Lavaan Warning during CFA Analysis with Ordinal Data (vcov does not appear to be positive definite)

Erdem Uygun

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Jan 2, 2021, 4:28:26 PM1/2/21

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Hi to all,

In AMOS, I performed a CFA with poor fit on 5-point-Likert Scale data(From Strongly Disagree to Strongly Agree). In fact, results are mostly accumulated on Agree (4) and Strongly Agree (5) options giving skewness and kurtosis to data. I performed CFA with lavaan by putting "ordered" command to treat answers as ordinal and performed calculations with automatically selected WLSMV estimator.

Results enhanced significantly except the warning below:

Warning message:
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
    (= -4.193201e-18) is smaller than zero. This may be a symptom that
    the model is not identified.

What does that mean? Should I ignore the warning and report what I have found or should I do something else to eliminate it? I put the whole lavaan results below. I spent hours on that issue but could not find any practical steps to be taken so far. Thank you in advance I really appreciate your help.

Lavaan Result

model<-'

+ IGA=~Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8
+ KATW=~Q9+Q10+Q11+Q12
+ KATC=~Q13+Q14+Q15+Q16+Q17+Q18+Q19+Q20+Q21+Q22+Q23
+ IM=~Q24+Q25+Q26+Q27+Q28+Q29+Q30+Q31
+ IS=~Q32+Q33+Q34+Q35+Q36'
>
> fit<-cfa(model,data=CFA_full,ordered=c("Q1","Q2","Q3","Q4","Q5","Q6","Q7","Q8","Q9","Q10","Q11","Q12","Q13","Q14","Q15","Q16","Q17","Q18","Q19","Q20","Q21","Q22","Q23","Q24","Q25","Q26","Q27","Q28","Q29","Q30","Q31","Q32","Q33","Q34","Q35","Q36"))
Warning message:
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
    (= -4.193201e-18) is smaller than zero. This may be a symptom that
    the model is not identified.
>
> summary(fit,fit.measures=TRUE,standardized = TRUE)
lavaan 0.6-7 ended normally after 125 iterations

Estimator                                       DWLS
Optimization method                           NLMINB
Number of free parameters                        189

Number of observations                          1165

Model Test User Model:
                                              Standard      Robust
Test Statistic                              3339.255    4326.233
Degrees of freedom                               584         584
P-value (Chi-square)                           0.000       0.000
Scaling correction factor                                  0.836
Shift parameter                                          332.453
       simple second-order correction

Model Test Baseline Model:

Test statistic                            971449.445 110645.100
Degrees of freedom                               630         630
P-value                                        0.000       0.000
Scaling correction factor                                  8.824

User Model versus Baseline Model:

Comparative Fit Index (CFI)                    0.997       0.966
Tucker-Lewis Index (TLI)                       0.997       0.963

Robust Comparative Fit Index (CFI)                            NA
Robust Tucker-Lewis Index (TLI)                               NA

Root Mean Square Error of Approximation:

RMSEA                                          0.064       0.074
90 Percent confidence interval - lower         0.062       0.072
90 Percent confidence interval - upper         0.066       0.076
P-value RMSEA <= 0.05                          0.000       0.000

Robust RMSEA                                                  NA
90 Percent confidence interval - lower                        NA
90 Percent confidence interval - upper                        NA

Standardized Root Mean Square Residual:

SRMR                                           0.044       0.044

Parameter Estimates:

Standard errors                           Robust.sem
Information                                 Expected
Information saturated (h1) model        Unstructured

Latent Variables:
                   Estimate Std.Err z-value P(>|z|)   Std.lv Std.all
IGA =~
    Q1                1.000                               0.677    0.677
    Q2                1.082    0.035   31.114    0.000    0.733    0.733
    Q3                1.194    0.036   33.603    0.000    0.809    0.809
    Q4                0.980    0.036   27.119    0.000    0.664    0.664
    Q5                1.180    0.035   33.485    0.000    0.799    0.799
    Q6                1.340    0.040   33.683    0.000    0.908    0.908
    Q7                1.277    0.041   31.423    0.000    0.865    0.865
    Q8                1.189    0.037   32.327    0.000    0.805    0.805
KATW =~
    Q9                1.000                               0.875    0.875
    Q10               0.797    0.027   29.347    0.000    0.698    0.698
    Q11               1.030    0.026   40.159    0.000    0.901    0.901
    Q12               0.772    0.030   25.445    0.000    0.676    0.676
KATC =~
    Q13               1.000                               0.791    0.791
    Q14               1.184    0.018   64.011    0.000    0.937    0.937
    Q15               1.168    0.018   65.770    0.000    0.924    0.924
    Q16               1.212    0.020   60.515    0.000    0.959    0.959
    Q17               1.220    0.020   60.296    0.000    0.965    0.965
    Q18               1.128    0.017   65.376    0.000    0.892    0.892
    Q19               1.172    0.018   64.040    0.000    0.928    0.928
    Q20               1.215    0.021   58.712    0.000    0.962    0.962
    Q21               1.226    0.020   59.882    0.000    0.970    0.970
    Q22               1.102    0.019   59.138    0.000    0.872    0.872
    Q23               1.160    0.019   62.383    0.000    0.918    0.918
IM =~
    Q24               1.000                               0.880    0.880
    Q25               0.933    0.011   81.340    0.000    0.821    0.821
    Q26               1.042    0.010 100.520    0.000    0.916    0.916
    Q27               1.044    0.010 103.791    0.000    0.919    0.919
    Q28               1.067    0.011 100.736    0.000    0.938    0.938
    Q29               0.993    0.013   78.005    0.000    0.873    0.873
    Q30               1.070    0.011   96.475    0.000    0.942    0.942
    Q31               0.931    0.014   65.183    0.000    0.819    0.819
IS =~
    Q32               1.000                               0.871    0.871
    Q33               1.032    0.013   79.794    0.000    0.899    0.899
    Q34               1.072    0.014   76.660    0.000    0.933    0.933
    Q35               1.077    0.014   74.990    0.000    0.938    0.938
    Q36               1.082    0.017   63.681    0.000    0.942    0.942

Covariances:
                   Estimate Std.Err z-value P(>|z|)   Std.lv Std.all
IGA ~~
    KATW              0.405    0.020   19.854    0.000    0.683    0.683
    KATC              0.452    0.020   22.629    0.000    0.844    0.844
    IM                0.524    0.021   25.216    0.000    0.879    0.879
    IS                0.443    0.020   22.412    0.000    0.751    0.751
KATW ~~
    KATC              0.498    0.020   25.141    0.000    0.720    0.720
    IM                0.499    0.020   24.522    0.000    0.647    0.647
    IS                0.541    0.019   28.412    0.000    0.711    0.711
KATC ~~
    IM                0.606    0.018   34.258    0.000    0.871    0.871
    IS                0.509    0.019   26.659    0.000    0.738    0.738
IM ~~
    IS                0.613    0.018   34.553    0.000    0.801    0.801

Intercepts:
                   Estimate Std.Err z-value P(>|z|)   Std.lv Std.all
   .Q1                0.000                               0.000    0.000
   .Q2                0.000                               0.000    0.000
   .Q3                0.000                               0.000    0.000
   .Q4                0.000                               0.000    0.000
   .Q5                0.000                               0.000    0.000
   .Q6                0.000                               0.000    0.000
   .Q7                0.000                               0.000    0.000
   .Q8                0.000                               0.000    0.000
   .Q9                0.000                               0.000    0.000
   .Q10               0.000                               0.000    0.000
   .Q11               0.000                               0.000    0.000
   .Q12               0.000                               0.000    0.000
   .Q13               0.000                               0.000    0.000
   .Q14               0.000                               0.000    0.000
   .Q15               0.000                               0.000    0.000
   .Q16               0.000                               0.000    0.000
   .Q17               0.000                               0.000    0.000
   .Q18               0.000                               0.000    0.000
   .Q19               0.000                               0.000    0.000
   .Q20               0.000                               0.000    0.000
   .Q21               0.000                               0.000    0.000
   .Q22               0.000                               0.000    0.000
   .Q23               0.000                               0.000    0.000
   .Q24               0.000                               0.000    0.000
   .Q25               0.000                               0.000    0.000
   .Q26               0.000                               0.000    0.000
   .Q27               0.000                               0.000    0.000
   .Q28               0.000                               0.000    0.000
   .Q29               0.000                               0.000    0.000
   .Q30               0.000                               0.000    0.000
   .Q31               0.000                               0.000    0.000
   .Q32               0.000                               0.000    0.000
   .Q33               0.000                               0.000    0.000
   .Q34               0.000                               0.000    0.000
   .Q35               0.000                               0.000    0.000
   .Q36               0.000                               0.000    0.000
    IGA               0.000                               0.000    0.000
    KATW              0.000                               0.000    0.000
    KATC              0.000                               0.000    0.000
    IM                0.000                               0.000    0.000
    IS                0.000                               0.000    0.000

Thresholds:
                   Estimate Std.Err z-value P(>|z|)   Std.lv Std.all
    Q1|t1            -2.096    0.088 -23.827    0.000   -2.096   -2.096
    Q1|t2            -1.906    0.075 -25.428    0.000   -1.906   -1.906
    Q1|t3            -1.526    0.057 -26.584    0.000   -1.526   -1.526
    Q1|t4            -0.122    0.037   -3.308    0.001   -0.122   -0.122
    Q2|t1            -2.285    0.105 -21.762    0.000   -2.285   -2.285
    Q2|t2            -2.059    0.085 -24.183    0.000   -2.059   -2.059
    Q2|t3            -1.561    0.059 -26.610    0.000   -1.561   -1.561
    Q2|t4            -0.303    0.037   -8.100    0.000   -0.303   -0.303
    Q3|t1            -2.285    0.105 -21.762    0.000   -2.285   -2.285
    Q3|t2            -2.116    0.090 -23.630    0.000   -2.116   -2.116
    Q3|t3            -1.777    0.068 -26.156    0.000   -1.777   -1.777
    Q3|t4            -0.168    0.037   -4.537    0.000   -0.168   -0.168
    Q4|t1            -2.116    0.090 -23.630    0.000   -2.116   -2.116
    Q4|t2            -1.699    0.064 -26.437    0.000   -1.699   -1.699
    Q4|t3            -1.145    0.047 -24.369    0.000   -1.145   -1.145
    Q4|t4             0.170    0.037    4.596    0.000    0.170    0.170
    Q5|t1            -2.422    0.121 -20.058    0.000   -2.422   -2.422
    Q5|t2            -1.880    0.073 -25.599    0.000   -1.880   -1.880
    Q5|t3            -1.467    0.055 -26.474    0.000   -1.467   -1.467
    Q5|t4             0.168    0.037    4.537    0.000    0.168    0.168
    Q6|t1            -2.383    0.116 -20.552    0.000   -2.383   -2.383
    Q6|t2            -2.077    0.087 -24.011    0.000   -2.077   -2.077
    Q6|t3            -1.718    0.065 -26.382    0.000   -1.718   -1.718
    Q6|t4            -0.154    0.037   -4.186    0.000   -0.154   -0.154
    Q7|t1            -2.230    0.100 -22.403    0.000   -2.230   -2.230
    Q7|t2            -2.077    0.087 -24.011    0.000   -2.077   -2.077
    Q7|t3            -1.673    0.063 -26.504    0.000   -1.673   -1.673
    Q7|t4            -0.355    0.038   -9.439    0.000   -0.355   -0.355
    Q8|t1            -2.348    0.112 -20.995    0.000   -2.348   -2.348
    Q8|t2            -2.008    0.081 -24.639    0.000   -2.008   -2.008
    Q8|t3            -1.351    0.052 -26.011    0.000   -1.351   -1.351
    Q8|t4             0.044    0.037    1.201    0.230    0.044    0.044
    Q9|t1            -2.383    0.116 -20.552    0.000   -2.383   -2.383
    Q9|t2            -1.673    0.063 -26.504    0.000   -1.673   -1.673
    Q9|t3            -1.003    0.044 -22.637    0.000   -1.003   -1.003
    Q9|t4             0.467    0.038   12.221    0.000    0.467    0.467
    Q10|t1           -2.137    0.091 -23.419    0.000   -2.137   -2.137
    Q10|t2           -1.065    0.045 -23.460    0.000   -1.065   -1.065
    Q10|t3           -0.079    0.037   -2.138    0.033   -0.079   -0.079
    Q10|t4            1.108    0.046   23.969    0.000    1.108    1.108
    Q11|t1           -2.383    0.116 -20.552    0.000   -2.383   -2.383
    Q11|t2           -1.809    0.070 -26.004    0.000   -1.809   -1.809
    Q11|t3           -1.187    0.048 -24.794    0.000   -1.187   -1.187
    Q11|t4            0.513    0.039   13.316    0.000    0.513    0.513
    Q12|t1           -1.788    0.068 -26.109    0.000   -1.788   -1.788
    Q12|t2           -0.725    0.040 -17.908    0.000   -0.725   -0.725
    Q12|t3           -0.027    0.037   -0.732    0.464   -0.027   -0.027
    Q12|t4            0.941    0.043   21.728    0.000    0.941    0.941
    Q13|t1           -2.383    0.116 -20.552    0.000   -2.383   -2.383
    Q13|t2           -1.821    0.070 -25.946    0.000   -1.821   -1.821
    Q13|t3           -1.218    0.049 -25.076    0.000   -1.218   -1.218
    Q13|t4            0.504    0.038   13.086    0.000    0.504    0.504
    Q14|t1           -2.315    0.108 -21.396    0.000   -2.315   -2.315
    Q14|t2           -2.116    0.090 -23.630    0.000   -2.116   -2.116
    Q14|t3           -1.880    0.073 -25.599    0.000   -1.880   -1.880
    Q14|t4           -0.122    0.037   -3.308    0.001   -0.122   -0.122
    Q15|t1           -2.315    0.108 -21.396    0.000   -2.315   -2.315
    Q15|t2           -1.992    0.080 -24.773    0.000   -1.992   -1.992
    Q15|t3           -1.737    0.066 -26.317    0.000   -1.737   -1.737
    Q15|t4           -0.137    0.037   -3.718    0.000   -0.137   -0.137
    Q16|t1           -2.257    0.102 -22.096    0.000   -2.257   -2.257
    Q16|t2           -2.008    0.081 -24.639    0.000   -2.008   -2.008
    Q16|t3           -1.690    0.064 -26.461    0.000   -1.690   -1.690
    Q16|t4           -0.233    0.037   -6.291    0.000   -0.233   -0.233
    Q17|t1           -2.285    0.105 -21.762    0.000   -2.285   -2.285
    Q17|t2           -1.962    0.078 -25.018    0.000   -1.962   -1.962
    Q17|t3           -1.655    0.062 -26.538    0.000   -1.655   -1.655
    Q17|t4           -0.181    0.037   -4.888    0.000   -0.181   -0.181
    Q18|t1           -2.285    0.105 -21.762    0.000   -2.285   -2.285
    Q18|t2           -2.008    0.081 -24.639    0.000   -2.008   -2.008
    Q18|t3           -1.655    0.062 -26.538    0.000   -1.655   -1.655
    Q18|t4            0.038    0.037    1.025    0.305    0.038    0.038
    Q19|t1           -2.205    0.097 -22.687    0.000   -2.205   -2.205
    Q19|t2           -2.041    0.084 -24.345    0.000   -2.041   -2.041
    Q19|t3           -1.777    0.068 -26.156    0.000   -1.777   -1.777
    Q19|t4           -0.343    0.038   -9.148    0.000   -0.343   -0.343
    Q20|t1           -2.257    0.102 -22.096    0.000   -2.257   -2.257
    Q20|t2           -2.041    0.084 -24.345    0.000   -2.041   -2.041
    Q20|t3           -1.856    0.072 -25.750    0.000   -1.856   -1.856
    Q20|t4           -0.178    0.037   -4.830    0.000   -0.178   -0.178
    Q21|t1           -2.285    0.105 -21.762    0.000   -2.285   -2.285
    Q21|t2           -2.008    0.081 -24.639    0.000   -2.008   -2.008
    Q21|t3           -0.203    0.037   -5.473    0.000   -0.203   -0.203
    Q22|t1           -2.230    0.100 -22.403    0.000   -2.230   -2.230
    Q22|t2           -2.096    0.088 -23.827    0.000   -2.096   -2.096
    Q22|t3           -1.767    0.067 -26.201    0.000   -1.767   -1.767
    Q22|t4           -0.305    0.037   -8.158    0.000   -0.305   -0.305
    Q23|t1           -2.315    0.108 -21.396    0.000   -2.315   -2.315
    Q23|t2           -2.158    0.093 -23.193    0.000   -2.158   -2.158
    Q23|t3           -1.821    0.070 -25.946    0.000   -1.821   -1.821
    Q23|t4           -0.135    0.037   -3.660    0.000   -0.135   -0.135
    Q24|t1           -2.383    0.116 -20.552    0.000   -2.383   -2.383
    Q24|t2           -1.947    0.077 -25.130    0.000   -1.947   -1.947
    Q24|t3           -1.607    0.060 -26.601    0.000   -1.607   -1.607
    Q24|t4            0.057    0.037    1.552    0.121    0.057    0.057
    Q25|t1           -2.422    0.121 -20.058    0.000   -2.422   -2.422
    Q25|t2           -1.832    0.071 -25.885    0.000   -1.832   -1.832
    Q25|t3           -1.178    0.048 -24.711    0.000   -1.178   -1.178
    Q25|t4            0.294    0.037    7.867    0.000    0.294    0.294
    Q26|t1           -2.422    0.121 -20.058    0.000   -2.422   -2.422
    Q26|t2           -2.041    0.084 -24.345    0.000   -2.041   -2.041
    Q26|t3           -1.329    0.051 -25.891    0.000   -1.329   -1.329
    Q26|t4            0.042    0.037    1.142    0.253    0.042    0.042
    Q27|t1           -2.512    0.133 -18.877    0.000   -2.512   -2.512
    Q27|t2           -2.096    0.088 -23.827    0.000   -2.096   -2.096
    Q27|t3           -1.533    0.058 -26.591    0.000   -1.533   -1.533
    Q27|t4            0.061    0.037    1.669    0.095    0.061    0.061
    Q28|t1           -2.348    0.112 -20.995    0.000   -2.348   -2.348
    Q28|t2           -2.181    0.095 -22.949    0.000   -2.181   -2.181
    Q28|t3           -1.777    0.068 -26.156    0.000   -1.777   -1.777
    Q28|t4           -0.222    0.037   -5.999    0.000   -0.222   -0.222
    Q29|t1           -2.348    0.112 -20.995    0.000   -2.348   -2.348
    Q29|t2           -2.230    0.100 -22.403    0.000   -2.230   -2.230
    Q29|t3           -1.737    0.066 -26.317    0.000   -1.737   -1.737
    Q29|t4           -0.422    0.038 -11.122    0.000   -0.422   -0.422
    Q30|t1           -2.348    0.112 -20.995    0.000   -2.348   -2.348
    Q30|t2           -2.116    0.090 -23.630    0.000   -2.116   -2.116
    Q30|t3           -1.767    0.067 -26.201    0.000   -1.767   -1.767
    Q30|t4           -0.341    0.038   -9.090    0.000   -0.341   -0.341
    Q31|t1           -2.315    0.108 -21.396    0.000   -2.315   -2.315
    Q31|t2           -2.137    0.091 -23.419    0.000   -2.137   -2.137
    Q31|t3           -1.540    0.058 -26.598    0.000   -1.540   -1.540
    Q31|t4           -0.170    0.037   -4.596    0.000   -0.170   -0.170
    Q32|t1           -2.348    0.112 -20.995    0.000   -2.348   -2.348
    Q32|t2           -1.933    0.077 -25.235    0.000   -1.933   -1.933
    Q32|t3           -1.157    0.047 -24.499    0.000   -1.157   -1.157
    Q32|t4            0.343    0.038    9.148    0.000    0.343    0.343
    Q33|t1           -2.512    0.133 -18.877    0.000   -2.512   -2.512
    Q33|t2           -1.767    0.067 -26.201    0.000   -1.767   -1.767
    Q33|t3           -1.032    0.045 -23.029    0.000   -1.032   -1.032
    Q33|t4            0.382    0.038   10.136    0.000    0.382    0.382
    Q34|t1           -2.512    0.133 -18.877    0.000   -2.512   -2.512
    Q34|t2           -1.798    0.069 -26.058    0.000   -1.798   -1.798
    Q34|t3           -0.968    0.044 -22.136    0.000   -0.968   -0.968
    Q34|t4            0.543    0.039   14.005    0.000    0.543    0.543
    Q35|t1           -2.703    0.166 -16.288    0.000   -2.703   -2.703
    Q35|t2           -1.906    0.075 -25.428    0.000   -1.906   -1.906
    Q35|t3           -1.120    0.046 -24.104    0.000   -1.120   -1.120
    Q35|t4            0.446    0.038   11.701    0.000    0.446    0.446
    Q36|t1           -2.464    0.126 -19.505    0.000   -2.464   -2.464
    Q36|t2           -1.933    0.077 -25.235    0.000   -1.933   -1.933
    Q36|t3           -1.335    0.051 -25.922    0.000   -1.335   -1.335
[ reached getOption("max.print") -- omitted 1 row ]

Variances:
                   Estimate Std.Err z-value P(>|z|)   Std.lv Std.all
   .Q1                0.541                               0.541    0.541
   .Q2                0.463                               0.463    0.463
   .Q3                0.346                               0.346    0.346
   .Q4                0.559                               0.559    0.559
   .Q5                0.362                               0.362    0.362
   .Q6                0.176                               0.176    0.176
   .Q7                0.252                               0.252    0.252
   .Q8                0.351                               0.351    0.351
   .Q9                0.234                               0.234    0.234
   .Q10               0.513                               0.513    0.513
   .Q11               0.187                               0.187    0.187
   .Q12               0.543                               0.543    0.543
   .Q13               0.374                               0.374    0.374
   .Q14               0.122                               0.122    0.122
   .Q15               0.146                               0.146    0.146
   .Q16               0.080                               0.080    0.080
   .Q17               0.069                               0.069    0.069
   .Q18               0.204                               0.204    0.204
   .Q19               0.139                               0.139    0.139
   .Q20               0.075                               0.075    0.075
   .Q21               0.060                               0.060    0.060
   .Q22               0.239                               0.239    0.239
   .Q23               0.158                               0.158    0.158
   .Q24               0.226                               0.226    0.226
   .Q25               0.326                               0.326    0.326
   .Q26               0.160                               0.160    0.160
   .Q27               0.156                               0.156    0.156
   .Q28               0.120                               0.120    0.120
   .Q29               0.237                               0.237    0.237
   .Q30               0.113                               0.113    0.113
   .Q31               0.330                               0.330    0.330
   .Q32               0.242                               0.242    0.242
   .Q33               0.192                               0.192    0.192
   .Q34               0.129                               0.129    0.129
   .Q35               0.121                               0.121    0.121
   .Q36               0.112                               0.112    0.112
    IGA               0.459    0.028   16.667    0.000    1.000    1.000
    KATW              0.766    0.026   29.218    0.000    1.000    1.000
    KATC              0.626    0.022   28.562    0.000    1.000    1.000
    IM                0.774    0.016   48.975    0.000    1.000    1.000
    IS                0.758    0.019   40.180    0.000    1.000    1.000

Scales y*:
                   Estimate Std.Err z-value P(>|z|)   Std.lv Std.all
    Q1                1.000                               1.000    1.000
    Q2                1.000                               1.000    1.000
    Q3                1.000                               1.000    1.000
    Q4                1.000                               1.000    1.000
    Q5                1.000                               1.000    1.000
    Q6                1.000                               1.000    1.000
    Q7                1.000                               1.000    1.000
    Q8                1.000                               1.000    1.000
    Q9                1.000                               1.000    1.000
    Q10               1.000                               1.000    1.000
    Q11               1.000                               1.000    1.000
    Q12               1.000                               1.000    1.000
    Q13               1.000                               1.000    1.000
    Q14               1.000                               1.000    1.000
    Q15               1.000                               1.000    1.000
    Q16               1.000                               1.000    1.000
    Q17               1.000                               1.000    1.000
    Q18               1.000                               1.000    1.000
    Q19               1.000                               1.000    1.000
    Q20               1.000                               1.000    1.000
    Q21               1.000                               1.000    1.000
    Q22               1.000                               1.000    1.000
    Q23               1.000                               1.000    1.000
    Q24               1.000                               1.000    1.000
    Q25               1.000                               1.000    1.000
    Q26               1.000                               1.000    1.000
    Q27               1.000                               1.000    1.000
    Q28               1.000                               1.000    1.000
    Q29               1.000                               1.000    1.000
    Q30               1.000                               1.000    1.000
    Q31               1.000                               1.000    1.000
    Q32               1.000                               1.000    1.000
    Q33               1.000                               1.000    1.000
    Q34               1.000                               1.000    1.000
    Q35               1.000                               1.000    1.000
    Q36               1.000                               1.000    1.000

Patrick (Malone Quantitative)

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Jan 2, 2021, 5:08:00 PM1/2/21

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Erdem,

Nothing jumps out at me. I suspect it reflects the fact that some of your factors are so highly correlated.

Pat

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Erdem Uygun

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Jan 3, 2021, 7:48:07 AM1/3/21

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Hi Patrick and thank you for your valuable response.

When I inspect correlations among factors, I get the results below:

> lavInspect(fit,"cor.lv")
IGA KATW KATC IM IS
IGA 1.000
KATW 0.683 1.000
KATC 0.844 0.720 1.000
IM 0.879 0.647 0.871 1.000
IS 0.751 0.711 0.738 0.801 1.000

Factors are indeed highly correlated. I repeated the test with one-factor solution but I am still getting the same warning. By the way, when I use any ML estimator (ML, MLM, MLR), there is no warning but with low global fit indices scores most probably because my data is significantly not normal:

> model<-'
+ GC=~Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9+Q10+Q11+Q12+Q13+Q14+Q15+Q16+Q17+Q18+Q19+Q20+Q21+Q22+Q23+Q24+Q25+Q26+Q27+Q28+Q29+Q30+Q31+Q32+Q33+Q34+Q35+Q36
+ '

>
> fit<-cfa(model,data=CFA_full,ordered=c("Q1","Q2","Q3","Q4","Q5","Q6","Q7","Q8","Q9","Q10","Q11","Q12","Q13","Q14","Q15","Q16","Q17","Q18","Q19","Q20","Q21","Q22","Q23","Q24","Q25","Q26","Q27","Q28","Q29","Q30","Q31","Q32","Q33","Q34","Q35","Q36"))
Warning message:
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

(= -3.130112e-19) is smaller than zero. This may be a symptom that

the model is not identified.

>
> summary(fit,fit.measures=TRUE,standardized = TRUE)
lavaan 0.6-7 ended normally after 85 iterations

Estimator DWLS
Optimization method NLMINB

Number of free parameters 179

Number of observations 1165

Model Test User Model:
Standard Robust

Test Statistic 12039.349 9221.853
Degrees of freedom 594 594
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.366
Shift parameter 409.172

simple second-order correction

Model Test Baseline Model:

Test statistic 971449.445 110645.100
Degrees of freedom 630 630
P-value 0.000 0.000
Scaling correction factor 8.824

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.988 0.922
Tucker-Lewis Index (TLI) 0.987 0.917

Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA

Root Mean Square Error of Approximation:

RMSEA 0.129 0.112
90 Percent confidence interval - lower 0.127 0.110
90 Percent confidence interval - upper 0.131 0.114

P-value RMSEA <= 0.05 0.000 0.000

Robust RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA

Standardized Root Mean Square Residual:

SRMR 0.082 0.082

Parameter Estimates:

Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured

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

GC =~
Q1 1.000 0.618 0.618
Q2 1.084 0.035 30.806 0.000 0.670 0.670
Q3 1.194 0.036 33.335 0.000 0.738 0.738
Q4 0.981 0.037 26.723 0.000 0.606 0.606
Q5 1.187 0.036 33.116 0.000 0.734 0.734
Q6 1.343 0.040 33.367 0.000 0.831 0.831
Q7 1.281 0.041 31.076 0.000 0.792 0.792
Q8 1.191 0.037 31.917 0.000 0.736 0.736
Q9 1.099 0.037 30.047 0.000 0.679 0.679
Q10 0.884 0.042 20.969 0.000 0.547 0.547
Q11 1.124 0.038 29.694 0.000 0.695 0.695
Q12 0.850 0.044 19.261 0.000 0.526 0.526
Q13 1.214 0.040 30.286 0.000 0.751 0.751
Q14 1.482 0.046 32.151 0.000 0.916 0.916
Q15 1.465 0.045 32.317 0.000 0.906 0.906
Q16 1.530 0.048 31.915 0.000 0.946 0.946
Q17 1.539 0.049 31.565 0.000 0.951 0.951
Q18 1.401 0.043 32.562 0.000 0.866 0.866
Q19 1.457 0.045 32.356 0.000 0.901 0.901
Q20 1.529 0.048 31.842 0.000 0.945 0.945
Q21 1.548 0.049 31.633 0.000 0.957 0.957
Q22 1.363 0.042 32.086 0.000 0.843 0.843
Q23 1.442 0.045 32.177 0.000 0.892 0.892
Q24 1.349 0.041 32.889 0.000 0.834 0.834
Q25 1.256 0.041 30.745 0.000 0.777 0.777
Q26 1.422 0.044 32.085 0.000 0.879 0.879
Q27 1.424 0.044 32.559 0.000 0.881 0.881
Q28 1.459 0.046 31.564 0.000 0.902 0.902
Q29 1.344 0.042 32.013 0.000 0.831 0.831
Q30 1.465 0.046 31.837 0.000 0.906 0.906
Q31 1.250 0.040 31.128 0.000 0.773 0.773
Q32 1.242 0.039 32.003 0.000 0.768 0.768
Q33 1.328 0.042 31.286 0.000 0.821 0.821
Q34 1.429 0.045 31.422 0.000 0.883 0.883
Q35 1.436 0.046 31.200 0.000 0.888 0.888
Q36 1.386 0.045 30.903 0.000 0.857 0.857

GC 0.000 0.000 0.000

.Q1 0.618 0.618 0.618
.Q2 0.551 0.551 0.551
.Q3 0.455 0.455 0.455
.Q4 0.632 0.632 0.632
.Q5 0.461 0.461 0.461
.Q6 0.310 0.310 0.310
.Q7 0.373 0.373 0.373
.Q8 0.458 0.458 0.458
.Q9 0.538 0.538 0.538
.Q10 0.701 0.701 0.701
.Q11 0.517 0.517 0.517
.Q12 0.724 0.724 0.724
.Q13 0.436 0.436 0.436
.Q14 0.160 0.160 0.160
.Q15 0.179 0.179 0.179
.Q16 0.105 0.105 0.105
.Q17 0.095 0.095 0.095
.Q18 0.250 0.250 0.250
.Q19 0.189 0.189 0.189
.Q20 0.107 0.107 0.107
.Q21 0.084 0.084 0.084
.Q22 0.290 0.290 0.290
.Q23 0.205 0.205 0.205
.Q24 0.304 0.304 0.304
.Q25 0.397 0.397 0.397
.Q26 0.227 0.227 0.227
.Q27 0.225 0.225 0.225
.Q28 0.186 0.186 0.186
.Q29 0.309 0.309 0.309
.Q30 0.180 0.180 0.180
.Q31 0.403 0.403 0.403
.Q32 0.410 0.410 0.410
.Q33 0.326 0.326 0.326
.Q34 0.220 0.220 0.220
.Q35 0.212 0.212 0.212
.Q36 0.265 0.265 0.265
GC 0.382 0.025 15.351 0.000 1.000 1.000

Do you have any idea why this occurs and what to do in such situations? Thank you very much.

Erdem UYGUN, Phd Student

Department of Educational Sciences/Curriculum and Instruction

Patrick (Malone Quantitative) <mal...@malonequantitative.com>, 3 Oca 2021 Paz, 01:08 tarihinde şunu yazdı:

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Patrick (Malone Quantitative)

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Jan 3, 2021, 8:15:26 AM1/3/21

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Weird. I have no idea why a one-factor model--where the variance is well significant--would give you that warning. I'll punt to others.

Pat

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Erdem Uygun

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Jan 3, 2021, 8:20:14 AM1/3/21

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I really appreciate it because I spent days and hours on that issue. I'm looking forward to seeing others' responses. Thank you.

Erdem UYGUN, Phd Student

Department of Educational Sciences/Curriculum and Instruction

Patrick (Malone Quantitative) <mal...@malonequantitative.com>, 3 Oca 2021 Paz, 16:15 tarihinde şunu yazdı:

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Edward Rigdon

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Jan 3, 2021, 10:50:19 AM1/3/21

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With ordinal variables, the set of parameters includes thresholds related parameters. With skewed data, there may be high uncertainty about these additional parameters, perhaps making identification marginal. You might try simulating a much larger dataset to see if sample size might be the problem.

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/CAJc%3DyOHYq-c9PRCicge7ZW-ZQjrHS8iqE%2BJWTn1ZkbnJuAx3Nw%40mail.gmail.com.

Juan Diego Hernández Lalinde

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Jan 3, 2021, 11:14:18 AM1/3/21

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Hello guys,

I have a question (it could be a suggestion) regarding this problem. Due to the eigenvalue is quite small, perhaps you could try by using different starting values and compare the results. If the chi-square statistic and fit indices are the same (or very similar), you could ignore this warning message.

What do you think about this? Again, I'm not sure if this is a good practice, but I have read this recommendation in several forums and it sounds logical to me.

Good luck.

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Erdem Uygun

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Jan 3, 2021, 1:21:23 PM1/3/21

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Hi all, I want to share a finding of mine with you. When I specifically write estimator = “DWSL”, I receive no warning with better results. So additionally I want to ask that what is the difference between “DWSL” and “WLSMV” estimators? I see in books referring WLSMV mostly.

At lavaan website it says:

In both cases, lavaan will automatically switch to the WLSMV estimator: it will use diagonally weighted least squares (DWLS) to estimate the model parameters, but it will use the full weight matrix to compute robust standard errors, and a mean- and variance-adjusted test stastistic.

I understand that lavaan actually uses DWSL when we put “ordered” command. Is it because there is a lavaan-related problem that generates previous warning with WLSMV that does not exist when specifically writing DWSL as the estimator for bypassing default WLSMV option, or do I miss something else?

Note: My sample size is 1165.

Thank you.

model<-'

+ IGA=~Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8

+ KATW=~Q9+Q10+Q11+Q12

+ KATC=~Q13+Q14+Q15+Q16+Q17+Q18+Q19+Q20+Q21+Q22+Q23

+ IM=~Q24+Q25+Q26+Q27+Q28+Q29+Q30+Q31

+ IS=~Q32+Q33+Q34+Q35+Q36

+ '

>

> fit<-cfa(model,data=CFA_full,estimator = "DWLS", ordered=c("Q1","Q2","Q3","Q4","Q5","Q6","Q7","Q8","Q9","Q10","Q11","Q12","Q13","Q14","Q15","Q16","Q17","Q18","Q19","Q20","Q21","Q22","Q23","Q24","Q25","Q26","Q27","Q28","Q29","Q30","Q31","Q32","Q33","Q34","Q35","Q36"))

>

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

lavaan 0.6-7 ended normally after 125 iterations

Estimator DWLS

Optimization method NLMINB

Number of free parameters 189

Number of observations 1165

Model Test User Model:

Test statistic 3339.255

Degrees of freedom 584

P-value (Chi-square) 0.000

Model Test Baseline Model:

Test statistic 971449.445

Degrees of freedom 630

P-value 0.000

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.997

Tucker-Lewis Index (TLI) 0.997

Root Mean Square Error of Approximation:

RMSEA 0.064

90 Percent confidence interval - lower 0.062

90 Percent confidence interval - upper 0.066

P-value RMSEA <= 0.05 0.000

Standardized Root Mean Square Residual:

SRMR 0.044

Parameter Estimates:

Standard errors Standard

Information Expected

Information saturated (h1) model Unstructured

Latent Variables:

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

IGA =~

Q1 1.000 0.677 0.677

Q2 1.082 0.013 84.772 0.000 0.733 0.733

Q3 1.194 0.013 91.334 0.000 0.809 0.809

Q4 0.980 0.012 81.989 0.000 0.664 0.664

Q5 1.180 0.013 91.794 0.000 0.799 0.799

Q6 1.340 0.014 98.539 0.000 0.908 0.908

Q7 1.277 0.013 95.960 0.000 0.865 0.865

Q8 1.189 0.013 92.767 0.000 0.805 0.805

KATW =~

Q9 1.000 0.875 0.875

Q10 0.797 0.010 78.080 0.000 0.698 0.698

Q11 1.030 0.011 96.872 0.000 0.901 0.901

Q12 0.772 0.010 76.490 0.000 0.676 0.676

KATC =~

Q13 1.000 0.791 0.791

Q14 1.184 0.008 145.214 0.000 0.937 0.937

Q15 1.168 0.008 145.083 0.000 0.924 0.924

Q16 1.212 0.008 150.084 0.000 0.959 0.959

Q17 1.220 0.008 150.581 0.000 0.965 0.965

Q18 1.128 0.008 140.263 0.000 0.892 0.892

Q19 1.172 0.008 144.850 0.000 0.928 0.928

Q20 1.215 0.008 151.737 0.000 0.962 0.962

Q21 1.226 0.008 152.827 0.000 0.970 0.970

Q22 1.102 0.008 135.024 0.000 0.872 0.872

Q23 1.160 0.008 144.441 0.000 0.918 0.918

IM =~

Q24 1.000 0.880 0.880

Q25 0.933 0.007 139.945 0.000 0.821 0.821

Q26 1.042 0.006 160.321 0.000 0.916 0.916

Q27 1.044 0.006 163.322 0.000 0.919 0.919

Q28 1.067 0.006 166.126 0.000 0.938 0.938

Q29 0.993 0.007 147.823 0.000 0.873 0.873

Q30 1.070 0.007 162.402 0.000 0.942 0.942

Q31 0.931 0.007 138.048 0.000 0.819 0.819

IS =~

Q32 1.000 0.871 0.871

Q33 1.032 0.008 132.329 0.000 0.899 0.899

Q34 1.072 0.008 140.234 0.000 0.933 0.933

Q35 1.077 0.008 142.589 0.000 0.938 0.938

Q36 1.082 0.008 140.853 0.000 0.942 0.942

Covariances:

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

IGA ~~

KATW 0.405 0.006 66.042 0.000 0.683 0.683

KATC 0.452 0.005 91.751 0.000 0.844 0.844

IM 0.524 0.006 94.672 0.000 0.879 0.879

IS 0.443 0.005 83.496 0.000 0.751 0.751

KATW ~~

KATC 0.498 0.005 92.114 0.000 0.720 0.720

IM 0.499 0.006 78.905 0.000 0.647 0.647

IS 0.541 0.007 81.675 0.000 0.711 0.711

KATC ~~

IM 0.606 0.005 130.906 0.000 0.871 0.871

IS 0.509 0.004 113.757 0.000 0.738 0.738

IM ~~

IS 0.613 0.005 122.415 0.000 0.801 0.801

IGA 0.459 0.008 55.252 0.000 1.000 1.000

KATW 0.766 0.014 56.289 0.000 1.000 1.000

KATC 0.626 0.007 85.688 0.000 1.000 1.000

IM 0.774 0.007 105.932 0.000 1.000 1.000

IS 0.758 0.009 86.681 0.000 1.000 1.000

Erdem UYGUN, Phd Student

Department of Educational Sciences/Curriculum and Instruction

Juan Diego Hernández Lalinde <hernandez...@gmail.com>, 3 Oca 2021 Paz, 19:14 tarihinde şunu yazdı:

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Terrence Jorgensen

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Jan 5, 2021, 10:39:54 PM1/5/21

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what is the difference between “DWLS” and “WLSMV” estimators?

"WLSMV" is a keyword, not an estimator. As the text states (which you pasted in your last post; see also the ?lavOptions help page), WLSMV implies DWLS. Specifically, when you set (or rely on the default setting when declaring any outcomes as ordered=), estimator = "WLSMV" is a shortcut for the following three arguments:

estimator = "DWLS"
se = "robust.sem"
test = "scaled.shifted"

So if you explicitly only declare (1) without also declaring (2) and (3), that might be the source of your discrepancy. You can always check your model results to verify:

lavInspect(fit, "options")[c("estimator","se","test")]

You need (2) and (3) to obtain robust results; otherwise, you cannot trust your test statistics or CIs to have nominal Type I error rates or CI coverage rates.

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

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