model=model_1, data=sem_sa, cluster="vilid", estimator="MLR")

summary (fit, fit.measures=TRUE)

lavaan’s results

Estimator ML

Optimization method NLMINB

Number of model parameters 34

Used Total

Number of observations 1150 1158

Number of clusters [vilid] 38

Model Test User Model:

Standard Scaled

Test Statistic 0.000 0.000

Degrees of freedom 7 7

P-value (Chi-square) 1.000 1.000

Scaling correction factor 0.837

Yuan-Bentler correction (Mplus variant)

Model Test Baseline Model:

Test statistic 216.748 127.675

Degrees of freedom 25 25

P-value 0.000 0.000

Scaling correction factor 1.698

User Model versus Baseline Model:

Comparative Fit Index (CFI) 1.000 1.000

Tucker-Lewis Index (TLI) 1.130 1.243

Robust Comparative Fit Index (CFI) 1.000

Robust Tucker-Lewis Index (TLI) 1.120

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -7587.851 -7587.851

Scaling correction factor 18.113

for the MLR correction

Loglikelihood unrestricted model (H1) -7719.755 -7719.755

Scaling correction factor 15.163

for the MLR correction

Akaike (AIC) 15243.702 15243.702

Bayesian (BIC) 15415.318 15415.318

Sample-size adjusted Bayesian (SABIC) 15307.323 15307.323

Root Mean Square Error of Approximation:

RMSEA 0.000 0.000

90 Percent confidence interval - lower 0.000 0.000

90 Percent confidence interval - upper 0.000 0.000

P-value H_0: RMSEA <= 0.050 1.000 1.000

P-value H_0: RMSEA >= 0.080 0.000 0.000

Robust RMSEA 0.000

90 Percent confidence interval - lower 0.000

90 Percent confidence interval - upper 0.000

P-value H_0: Robust RMSEA <= 0.050 1.000

P-value H_0: Robust RMSEA >= 0.080 0.000

Standardized Root Mean Square Residual (corr metric):

SRMR (within covariance matrix) 0.092 0.092

SRMR (between covariance matrix) 0.004 0.004

Parameter Estimates:

Standard errors Sandwich

Information bread Observed

Observed information based on Hessian

Level 1 [within]:

Regressions:

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

diet_ind ~

crop_indi 0.234 0.046 5.096 0.000

ploti 0.052 0.048 1.080 0.280

mktparti 0.047 0.044 1.085 0.278

inctrli -0.044 0.024 -1.800 0.072

crop_indi ~

ploti 0.043 0.059 0.731 0.465

mktparti ~

crop_indi 0.227 0.077 2.958 0.003

inctrli 0.090 0.048 1.864 0.062

inctrli ~

ploti -0.137 0.033 -4.174 0.000

veg_inc ~

mktparti 0.072 0.047 1.521 0.128

inctrli 0.057 0.055 1.026 0.305

Covariances:

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

.diet_ind ~~

.veg_inc 0.000

Intercepts:

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

.mktparti -0.000 0.001 -0.190 0.849

.inctrli 0.001 0.001 0.955 0.340

.veg_inc 0.000 0.000 12.363 0.000

Variances:

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

.diet_ind 0.549 0.051 10.706 0.000

.crop_indi 0.638 0.112 5.684 0.000

.mktparti 0.958 0.072 13.306 0.000

.inctrli 0.981 0.066 14.818 0.000

.veg_inc 0.997 0.965 1.033 0.302

Level 2 [vilid]:

Regressions:

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

crop_indi ~

sa 0.159 0.068 2.329 0.020

crop_com 0.438 0.066 6.600 0.000

diet_ind ~

crop_indi 0.994 0.248 4.012 0.000

crop_com -0.385 0.140 -2.747 0.006

diet_com 0.414 0.056 7.366 0.000

crop_com ~

sa 0.873 0.094 9.303 0.000

diet_com ~

crop_com 0.467 0.104 4.485 0.000

sa 0.481 0.110 4.388 0.000

Covariances:

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

.crop_com ~~

.diet_com 0.000

.diet_ind ~~

.crop_indi 0.000

Intercepts:

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

.crop_indi 0.018 0.034 0.521 0.602

.diet_ind -0.004 0.031 -0.134 0.893

.crop_com 0.004 0.089 0.047 0.963

.diet_com -0.016 0.060 -0.272 0.786

Variances:

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

.crop_indi 0.021 0.010 2.032 0.042

.diet_ind 0.006 0.009 0.654 0.513

.crop_com 0.303 0.063 4.806 0.000

.diet_com 0.136 0.023 5.869 0.000

Following is the excerpt from my Mplus's outputs:

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters 34

Loglikelihood

H0 Value -6659.876
H0 Scaling Correction Factor 18.1145
for MLR
H1 Value -6658.466
H1 Scaling Correction Factor 15.1335
for MLR

Information Criteria

Akaike (AIC) 13387.751
Bayesian (BIC) 13559.544
Sample-Size Adjusted BIC 13451.549

(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value 4.306*
Degrees of Freedom 7
P-Value 0.7439
Scaling Correction Factor 0.6549
for MLR

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.000

CFI/TLI

CFI 1.000
TLI 1.000

Chi-Square Test of Model Fit for the Baseline Model

Value 502.160
Degrees of Freedom 25

P-Value 0.0000

SRMR (Standardized Root Mean Square Residual)

Value for Within 0.010
Value for Between 0.002

MODEL RESULTS

Two-Tailed
Estimate S.E. Est./S.E. P-Value

Within Level

DIET_IND ON
CROP_INDI 0.231 0.038 5.996 0.000
PLOTI 0.064 0.030 2.146 0.032
MKTPARTI 0.064 0.030 2.146 0.032
INCTRLI -0.148 0.040 -3.648 0.000

CROP_INDI ON
PLOTI 0.067 0.022 2.995 0.003

MKTPARTI ON
CROP_INDI 0.250 0.048 5.181 0.000
INCTRLI 0.204 0.102 2.003 0.045

INCTRLI ON
PLOTI -0.060 0.015 -4.117 0.000

VEG_INC ON
MKTPARTI 0.072 0.047 1.521 0.128
INCTRLI 0.128 0.125 1.026 0.305

DIET_IND WITH
VEG_INC 0.000 0.000 999.000 999.000

Intercepts
MKTPARTI -0.053 0.072 -0.744 0.457
VEG_INC -0.034 0.007 -5.041 0.000
INCTRLI 0.264 0.025 10.469 0.000

Residual Variances
MKTPARTI 0.952 0.064 14.942 0.000
VEG_INC 0.991 0.960 1.033 0.302
INCTRLI 0.190 0.013 14.836 0.000
CROP_INDI 0.637 0.115 5.553 0.000
DIET_IND 0.550 0.052 10.646 0.000

Between Level

CROP_INDI ON
SA 0.139 0.067 2.063 0.039
CROP_COM 0.430 0.066 6.529 0.000

DIET_IND ON
CROP_INDI 0.893 0.220 4.064 0.000
CROP_COM -0.355 0.123 -2.874 0.004
DIET_COM 0.425 0.052 8.118 0.000

CROP_COM ON
SA 0.847 0.091 9.303 0.000

DIET_COM ON
CROP_COM 0.484 0.108 4.485 0.000
SA 0.483 0.110 4.389 0.000

DIET_COM WITH
CROP_COM 0.000 0.000 999.000 999.000

DIET_IND WITH
CROP_INDI 0.000 0.000 999.000 999.000

Intercepts
CROP_COM 0.000 0.086 0.000 1.000
DIET_COM 0.000 0.060 0.000 1.000
CROP_INDI 0.023 0.034 0.665 0.506
DIET_IND 0.031 0.033 0.938 0.348

Residual Variances
CROP_COM 0.282 0.059 4.806 0.000
DIET_COM 0.136 0.023 5.869 0.000
CROP_INDI 0.022 0.011 2.007 0.045
DIET_IND 0.004 0.008 0.477 0.634

New/Additional Parameters
SAEFF 0.378 0.126 2.994 0.003
MP 0.016 0.008 2.005 0.045
COM 0.215 0.039 5.444 0.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix 0.948E-08

(ratio of smallest to largest eigenvalue)

Terrence Jorgensen

未読、

2023/11/22 7:22:112023/11/22

To: lavaan

I also have the same problem when running a two-level model using MLR estimator in both lavaan and Mplus.

If you used the default estimators, they are not the same. Mplus uses an accelerated EM algorithm to obtain ML estimates, whereas lavaan uses a quasi-Newton algorithm. Some technical details are provided here:

https://doi.org/10.3390/psych3020012

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

http://www.uva.nl/profile/t.d.jorgensen

Lan Nguyen

未読、

2023/11/23 14:12:372023/11/23

To: lavaan

Hi,

I changed the Algorithm to EM in Mplus as suggested by the article, and also ran EM algorithm again with lavaan with MLR estimator to compare. Interestingly, with the EM algorithm, lavaan did not produce Scaled Test Statistics, and a scaling factor for Yuan-Bentler correction. The path coefficients were significantly larger with smaller SE, which leads to insignificance paths estimated by default algorithm becoming significant (!). Also, I received the warning "In lav_partable_check(lavpartable, categorical = lavoptions$.categorical, ... :

lavaan WARNING: automatically added intercepts are set to zero:"

Even though my data contains only continuous variables.

Meanwhile, the Mplus results using EM did not change much to the default. This result is also similar to Bayes estimation in Mplus. I have tried Bayes because I am afraid that I have a small number of groups (38). It seems to me that my model does not have the forced convergence issue due to default Mplus settings for two-level models that the article suggests. Can I say that?

My lavaan code is:

fit <- sem(model=model_1, data=sem_sa, cluster="vilid", estimator="MLR", optim.method = "em", em.iter.max = 20000,
em.fx.tol = 1e-08, em.dx.tol = 1e-04)

Many thanks.

Lan Nguyen.

Terrence Jorgensen

未読、

2023/11/24 4:51:542023/11/24

To: lavaan

lavaan's EM is quite slow (because R is slow). Did you try telling Mplus to use QN instead of EM(A)?

メッセージは削除されました

Lan Nguyen

未読、

2023/11/27 10:05:022023/11/27

To: lavaan

Hi,

I changed the algorithm in Mplus into QN, and I found the same results as using EM or EMA. Interestingly, the Chi-square test in lavaan is always 0, regardless of how I modify the model. It seems like a noise because the residuals matrices did not contain just 0 0. Does it signal some rechecks on multi-level function in lavaan?

> summary(fit.robust2.test) lavaan 0.6.17.1955 ended normally after 62 iterations Estimator ML Optimization method NLMINB Number of model parameters 34 Used Total Number of observations 899 906 Number of clusters [vilid] 29 Model Test User Model: Test statistic 0.000 Degrees of freedom 12 P-value (Chi-square) 1.000 Parameter Estimates: Standard errors Standard Information Observed Observed information based on Hessian

> residuals(fit.robust2.test) $within $within$type [1] "raw" $within$cov dit_nd crop_i mkti inci veg_nc ploti ma_fi diet_ind -0.003 crop_i -0.003 -0.003 mkti -0.007 -0.016 0.000 inci -0.133 -0.094 0.001 0.000 veg_inc -0.007 -0.043 0.000 0.000 0.000 ploti 0.219 0.236 0.004 0.000 0.028 0.000 ma_fi -0.117 -0.125 -0.002 -0.013 0.010 0.000 0.000 $within$mean diet_ind crop_i mkti inci veg_inc ploti ma_fi -0.005 -0.002 0.000 0.000 0.000 0.000 0.000 $vilid $vilid$type [1] "raw" $vilid$cov crop_i dit_nd crp_cm dit_cm sa crop_i 0.001 diet_ind 0.007 0.010 crop_com -0.003 -0.002 0.000 diet_com 0.012 0.008 0.000 0.000 sa 0.040 0.041 0.000 0.000 0.000 $vilid$mean crop_i diet_ind crop_com diet_com sa 0.002 0.006 0.000 0.000 0.000

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