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Conal Monaghan
Jan 16, 2019, 2:25:36 AM1/16/19
to lavaan
Hi,
I am looking for basic solutions to the negative variance problem. The model is a two-tier hierarchical model, comprising one higher order factor with three lower level factors. One factor, critical, has a negative variance issue (-88.070; see below) with a loading on 210.805. I was wondering what the problem solving strategy would be from here? Please find appropriate output below.
I tried placing "Critical" first to force lavaan to constrain this to one. However, this exacerbated the issue ( Variances with critical placed first: Critical = -1132.998; minimising = 0.925; helpful =1.075; support =1133.969)
Cheers and thank you very much in advance,
Conal
########## Model definition #####################
Model6 <- 'Critical =~ Q3.1_9 + Q3.1_7 + Q3.1_8 + Q3.1_14 + Q3.1_15 + Q3.1_12 + Q3.1_6 + Q3.1_16 + Q3.1_11 + Q3.1_13 + Q3.1_10 # Critical items
minimising =~ Q3.1_19 + Q3.1_18 + Q3.1_29 + Q3.1_35 + Q3.1_20 + Q3.1_17 + Q3.1_33 + Q3.1_27 + Q3.1_31 + Q3.1_36 + Q3.1_4 + Q3.1_28 + Q3.1_25 + Q3.1_30 + Q3.1_26 # minimising items
helpful =~ Q4_17 + Q4_19 + Q4_13 + Q4_12 + Q4_18 + Q4_16 + Q4_15 + Q4_11 + Q4_10 + Q4_9 + Q4_3 + Q4_8 + Q4_4 + Q4_6 + Q4_2 # helpful items
Support =~ helpful + minimising + Critical # higher-order factor definition
# error covariances #
Q4_16 ~~ Q4_15
Q3.1_27 ~~ Q3.1_28
Q3.1_7 ~~ Q3.1_8
Q3.1_19 ~~ Q3.1_18
Q3.1_31 ~~ Q3.1_28
Q3.1_35 ~~ Q3.1_36
'
> summary(cfa(Model6, data = Sample2, estimator="MLR"))
lavaan 0.6-3 did NOT end normally after 1665 iterations
** WARNING ** Estimates below are most likely unreliable
Optimization method NLMINB
Number of free parameters 91
Number of observations 368
Estimator ML
Model Fit Test Statistic NA
Degrees of freedom NA
P-value NA
Parameter Estimates:
Information Observed
Observed information based on Hessian
Standard Errors Robust.huber.white
Latent Variables:
Estimate Std.Err z-value P(>|z|)
Critical =~
Q3.1_9 1.000
Q3.1_7 0.990 NA
Q3.1_8 0.964 NA
Q3.1_14 0.947 NA
Q3.1_15 1.009 NA
Q3.1_12 1.028 NA
Q3.1_6 0.897 NA
Q3.1_16 1.018 NA
Q3.1_11 0.913 NA
Q3.1_13 1.035 NA
Q3.1_10 1.017 NA
minimising =~
Q3.1_19 1.000
Q3.1_18 0.918 NA
Q3.1_29 0.794 NA
Q3.1_35 0.788 NA
Q3.1_20 0.993 NA
Q3.1_17 0.880 NA
Q3.1_33 0.871 NA
Q3.1_27 0.938 NA
Q3.1_31 0.864 NA
Q3.1_36 0.769 NA
Q3.1_4 0.810 NA
Q3.1_28 0.899 NA
Q3.1_25 0.930 NA
Q3.1_30 0.827 NA
Q3.1_26 0.794 NA
helpful =~
Q4_17 1.000
Q4_19 1.101 NA
Q4_13 1.003 NA
Q4_12 0.854 NA
Q4_18 1.046 NA
Q4_16 0.797 NA
Q4_15 0.781 NA
Q4_11 0.853 NA
Q4_10 0.842 NA
Q4_9 0.954 NA
Q4_3 0.690 NA
Q4_8 0.801 NA
Q4_4 0.861 NA
Q4_6 0.946 NA
Q4_2 0.575 NA
support =~
helpful 1.000
minimising 1.320 NA
Critical 210.805 NA
Covariances:
Estimate Std.Err z-value P(>|z|)
.Q4_16 ~~
.Q4_15 0.339 NA
.Q3.1_27 ~~
.Q3.1_28 0.392 NA
.Q3.1_7 ~~
.Q3.1_8 0.397 NA
.Q3.1_19 ~~
.Q3.1_18 0.279 NA
.Q3.1_31 ~~
.Q3.1_28 0.336 NA
.Q3.1_35 ~~
.Q3.1_36 0.308 NA
Variances:
Estimate Std.Err z-value P(>|z|)
.Q3.1_9 0.696 NA
.Q3.1_7 0.740 NA
.Q3.1_8 0.786 NA
.Q3.1_14 0.745 NA
.Q3.1_15 0.681 NA
.Q3.1_12 0.614 NA
.Q3.1_6 0.741 NA
.Q3.1_16 0.694 NA
.Q3.1_11 0.776 NA
.Q3.1_13 0.599 NA
.Q3.1_10 0.797 NA
.Q3.1_19 0.760 NA
.Q3.1_18 0.698 NA
.Q3.1_29 0.861 NA
.Q3.1_35 0.830 NA
.Q3.1_20 0.803 NA
.Q3.1_17 0.707 NA
.Q3.1_33 0.957 NA
.Q3.1_27 0.955 NA
.Q3.1_31 1.109 NA
.Q3.1_36 0.981 NA
.Q3.1_4 1.058 NA
.Q3.1_28 1.015 NA
.Q3.1_25 0.980 NA
.Q3.1_30 0.937 NA
.Q3.1_26 1.052 NA
.Q4_17 0.524 NA
.Q4_19 0.396 NA
.Q4_13 0.491 NA
.Q4_12 0.700 NA
.Q4_18 0.480 NA
.Q4_16 0.805 NA
.Q4_15 0.721 NA
.Q4_11 0.724 NA
.Q4_10 0.710 NA
.Q4_9 0.456 NA
.Q4_3 0.676 NA
.Q4_8 0.650 NA
.Q4_4 0.636 NA
.Q4_6 0.590 NA
.Q4_2 0.651 NA
Critical -88.070 NA
minimising 0.921 NA
helpful 1.073 NA
support 0.002 NA
Warning message:
In lavaan::lavaan(model = Model6, data = Sample2, estimator = "MLR", :
lavaan WARNING: the optimizer warns that a solution has NOT been found!
Gary Burns
Jan 16, 2019, 1:47:38 PM1/16/19
to lavaan
Tried to respond via email but it didn't work. Or I'm double posting.
Hi Conal,
I'm following this to see what others suggest as well.
You could try to constrain the variance of critical latent variable to small negative value. In LISREL I would constrain to be greater than zero, but I haven't found that option in lavaan. So you could do something like: Critical~~.05*Critical
I've seen others post something like the below code, but it has been unsuccessful for me:
Critical~~x*Crtical
x > 0
However, these solutions don't address the underlying problem of why this is happening.
Do you have these problems when you try to estimate the model without the error covariances? That would be my first step in trouble shooting this. Next I would constrain the second-order loadings to be equal and see how the model responded.
Terrence Jorgensen
Jan 16, 2019, 6:23:28 PM1/16/19
to lavaan
One factor, critical, has a negative variance issue (-88.070; see below) with a loading on 210.805.
I would hesitate to conclude that. Your model did not converge, so that is not a ML estimate, just the place where the optimizer gave up trying. What does your factor covariance matrix look like in the first-order CFA (without a higher-order factor)? I expect it could provide a clue as to why this model fails to converge.
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
Conal Monaghan
Jan 16, 2019, 7:53:51 PM1/16/19
to lavaan
Thank you both for the help. Without the higher-order factor, the model fits the data relatively well:
chisq df pvalue cfi.robust srmr rmsea.robust rmsea.ci.lower.robust rmsea.ci.upper.robust
1886.076 770.000 0.000 0.900 0.069 0.059 0.055 0.063
I think you raise a good point, there is an issue with negative covar between two of the factors; minimising ~~ helpful = -0.010
Covariances:
Estimate Std.Err z-value P(>|z|)
.Q4_16 ~~
.Q4_15 0.339 0.061 5.568 0.000
.Q3.1_27 ~~
.Q3.1_28 0.393 0.073 5.375 0.000
.Q3.1_7 ~~
.Q3.1_8 0.397 0.058 6.858 0.000
.Q3.1_19 ~~
.Q3.1_18 0.279 0.056 5.025 0.000
.Q3.1_31 ~~
.Q3.1_28 0.336 0.070 4.809 0.000
.Q3.1_35 ~~
.Q3.1_36 0.308 0.068 4.512 0.000
Critical ~~
minimising 0.553 0.065 8.555 0.000
helpful 0.415 0.065 6.386 0.000
minimising ~~
helpful -0.010 0.068 -0.148 0.882
Variances:
Estimate Std.Err z-value P(>|z|)
.Q3.1_9 0.696 0.065 10.780 0.000
.Q3.1_7 0.740 0.064 11.517 0.000
.Q3.1_8 0.786 0.063 12.462 0.000
.Q3.1_14 0.745 0.068 11.028 0.000
.Q3.1_15 0.681 0.059 11.625 0.000
.Q3.1_12 0.614 0.057 10.773 0.000
.Q3.1_6 0.741 0.054 13.817 0.000
.Q3.1_16 0.694 0.062 11.129 0.000
.Q3.1_11 0.776 0.065 11.894 0.000
.Q3.1_13 0.599 0.056 10.668 0.000
.Q3.1_10 0.797 0.076 10.431 0.000
.Q3.1_19 0.760 0.075 10.179 0.000
.Q3.1_18 0.697 0.070 9.975 0.000
.Q3.1_29 0.860 0.073 11.822 0.000
.Q3.1_35 0.830 0.078 10.665 0.000
.Q3.1_20 0.803 0.084 9.575 0.000
.Q3.1_17 0.707 0.064 10.993 0.000
.Q3.1_33 0.957 0.086 11.107 0.000
.Q3.1_27 0.955 0.096 9.938 0.000
.Q3.1_31 1.109 0.098 11.360 0.000
.Q3.1_36 0.981 0.082 12.003 0.000
.Q3.1_4 1.058 0.083 12.781 0.000
.Q3.1_28 1.015 0.081 12.512 0.000
.Q3.1_25 0.980 0.088 11.095 0.000
.Q3.1_30 0.937 0.080 11.651 0.000
.Q3.1_26 1.052 0.085 12.346 0.000
.Q4_17 0.524 0.047 11.080 0.000
.Q4_19 0.396 0.043 9.309 0.000
.Q4_13 0.490 0.048 10.285 0.000
.Q4_12 0.700 0.065 10.758 0.000
.Q4_18 0.481 0.046 10.546 0.000
.Q4_16 0.804 0.073 11.064 0.000
.Q4_15 0.721 0.060 11.950 0.000
.Q4_11 0.724 0.065 11.095 0.000
.Q4_10 0.710 0.061 11.557 0.000
.Q4_9 0.456 0.044 10.337 0.000
.Q4_3 0.676 0.053 12.785 0.000
.Q4_8 0.650 0.055 11.908 0.000
.Q4_4 0.636 0.058 10.974 0.000
.Q4_6 0.590 0.055 10.812 0.000
.Q4_2 0.651 0.047 13.922 0.000
Critical 0.967 0.092 10.531 0.000
minimising 0.925 0.099 9.366 0.000
helpful 1.075 0.089 12.072 0.000
Terrence Jorgensen
Jan 25, 2019, 9:18:32 AM1/25/19
to lavaan
there is an issue with negative covar between two of the factors; minimising ~~ helpful = -0.010
In that case, the higher-order factor is empirically underidentified. That covariance is essentially zero, so many combinations of factor loading estimates could yield essentially identical model-implied covariance matrices. If any of your (lower-order factor) covariances are zero, that implies a (higher-order) factor model is not appropriate. Higher scores on the higher-order factor should simultaneously increase all lower-order factor scores, which is why they should positively covary.
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