I am attempting to run a CFA in lavaan but the model will not converge unless std.lv = TRUE. This is causing me concern, and I would like some help understanding some possible reasons why the model won't converge.
Here's a bit more details about the data:
- I have run a multivariate normality test and confirmed the data is non-normal, and I did not expect it to be as this is Likert scale data on a 5-point scale. However, each observation is the average score of 9 survey respondents, so I believe this means the data is continuous within lower and upper limits (1 and 5).
- Since it failed the normality test, I am using the
MLMestimator and robust standard errors. - There are 873 observations, 61 variables, and the CFA has 6 factors.
Below shows the R code. I show where the model fails and then I show the statistics with std.lv = TRUE so you can see the full summary of the model. I would appreciate any points on where there might be things I need to look further into or improve to help the model run better.
> model4 <-'
+ engage =~ V1.A.1.a.1 + V1.A.1.a.3 + V1.A.1.a.4 + V2.A.1.b + V2.A.1.d
+ + V2.B.1.a + V2.B.1.c + V2.B.1.d + V2.B.1.f
+ + V1.C.5.c + V2.A.1.c + V1.A.1.a.2 + V2.A.1.a + V2.A.2.b
+ + V1.A.1.e.1 + V1.C.2.b
+ decisive =~ V1.C.1.a + V1.C.1.b + V1.C.1.c + V1.C.2.b
+ + V1.C.6 + V1.C.4.b
+ relate =~ V1.A.1.a.1 + V1.A.1.a.3 + V1.A.1.b.3 + V2.A.1.b + V2.A.1.d
+ + V2.B.1.a + V2.B.1.f + V2.B.1.b
+ + V1.C.3.a + V1.C.3.b + V1.C.3.c + V1.C.4.a + V1.C.4.b + V1.C.4.c
+ + V1.C.5.a + V1.C.5.c + V1.A.1.g.2 + V1.C.2.b
+ manage =~ V2.A.2.c + V2.A.2.d + V2.B.1.a + V2.B.1.b + V2.B.1.c + V2.B.1.d
+ + V2.B.1.e + V2.B.4.e + V2.B.4.g + V2.B.4.h + V2.B.5.a + V2.B.5.b
+ + V2.B.5.c + V2.B.5.d + V2.C.1.a
+ + V1.C.2.b
+ insight =~ V1.A.1.b.1 + V1.A.1.b.2 + V2.B.3.a + V2.B.3.b
+ + V1.C.7.a + V1.C.4.c
+ intuition =~ V1.A.1.b.3 + V1.A.1.e.1 + V1.A.1.e.2
+ + V1.A.1.e.3 + V1.A.1.f.2 + V1.A.1.g.1 + V1.A.1.g.2 + V2.A.2.d
+ analysis =~ V1.A.1.a.1 + V1.A.1.a.2 + V1.A.1.a.4 + V1.A.1.b.3
+ + V1.A.1.b.4 + V1.A.1.b.5 + V1.A.1.b.6 + V1.A.1.b.7 + V1.A.1.c.1
+ + V1.A.1.c.2 + V1.A.1.d.1 + V2.A.1.a + V2.A.1.c + V2.A.1.e
+ + V2.A.2.a + V2.A.2.b + V2.A.2.c + V2.B.2.i + V2.B.4.e
+ + V2.B.4.g + V2.B.4.h + V1.C.7.b + V2.B.1.e
+
+ # Correlated residuals
+ V2.A.1.e ~~ V1.A.1.c.1
+ V2.A.1.e ~~ V1.A.1.c.2
+ V2.B.5.b ~~ V2.B.5.c
+ V1.A.1.a.2 ~~ V2.A.1.a
+ V2.B.4.g ~~ V2.B.4.h
+ V2.A.2.c ~~ V2.B.1.e
+ V2.B.1.c ~~ V2.B.1.d
+ V2.A.1.a ~~ V2.A.1.c
+ V1.A.1.b.4 ~~ V1.A.1.b.5
+ V1.A.1.a.4 ~~ V2.A.1.c
+ V1.A.1.a.2 ~~ V2.A.1.c
+ V1.A.1.a.3 ~~ V1.A.1.a.1
+ V1.A.1.a.4 ~~ V1.A.1.a.2
+ V2.A.1.b ~~ V1.A.1.a.1
+ V2.A.1.b ~~ V1.A.1.a.3
+ V2.A.1.a ~~ V1.A.1.a.4
+ V2.A.1.d ~~ V1.A.1.a.3
+ V2.A.1.d ~~ V2.A.1.b
+ V1.A.1.c.2 ~~ V1.A.1.c.1
+ V2.A.2.a ~~ V1.A.1.b.4
+ V2.A.2.a ~~ V1.A.1.b.5
+ V1.A.1.b.2 ~~ V1.A.1.b.1
+ '
> fitmodel4 <- cfa(model4, data = onet.active, estimator = "MLM", se="robust")
Warning message:
In lavaan::lavaan(model = model4, data = onet.active, estimator = "MLM", :
lavaan WARNING:
the optimizer (NLMINB) claimed the model converged, but not all
elements of the gradient are (near) zero; the optimizer may not
have found a local solution use check.gradient = FALSE to skip
this check.
> fitmodel4 <- cfa(model4, data = onet.active, estimator = "MLM", se="robust", std.lv=TRUE)
> summary(fitmodel4, fit.measures=TRUE)
lavaan 0.6-9 ended normally after 366 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 197
Number of observations 873
Model Test User Model:
Standard Robust
Test Statistic 12059.219 11161.254
Degrees of freedom 1694 1694
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.080
Satorra-Bentler correction
Model Test Baseline Model:
Test statistic 75850.659 72601.538
Degrees of freedom 1830 1830
P-value 0.000 0.000
Scaling correction factor 1.045
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.860 0.866
Tucker-Lewis Index (TLI) 0.849 0.855
Robust Comparative Fit Index (CFI) 0.862
Robust Tucker-Lewis Index (TLI) 0.851
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1182.893 -1182.893
Loglikelihood unrestricted model (H1) 4846.716 4846.716
Akaike (AIC) 2759.786 2759.786
Bayesian (BIC) 3699.858 3699.858
Sample-size adjusted Bayesian (BIC) 3074.232 3074.232
Root Mean Square Error of Approximation:
RMSEA 0.084 0.080
90 Percent confidence interval - lower 0.082 0.079
90 Percent confidence interval - upper 0.085 0.081
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.083
90 Percent confidence interval - lower 0.082
90 Percent confidence interval - upper 0.085
Standardized Root Mean Square Residual:
SRMR 0.093 0.093
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
engage =~
V1.A.1.a.1 0.334 0.014 23.924 0.000
V1.A.1.a.3 0.413 0.010 39.524 0.000
V1.A.1.a.4 0.368 0.021 17.519 0.000
V2.A.1.b 0.417 0.010 41.164 0.000
V2.A.1.d 0.436 0.010 41.697 0.000
V2.B.1.a 0.212 0.014 15.400 0.000
V2.B.1.c 0.280 0.017 16.039 0.000
V2.B.1.d 0.224 0.018 12.757 0.000
V2.B.1.f 0.256 0.014 18.464 0.000
V1.C.5.c 0.232 0.012 19.814 0.000
V2.A.1.c 0.331 0.021 15.382 0.000
V1.A.1.a.2 0.296 0.018 15.989 0.000
V2.A.1.a 0.261 0.017 15.804 0.000
V2.A.2.b 0.158 0.015 10.300 0.000
V1.A.1.e.1 0.147 0.008 18.424 0.000
V1.C.2.b -0.182 0.017 -10.450 0.000
decisive =~
V1.C.1.a 0.347 0.011 32.334 0.000
V1.C.1.b 0.359 0.010 35.701 0.000
V1.C.1.c 0.325 0.009 35.644 0.000
V1.C.2.b 0.197 0.017 11.365 0.000
V1.C.6 0.200 0.012 16.841 0.000
V1.C.4.b 0.128 0.014 9.427 0.000
relate =~
V1.A.1.a.1 0.042 0.010 4.221 0.000
V1.A.1.a.3 0.048 0.011 4.368 0.000
V1.A.1.b.3 0.103 0.008 12.431 0.000
V2.A.1.b 0.019 0.010 1.853 0.064
V2.A.1.d 0.030 0.012 2.543 0.011
V2.B.1.a 0.180 0.011 16.661 0.000
V2.B.1.f 0.238 0.014 16.833 0.000
V2.B.1.b 0.074 0.009 8.688 0.000
V1.C.3.a 0.254 0.009 28.722 0.000
V1.C.3.b 0.471 0.013 36.169 0.000
V1.C.3.c 0.483 0.014 35.235 0.000
V1.C.4.a 0.367 0.009 41.581 0.000
V1.C.4.b 0.282 0.011 25.105 0.000
V1.C.4.c 0.249 0.009 27.033 0.000
V1.C.5.a 0.191 0.008 25.242 0.000
V1.C.5.c 0.138 0.012 11.831 0.000
V1.A.1.g.2 0.142 0.009 16.425 0.000
V1.C.2.b 0.169 0.012 14.275 0.000
manage =~
V2.A.2.c 0.170 0.017 9.863 0.000
V2.A.2.d 0.253 0.010 26.397 0.000
V2.B.1.a 0.086 0.013 6.501 0.000
V2.B.1.b 0.290 0.011 27.188 0.000
V2.B.1.c 0.169 0.019 9.059 0.000
V2.B.1.d 0.226 0.018 12.642 0.000
V2.B.1.e 0.263 0.020 13.328 0.000
V2.B.4.e 0.111 0.010 10.655 0.000
V2.B.4.g 0.088 0.013 6.594 0.000
V2.B.4.h 0.114 0.013 8.639 0.000
V2.B.5.a 0.271 0.010 26.364 0.000
V2.B.5.b 0.320 0.018 17.601 0.000
V2.B.5.c 0.276 0.017 16.593 0.000
V2.B.5.d 0.446 0.014 32.146 0.000
V2.C.1.a 0.383 0.019 20.377 0.000
V1.C.2.b 0.334 0.014 23.142 0.000
insight =~
V1.A.1.b.1 0.489 0.012 40.962 0.000
V1.A.1.b.2 0.487 0.012 41.234 0.000
V2.B.3.a 0.463 0.017 27.016 0.000
V2.B.3.b 0.236 0.014 16.315 0.000
V1.C.7.a 0.316 0.014 21.854 0.000
V1.C.4.c 0.146 0.009 17.110 0.000
intuition =~
V1.A.1.b.3 0.162 0.010 15.559 0.000
V1.A.1.e.1 0.265 0.011 25.234 0.000
V1.A.1.e.2 0.333 0.011 29.485 0.000
V1.A.1.e.3 0.325 0.013 25.409 0.000
V1.A.1.f.2 0.280 0.016 18.006 0.000
V1.A.1.g.1 0.151 0.011 13.742 0.000
V1.A.1.g.2 0.172 0.011 15.207 0.000
V2.A.2.d 0.088 0.011 8.004 0.000
analysis =~
V1.A.1.a.1 0.030 0.011 2.691 0.007
V1.A.1.a.2 0.244 0.019 12.839 0.000
V1.A.1.a.4 0.225 0.022 10.225 0.000
V1.A.1.b.3 0.209 0.010 20.933 0.000
V1.A.1.b.4 0.409 0.007 55.611 0.000
V1.A.1.b.5 0.444 0.008 54.941 0.000
V1.A.1.b.6 0.262 0.009 30.217 0.000
V1.A.1.b.7 0.247 0.010 23.974 0.000
V1.A.1.c.1 0.417 0.017 24.190 0.000
V1.A.1.c.2 0.336 0.015 22.152 0.000
V1.A.1.d.1 0.260 0.009 29.587 0.000
V2.A.1.a 0.265 0.017 15.710 0.000
V2.A.1.c 0.264 0.023 11.509 0.000
V2.A.1.e 0.375 0.018 21.428 0.000
V2.A.2.a 0.421 0.008 53.015 0.000
V2.A.2.b 0.330 0.017 19.737 0.000
V2.A.2.c 0.313 0.017 18.448 0.000
V2.B.2.i 0.452 0.011 42.102 0.000
V2.B.4.e 0.310 0.012 25.677 0.000
V2.B.4.g 0.446 0.014 30.878 0.000
V2.B.4.h 0.419 0.014 29.566 0.000
V1.C.7.b 0.461 0.014 33.123 0.000
V2.B.1.e 0.215 0.018 11.867 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
.V1.A.1.c.1 ~~
.V2.A.1.e 0.180 0.011 16.812 0.000
.V1.A.1.c.2 ~~
.V2.A.1.e 0.160 0.009 16.859 0.000
.V2.B.5.b ~~
.V2.B.5.c 0.100 0.006 15.777 0.000
.V1.A.1.a.2 ~~
.V2.A.1.a 0.043 0.004 9.964 0.000
.V2.B.4.g ~~
.V2.B.4.h 0.043 0.003 16.062 0.000
.V2.A.2.c ~~
.V2.B.1.e 0.096 0.008 11.694 0.000
.V2.B.1.c ~~
.V2.B.1.d 0.047 0.004 10.798 0.000
.V2.A.1.c ~~
.V2.A.1.a 0.031 0.004 8.082 0.000
.V1.A.1.b.4 ~~
.V1.A.1.b.5 0.019 0.001 13.788 0.000
.V1.A.1.a.4 ~~
.V2.A.1.c 0.049 0.004 11.212 0.000
.V2.A.1.c ~~
.V1.A.1.a.2 0.032 0.004 7.824 0.000
.V1.A.1.a.1 ~~
.V1.A.1.a.3 0.017 0.001 11.245 0.000
.V1.A.1.a.4 ~~
.V1.A.1.a.2 0.039 0.004 9.535 0.000
.V1.A.1.a.1 ~~
.V2.A.1.b 0.011 0.002 6.502 0.000
.V1.A.1.a.3 ~~
.V2.A.1.b 0.007 0.002 4.275 0.000
.V1.A.1.a.4 ~~
.V2.A.1.a 0.034 0.004 9.094 0.000
.V1.A.1.a.3 ~~
.V2.A.1.d 0.011 0.002 6.475 0.000
.V2.A.1.b ~~
.V2.A.1.d 0.003 0.001 1.886 0.059
.V1.A.1.c.1 ~~
.V1.A.1.c.2 0.162 0.010 16.766 0.000
.V1.A.1.b.4 ~~
.V2.A.2.a 0.010 0.001 8.206 0.000
.V1.A.1.b.5 ~~
.V2.A.2.a 0.010 0.001 7.880 0.000
.V1.A.1.b.1 ~~
.V1.A.1.b.2 0.031 0.004 7.905 0.000
engage ~~
decisive 0.665 0.020 33.429 0.000
relate 0.442 0.033 13.453 0.000
manage 0.693 0.018 38.167 0.000
insight 0.715 0.019 37.534 0.000
intuition 0.075 0.039 1.939 0.052
analysis 0.796 0.016 48.750 0.000
decisive ~~
relate 0.419 0.033 12.498 0.000
manage 0.572 0.023 24.807 0.000
insight 0.723 0.019 38.969 0.000
intuition 0.093 0.042 2.239 0.025
analysis 0.681 0.020 33.576 0.000
relate ~~
manage 0.398 0.028 14.351 0.000
insight 0.113 0.039 2.912 0.004
intuition -0.062 0.035 -1.769 0.077
analysis 0.148 0.037 3.990 0.000
manage ~~
insight 0.706 0.020 34.673 0.000
intuition 0.300 0.032 9.262 0.000
analysis 0.725 0.016 44.293 0.000
insight ~~
intuition 0.331 0.034 9.659 0.000
analysis 0.867 0.014 64.139 0.000
intuition ~~
analysis 0.488 0.030 16.266 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.V1.A.1.a.1 0.032 0.002 15.093 0.000
.V1.A.1.a.3 0.031 0.002 14.565 0.000
.V1.A.1.a.4 0.066 0.004 15.018 0.000
.V2.A.1.b 0.023 0.002 10.771 0.000
.V2.A.1.d 0.027 0.002 11.825 0.000
.V2.B.1.a 0.050 0.003 18.763 0.000
.V2.B.1.c 0.065 0.005 12.182 0.000
.V2.B.1.d 0.073 0.006 11.647 0.000
.V2.B.1.f 0.091 0.005 17.876 0.000
.V1.C.5.c 0.075 0.005 15.635 0.000
.V2.A.1.c 0.069 0.005 12.721 0.000
.V1.A.1.a.2 0.062 0.005 12.837 0.000
.V2.A.1.a 0.051 0.004 12.036 0.000
.V2.A.2.b 0.043 0.002 19.813 0.000
.V1.A.1.e.1 0.038 0.002 17.041 0.000
.V1.C.2.b 0.060 0.004 14.764 0.000
.V1.C.1.a 0.031 0.002 13.799 0.000
.V1.C.1.b 0.022 0.002 12.198 0.000
.V1.C.1.c 0.022 0.001 15.205 0.000
.V1.C.6 0.087 0.004 21.463 0.000
.V1.C.4.b 0.058 0.005 12.601 0.000
.V1.A.1.b.3 0.045 0.003 16.994 0.000
.V2.B.1.b 0.035 0.002 18.132 0.000
.V1.C.3.a 0.039 0.002 16.077 0.000
.V1.C.3.b 0.068 0.004 16.604 0.000
.V1.C.3.c 0.076 0.005 15.998 0.000
.V1.C.4.a 0.035 0.002 15.566 0.000
.V1.C.4.c 0.042 0.002 16.895 0.000
.V1.C.5.a 0.039 0.003 15.408 0.000
.V1.A.1.g.2 0.061 0.003 21.130 0.000
.V2.A.2.c 0.115 0.008 14.761 0.000
.V2.A.2.d 0.057 0.003 20.162 0.000
.V2.B.1.e 0.133 0.010 13.728 0.000
.V2.B.4.e 0.030 0.002 18.543 0.000
.V2.B.4.g 0.061 0.003 19.224 0.000
.V2.B.4.h 0.056 0.003 18.973 0.000
.V2.B.5.a 0.037 0.002 15.770 0.000
.V2.B.5.b 0.134 0.009 15.487 0.000
.V2.B.5.c 0.118 0.007 18.046 0.000
.V2.B.5.d 0.048 0.003 15.130 0.000
.V2.C.1.a 0.186 0.009 20.059 0.000
.V1.A.1.b.1 0.042 0.004 10.720 0.000
.V1.A.1.b.2 0.053 0.005 11.184 0.000
.V2.B.3.a 0.184 0.010 17.936 0.000
.V2.B.3.b 0.103 0.007 15.287 0.000
.V1.C.7.a 0.123 0.007 18.889 0.000
.V1.A.1.e.2 0.034 0.003 13.394 0.000
.V1.A.1.e.3 0.045 0.003 14.384 0.000
.V1.A.1.f.2 0.169 0.009 18.070 0.000
.V1.A.1.g.1 0.033 0.002 13.505 0.000
.V1.A.1.b.4 0.027 0.001 18.219 0.000
.V1.A.1.b.5 0.034 0.002 18.610 0.000
.V1.A.1.b.6 0.044 0.003 17.361 0.000
.V1.A.1.b.7 0.043 0.003 16.667 0.000
.V1.A.1.c.1 0.193 0.011 17.502 0.000
.V1.A.1.c.2 0.166 0.009 17.823 0.000
.V1.A.1.d.1 0.060 0.005 13.001 0.000
.V2.A.1.e 0.200 0.011 17.946 0.000
.V2.A.2.a 0.025 0.002 16.444 0.000
.V2.B.2.i 0.030 0.002 17.940 0.000
.V1.C.7.b 0.105 0.006 18.439 0.000
engage 1.000
decisive 1.000
relate 1.000
manage 1.000
insight 1.000
intuition 1.000
analysis 1.000
```
Best Answer
Just to add a few things to @Preston Botter's answer above, none of your fit indices show that your model shows even an adequate fit. For the comparative fit indices CFI and TLI, you need at least >.900. For the absolute fit indices RMSEA and SRMR, you should have <.080.
Your process of modelling can be greatly improved if you assess the individual CFA fit of each model first, and also check for the magnitude of factor loadings (every standardised factor loading should be at least > |.30|, meaning that each item explains at least about 10% of the variance in its latent factor). After modelling each factor individually, you will most likely identify the culprit that pushes your 6-factor model fit down. I've noticed that in your 6-factor model some standardised factor loadings are low.
Remember you always want to follow a three-step process: 1) Assess the CFA fit of each individual model; 2) Measurement model (all factors correlated); 3) Structural Model (where you specify the exact relationships among the factors tested in Step 2).
Also, you can use DWLS (it was developed to assess parameters for the Likert scale type items), but you can also try a Robust variant of the Maximum Likelihood ("MLR") - this estimator is robust against non-extreme deviations from normality. From experience, on an odd occasion, you might get a better fit with it than DWLS. However, DWLS should be your preferred choice.