Inspecting specific imputed datasets in cfa.mi() for Heywood cases

Bryan Stiles

unread,

Mar 25, 2025, 9:27:12 PM3/25/25

to lavaan

Hello lavaan community, I am fitting a higher-order CFA model (output below) using cfa.mi() on 20 imputed datasets. I received a warning that some of the estimated lv variances were negative and that Heywood cases were detected in six of the imputed datasets, although it doesn't appear to be the case in the pooled estimates.

I would like to inspect these six specific datasets to investigate the nature of the Heywood case, but I'm unsure how to access them. I couldn't find much of a response to this specific question in the forum. Is there a workaround to pull this data?

Thank you!

> summary(cfa4out, standardized = TRUE, rsquare=TRUE, fit.measures=TRUE, test = "D2")
lavaan.mi object fit to 20 imputed data sets using:
- lavaan (0.6-19)
- lavaan.mi (0.1-0)
See class?lavaan.mi help page for available methods.

Convergence information:
The model converged on 20 imputed data sets.
Standard errors were available for all imputations.
Heywood cases detected for data set(s) 1, 6, 9, 13, 14, 15
These are not necessarily a cause for concern, unless a pooled estimate is also a Heywood case.

Estimator DWLS
Optimization method NLMINB
Number of model parameters 60

Number of observations 170

Model Test User Model:

Standard Scaled
Test statistic 185.011 189.161
Degrees of freedom 54 54
P-value 0.000 0.000
Average scaling correction factor 1.092
Average shift parameter 19.694
simple second-order correction
Pooling method D2
Pooled statistic “standard”
“scaled.shifted” correction applied AFTER pooling

Model Test Baseline Model:

Test statistic 757.618 406.820
Degrees of freedom 66 66
P-value 0.000 0.000
Scaling correction factor 2.029

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.811 0.603
Tucker-Lewis Index (TLI) 0.768 0.515

Robust Comparative Fit Index (CFI) 0.723
Robust Tucker-Lewis Index (TLI) 0.662

Root Mean Square Error of Approximation:

RMSEA 0.120 0.122
90 Percent confidence interval - lower 0.101 0.103
90 Percent confidence interval - upper 0.139 0.141
P-value H_0: RMSEA <= 0.050 0.000 0.000
P-value H_0: RMSEA >= 0.080 1.000 1.000

Robust RMSEA 0.151
90 Percent confidence interval - lower 0.133
90 Percent confidence interval - upper 0.169
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 1.000

Standardized Root Mean Square Residual:

SRMR 0.152 0.152

Parameter Estimates:

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

Pooled across imputations Rubin's (1987) rules
Augment within-imputation variance Scale by average RIV
Wald test for pooled parameters t(df) distribution

Pooled t statistics with df >= 1000 are displayed with
df = Inf(inity) to save space. Although the t distribution
with large df closely approximates a standard normal
distribution, exact df for reporting these t tests can be
obtained from parameterEstimates.mi()

Latent Variables:
Estimate Std.Err t-value df P(>|t|) Std.lv Std.all
sk =~
SCS_SF_q2 (a) 1.000 0.588 0.588
SCS_SF_q6 (a) 1.000 0.588 0.588
sj =~
SCS_SF_q11 (b) 1.000 0.819 0.819
SCS_SF_q12 (b) 1.000 0.819 0.819
ch =~
SCS_SF_q5 (c) 1.000 0.563 0.563
SCS_SF_q10 (c) 1.000 0.563 0.563
is =~
SCS_SF_q4r (d) 1.000 0.751 0.751
SCS_SF_q8r (d) 1.000 0.751 0.751
mi =~
SCS_SF_q3 (e) 1.000 0.736 0.736
SCS_SF_q7 (e) 1.000 0.736 0.736
oi =~
SCS_SF_q1r (f) 1.000 0.696 0.696
SCS_SF_q9r (f) 1.000 0.696 0.696
sc =~
sk 0.388 0.065 5.974 809.520 0.000 0.660 0.660
sj 0.695 0.044 15.732 390.734 0.000 0.849 0.849
ch 0.240 0.062 3.866 Inf 0.000 0.427 0.427
is 0.714 0.040 17.905 650.033 0.000 0.951 0.951
mi 0.327 0.064 5.127 279.663 0.000 0.445 0.445
oi 0.683 0.045 15.345 937.094 0.000 0.981 0.981

Thresholds:
Estimate Std.Err t-value df P(>|t|) Std.lv Std.all
SCS_SF_q2|t1 -1.367 0.154 -8.871 866.684 0.000 -1.367 -1.367
SCS_SF_q2|t2 -0.743 0.119 -6.219 Inf 0.000 -0.743 -0.743
SCS_SF_q2|t3 0.250 0.109 2.287 Inf 0.022 0.250 0.250
SCS_SF_q2|t4 1.273 0.147 8.680 Inf 0.000 1.273 1.273
SCS_SF_q6|t1 -1.109 0.136 -8.160 Inf 0.000 -1.109 -1.109
SCS_SF_q6|t2 -0.075 0.108 -0.690 Inf 0.490 -0.075 -0.075
SCS_SF_q6|t3 0.527 0.114 4.643 Inf 0.000 0.527 0.527
SCS_SF_q6|t4 1.253 0.145 8.630 Inf 0.000 1.253 1.253
SCS_SF_q11rv|1 -0.755 0.120 -6.297 Inf 0.000 -0.755 -0.755
SCS_SF_q11rv|2 -0.035 0.108 -0.321 Inf 0.748 -0.035 -0.035
SCS_SF_q11rv|3 0.674 0.117 5.744 Inf 0.000 0.674 0.674
SCS_SF_q11rv|4 1.297 0.148 8.734 Inf 0.000 1.297 1.297
SCS_SF_q12rv|1 -1.202 0.142 -8.479 787.658 0.000 -1.202 -1.202
SCS_SF_q12rv|2 -0.360 0.111 -3.260 Inf 0.001 -0.360 -0.360
SCS_SF_q12rv|3 0.463 0.112 4.125 Inf 0.000 0.463 0.463
SCS_SF_q12rv|4 1.323 0.150 8.791 Inf 0.000 1.323 1.323
SCS_SF_q5|t1 -1.205 0.142 -8.489 Inf 0.000 -1.205 -1.205
SCS_SF_q5|t2 -0.406 0.111 -3.653 Inf 0.000 -0.406 -0.406
SCS_SF_q5|t3 0.294 0.110 2.682 Inf 0.007 0.294 0.294
SCS_SF_q5|t4 1.096 0.135 8.107 Inf 0.000 1.096 1.096
SCS_SF_q10|t1 -1.146 0.138 -8.294 857.868 0.000 -1.146 -1.146
SCS_SF_q10|t2 -0.401 0.111 -3.605 Inf 0.000 -0.401 -0.401
SCS_SF_q10|t3 0.440 0.112 3.936 Inf 0.000 0.440 0.440
SCS_SF_q10|t4 1.305 0.149 8.755 Inf 0.000 1.305 1.305
SCS_SF_q4rv|t1 -0.855 0.124 -6.918 Inf 0.000 -0.855 -0.855
SCS_SF_q4rv|t2 0.118 0.108 1.087 874.286 0.278 0.118 0.118
SCS_SF_q4rv|t3 0.833 0.123 6.786 Inf 0.000 0.833 0.833
SCS_SF_q4rv|t4 1.456 0.162 8.989 997.836 0.000 1.456 1.456
SCS_SF_q8rv|t1 -0.740 0.119 -6.200 Inf 0.000 -0.740 -0.740
SCS_SF_q8rv|t2 0.188 0.109 1.735 Inf 0.083 0.188 0.188
SCS_SF_q8rv|t3 0.748 0.120 6.252 Inf 0.000 0.748 0.748
SCS_SF_q8rv|t4 1.137 0.138 8.257 450.838 0.000 1.137 1.137
SCS_SF_q3|t1 -1.373 0.155 -8.878 637.285 0.000 -1.373 -1.373
SCS_SF_q3|t2 -0.780 0.121 -6.458 418.631 0.000 -0.780 -0.780
SCS_SF_q3|t3 -0.110 0.108 -1.018 917.748 0.309 -0.110 -0.110
SCS_SF_q3|t4 1.009 0.130 7.730 Inf 0.000 1.009 1.009
SCS_SF_q7|t1 -1.508 0.167 -9.019 575.832 0.000 -1.508 -1.508
SCS_SF_q7|t2 -1.095 0.135 -8.102 Inf 0.000 -1.095 -1.095
SCS_SF_q7|t3 -0.078 0.108 -0.718 Inf 0.473 -0.078 -0.078
SCS_SF_q7|t4 0.775 0.121 6.425 941.048 0.000 0.775 0.775
SCS_SF_q1rv|t1 -0.814 0.122 -6.673 Inf 0.000 -0.814 -0.814
SCS_SF_q1rv|t2 0.038 0.108 0.349 Inf 0.727 0.038 0.038
SCS_SF_q1rv|t3 0.629 0.116 5.421 Inf 0.000 0.629 0.629
SCS_SF_q1rv|t4 1.334 0.151 8.821 Inf 0.000 1.334 1.334
SCS_SF_q9rv|t1 -0.618 0.116 -5.336 Inf 0.000 -0.618 -0.618
SCS_SF_q9rv|t2 0.097 0.108 0.895 Inf 0.371 0.097 0.097
SCS_SF_q9rv|t3 0.697 0.118 5.908 Inf 0.000 0.697 0.697
SCS_SF_q9rv|t4 1.248 0.145 8.616 Inf 0.000 1.248 1.248

Variances:
Estimate Std.Err t-value df P(>|t|) Std.lv Std.all
sc 1.000 1.000 1.000
.SCS_SF_q2 0.654 0.654 0.654
.SCS_SF_q6 0.654 0.654 0.654
.SCS_SF_q11rev 0.329 0.329 0.329
.SCS_SF_q12rev 0.329 0.329 0.329
.SCS_SF_q5 0.683 0.683 0.683
.SCS_SF_q10 0.683 0.683 0.683
.SCS_SF_q4rev 0.436 0.436 0.436
.SCS_SF_q8rev 0.436 0.436 0.436
.SCS_SF_q3 0.457 0.457 0.457
.SCS_SF_q7 0.457 0.457 0.457
.SCS_SF_q1rev 0.515 0.515 0.515
.SCS_SF_q9rev 0.515 0.515 0.515
.sk 0.195 0.079 2.466 265.155 0.014 0.564 0.564
.sj 0.188 0.055 3.417 183.501 0.001 0.280 0.280
.ch 0.259 0.070 3.687 130.944 0.000 0.818 0.818
.is 0.054 0.047 1.141 87.529 0.257 0.096 0.096
.mi 0.435 0.066 6.586 228.110 0.000 0.802 0.802
.oi 0.018 0.059 0.301 198.335 0.764 0.037 0.037

R-Square:
Estimate
SCS_SF_q2 0.346
SCS_SF_q6 0.346
SCS_SF_q11rev 0.671
SCS_SF_q12rev 0.671
SCS_SF_q5 0.317
SCS_SF_q10 0.317
SCS_SF_q4rev 0.564
SCS_SF_q8rev 0.564
SCS_SF_q3 0.543
SCS_SF_q7 0.543
SCS_SF_q1rev 0.485
SCS_SF_q9rev 0.485
sk 0.436
sj 0.720
ch 0.182
is 0.904
mi 0.198
oi 0.963

Warning messages:
1: lavaan->lav_object_post_check():
some estimated lv variances are negative
2: lavaan->lav_object_post_check():
some estimated lv variances are negative
3: lavaan->lav_object_post_check():
some estimated lv variances are negative
4: lavaan->lav_object_post_check():
some estimated lv variances are negative
5: lavaan->lav_object_post_check():
some estimated lv variances are negative
6: lavaan->lav_object_post_check():
some estimated lv variances are negative

Terrence Jorgensen

unread,

Apr 1, 2025, 4:23:09 AM4/1/25

to lavaan

Heywood cases were detected in six of the imputed datasets, although it doesn't appear to be the case in the pooled estimates.

The pooled estimates are what you draw inferences from, so that's all I would be concerned with. But there are very smart people who disagree with me on that, including (if I recall correctly) my coauthors Craig Enders and Max Mansolf.

I would like to inspect these six specific datasets to investigate the nature of the Heywood case, but I'm unsure how to access them.

The message is telling you which imputations to inspect:

Heywood cases detected for data set(s) 1, 6, 9, 13, 14, 15

If you fit you model to a list of imputed data sets (rather than a mids object), then you can extract them like any list item.

dataList[[1]]

dataList[[6]]

And fit models to them using cfa()

Also read about the omit.imps= argument on the class?lavaan.mi help page (and most other help pages in the lavaan.mi package), if you wanted to see results pooled from imputations without Heywood cases:

summary(cfa4out, standardized = TRUE, rsquare=TRUE, fit.measures=TRUE, test = "D2",

omit.imps = c("no.conv", "no.se", 1, 6, 9, 13, 14, 15) )

## or

summary(cfa4out, standardized = TRUE, rsquare=TRUE, fit.measures=TRUE, test = "D2",

omit.imps = c("no.conv", "no.se", "no.npd") )

Terrence D. Jorgensen (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen

Bryan Stiles

unread,

Apr 1, 2025, 1:41:15 PM4/1/25

to lavaan

Thank you, Dr. Jorgensen! Very helpful.

Reply all

Reply to author

Forward