I have a model with negative estimated observed variance and I would like to calculate CIs for this.
I am estimating a bifactor model with ordinal data for the purpose of determining proportion of variance attributable to a general factor vs specific factors.
I am estimating the model using 100 multiply imputed data sets with a sample of 452 using the semTools cfa.mi function. The output of the model is pasted below. One Item (.CSH_S4a) has a negative estimated variance. My question is, how do I calculate the CI for this variance using any of the methods in "Savalei, V., & Kolenikov, S. (2008). Constrained versus unconstrained estimation in structural equation modeling. Psychological Methods, 13(2), 150." ?
Sorry if I am missing something obvious here and thank you in advance for your time.
Parameter Estimates:
Information Expected
Information saturated (h1) model Unstructured
Standard errors Robust.sem
Latent Variables:
Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper
A =~
CSH_B3a 0.155 0.074 2.098 Inf 0.036 0.010 0.299
CSH_S4a 0.793 0.103 7.663 Inf 0.000 0.590 0.996
CSH_S5a 0.430 0.080 5.406 Inf 0.000 0.274 0.586
CSH_S2a 0.443 0.073 6.103 Inf 0.000 0.301 0.585
CSH_B11a 0.069 0.081 0.852 Inf 0.394 -0.090 0.229
CSH_B2a 0.071 0.087 0.815 Inf 0.415 -0.100 0.243
B =~
CSH_B8a 0.737 0.037 20.089 Inf 0.000 0.665 0.808
CSH_B13a 0.573 0.054 10.691 Inf 0.000 0.468 0.679
CSH_B4a 0.842 0.036 23.644 Inf 0.000 0.772 0.912
CSH_B5a 0.730 0.041 17.997 Inf 0.000 0.650 0.809
CSH_S10a 0.272 0.063 4.316 Inf 0.000 0.149 0.396
C =~
CSH_S19a 0.461 0.083 5.558 Inf 0.000 0.299 0.624
CSH_W2a 0.557 0.075 7.468 Inf 0.000 0.411 0.703
CSH_S7a 0.377 0.089 4.247 Inf 0.000 0.203 0.551
CSH_S8a 0.213 0.073 2.924 Inf 0.003 0.070 0.355
CSH_W1a 0.506 0.078 6.515 Inf 0.000 0.354 0.658
D =~
CSH_M7a 0.646 0.049 13.058 Inf 0.000 0.549 0.743
CSH_M6a 0.791 0.035 22.329 Inf 0.000 0.721 0.860
CSH_M4a 0.422 0.052 8.155 Inf 0.000 0.321 0.524
CSH_D3a -0.019 0.060 -0.320 Inf 0.749 -0.137 0.098
CSH_M5a 0.861 0.030 28.740 Inf 0.000 0.802 0.919
CSH_M2a 0.909 0.031 29.240 Inf 0.000 0.848 0.970
G =~
CSH_B3a 0.536 0.050 10.613 Inf 0.000 0.437 0.635
CSH_S4a 0.711 0.053 13.491 Inf 0.000 0.608 0.814
CSH_S5a 0.487 0.065 7.438 Inf 0.000 0.359 0.615
CSH_S2a 0.710 0.043 16.345 Inf 0.000 0.625 0.796
CSH_B11a 0.673 0.044 15.246 Inf 0.000 0.587 0.760
CSH_B2a 0.645 0.054 11.932 Inf 0.000 0.539 0.751
CSH_B8a 0.486 0.052 9.266 Inf 0.000 0.383 0.589
CSH_B13a 0.514 0.055 9.325 Inf 0.000 0.406 0.622
CSH_B4a 0.526 0.052 10.144 Inf 0.000 0.424 0.627
CSH_B5a 0.447 0.057 7.893 Inf 0.000 0.336 0.558
CSH_S10a 0.449 0.057 7.898 Inf 0.000 0.337 0.560
CSH_S19a 0.403 0.067 6.024 Inf 0.000 0.272 0.534
CSH_W2a 0.607 0.054 11.214 Inf 0.000 0.501 0.713
CSH_S7a 0.313 0.070 4.466 Inf 0.000 0.176 0.451
CSH_S8a 0.569 0.048 11.885 Inf 0.000 0.475 0.662
CSH_W1a 0.539 0.050 10.887 Inf 0.000 0.442 0.636
CSH_M7a 0.377 0.064 5.861 Inf 0.000 0.251 0.503
CSH_M6a 0.316 0.066 4.771 Inf 0.000 0.186 0.445
CSH_M4a 0.437 0.057 7.700 Inf 0.000 0.325 0.548
CSH_D3a 0.380 0.059 6.428 4801.702 0.000 0.264 0.496
CSH_M5a 0.098 0.061 1.594 Inf 0.111 -0.022 0.218
CSH_M2a 0.089 0.069 1.276 Inf 0.202 -0.047 0.224
Covariances:
Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper
A ~~
G 0.000 0.000 0.000
B ~~
G 0.000 0.000 0.000
C ~~
G 0.000 0.000 0.000
D ~~
G 0.000 0.000 0.000
A ~~
B 0.000 0.000 0.000
C 0.000 0.000 0.000
D 0.000 0.000 0.000
B ~~
C 0.000 0.000 0.000
D 0.000 0.000 0.000
C ~~
D 0.000 0.000 0.000
Intercepts:
Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper
.CSH_B3a 0.000 0.000 0.000
.CSH_S4a 0.000 0.000 0.000
.CSH_S5a 0.000 0.000 0.000
.CSH_S2a 0.000 0.000 0.000
.CSH_B11a 0.000 0.000 0.000
.CSH_B2a 0.000 0.000 0.000
.CSH_B8a 0.000 0.000 0.000
.CSH_B13a 0.000 0.000 0.000
.CSH_B4a 0.000 0.000 0.000
.CSH_B5a 0.000 0.000 0.000
.CSH_S10a 0.000 0.000 0.000
.CSH_S19a 0.000 0.000 0.000
.CSH_W2a 0.000 0.000 0.000
.CSH_S7a 0.000 0.000 0.000
.CSH_S8a 0.000 0.000 0.000
.CSH_W1a 0.000 0.000 0.000
.CSH_M7a 0.000 0.000 0.000
.CSH_M6a 0.000 0.000 0.000
.CSH_M4a 0.000 0.000 0.000
.CSH_D3a 0.000 0.000 0.000
.CSH_M5a 0.000 0.000 0.000
.CSH_M2a 0.000 0.000 0.000
A 0.000 0.000 0.000
B 0.000 0.000 0.000
C 0.000 0.000 0.000
D 0.000 0.000 0.000
G 0.000 0.000 0.000
Thresholds:
Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper
CSH_B3a|t1 0.058 0.057 1.021 Inf 0.307 -0.053 0.169
CSH_B3a|t2 0.999 0.068 14.645 Inf 0.000 0.865 1.132
CSH_S4a|t1 0.476 0.059 8.074 Inf 0.000 0.361 0.592
CSH_S4a|t2 1.250 0.076 16.457 Inf 0.000 1.101 1.399
CSH_S5a|t1 0.845 0.065 13.086 Inf 0.000 0.718 0.971
CSH_S5a|t2 1.637 0.095 17.255 Inf 0.000 1.451 1.823
CSH_S2a|t1 0.231 0.057 4.050 Inf 0.000 0.119 0.343
CSH_S2a|t2 1.217 0.075 16.280 Inf 0.000 1.071 1.364
CSH_B11a|t1 0.058 0.057 1.019 Inf 0.308 -0.053 0.169
CSH_B11a|t2 1.050 0.070 15.088 Inf 0.000 0.914 1.187
CSH_B2a|t1 0.569 0.060 9.486 Inf 0.000 0.452 0.687
CSH_B2a|t2 1.514 0.088 17.255 Inf 0.000 1.342 1.686
CSH_B8a|t1 0.115 0.057 2.030 Inf 0.042 0.004 0.226
CSH_B8a|t2 0.510 0.059 8.600 Inf 0.000 0.394 0.627
CSH_B13a|t1 0.530 0.060 8.882 Inf 0.000 0.413 0.647
CSH_B13a|t2 0.957 0.067 14.252 Inf 0.000 0.826 1.089
CSH_B4a|t1 0.227 0.057 3.978 Inf 0.000 0.115 0.339
CSH_B4a|t2 0.543 0.060 9.079 Inf 0.000 0.426 0.660
CSH_B5a|t1 0.316 0.058 5.485 Inf 0.000 0.203 0.429
CSH_B5a|t2 0.707 0.062 11.399 Inf 0.000 0.585 0.828
CSH_S10a|t1 0.433 0.059 7.388 Inf 0.000 0.318 0.548
CSH_S10a|t2 1.117 0.072 15.564 Inf 0.000 0.976 1.258
CSH_S19a|t1 0.735 0.063 11.642 Inf 0.000 0.611 0.859
CSH_S19a|t2 1.981 0.129 15.310 Inf 0.000 1.727 2.234
CSH_W2a|t1 0.500 0.060 8.397 Inf 0.000 0.383 0.617
CSH_W2a|t2 1.406 0.083 17.008 Inf 0.000 1.244 1.568
CSH_S7a|t1 0.731 0.062 11.693 Inf 0.000 0.608 0.853
CSH_S7a|t2 2.133 0.141 15.151 Inf 0.000 1.857 2.409
CSH_S8a|t1 -0.373 0.058 -6.408 Inf 0.000 -0.487 -0.259
CSH_S8a|t2 0.778 0.063 12.274 Inf 0.000 0.654 0.902
CSH_W1a|t1 -0.269 0.058 -4.667 Inf 0.000 -0.382 -0.156
CSH_W1a|t2 0.813 0.064 12.647 Inf 0.000 0.687 0.940
CSH_M7a|t1 0.695 0.062 11.165 Inf 0.000 0.573 0.817
CSH_M7a|t2 1.598 0.095 16.869 Inf 0.000 1.412 1.783
CSH_M6a|t1 0.655 0.062 10.619 Inf 0.000 0.534 0.776
CSH_M6a|t2 1.591 0.094 16.917 Inf 0.000 1.407 1.775
CSH_M4a|t1 0.234 0.058 4.075 Inf 0.000 0.122 0.347
CSH_M4a|t2 1.673 0.099 16.879 Inf 0.000 1.479 1.867
CSH_D3a|t1 -0.263 0.059 -4.465 Inf 0.000 -0.378 -0.148
CSH_D3a|t2 1.553 0.096 16.152 6322.319 0.000 1.365 1.742
CSH_M5a|t1 -0.130 0.057 -2.278 Inf 0.023 -0.241 -0.018
CSH_M5a|t2 0.954 0.067 14.142 Inf 0.000 0.822 1.086
CSH_M2a|t1 0.634 0.061 10.359 Inf 0.000 0.514 0.755
CSH_M2a|t2 1.466 0.086 16.997 Inf 0.000 1.297 1.635
Variances:
Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper
.CSH_B3a 0.689 0.689 0.689
.CSH_S4a -0.135 -0.135 -0.135
.CSH_S5a 0.578 0.578 0.578
.CSH_S2a 0.299 0.299 0.299
.CSH_B11a 0.542 0.542 0.542
.CSH_B2a 0.579 0.579 0.579
.CSH_B8a 0.221 0.221 0.221
.CSH_B13a 0.407 0.407 0.407
.CSH_B4a 0.014 0.014 0.014
.CSH_B5a 0.268 0.268 0.268
.CSH_S10a 0.724 0.724 0.724
.CSH_S19a 0.624 0.624 0.624
.CSH_W2a 0.322 0.322 0.322
.CSH_S7a 0.760 0.760 0.760
.CSH_S8a 0.631 0.631 0.631
.CSH_W1a 0.453 0.453 0.453
.CSH_M7a 0.440 0.440 0.440
.CSH_M6a 0.275 0.275 0.275
.CSH_M4a 0.631 0.631 0.631
.CSH_D3a 0.854 0.854 0.854
.CSH_M5a 0.250 0.250 0.250
.CSH_M2a 0.165 0.165 0.165
A 1.000 1.000 1.000
B 1.000 1.000 1.000
C 1.000 1.000 1.000
D 1.000 1.000 1.000
G 1.000 1.000 1.000
Scales y*:
Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper
CSH_B3a 1.000 1.000 1.000
CSH_S4a 1.000 1.000 1.000
CSH_S5a 1.000 1.000 1.000
CSH_S2a 1.000 1.000 1.000
CSH_B11a 1.000 1.000 1.000
CSH_B2a 1.000 1.000 1.000
CSH_B8a 1.000 1.000 1.000
CSH_B13a 1.000 1.000 1.000
CSH_B4a 1.000 1.000 1.000
CSH_B5a 1.000 1.000 1.000
CSH_S10a 1.000 1.000 1.000
CSH_S19a 1.000 1.000 1.000
CSH_W2a 1.000 1.000 1.000
CSH_S7a 1.000 1.000 1.000
CSH_S8a 1.000 1.000 1.000
CSH_W1a 1.000 1.000 1.000
CSH_M7a 1.000 1.000 1.000
CSH_M6a 1.000 1.000 1.000
CSH_M4a 1.000 1.000 1.000
CSH_D3a 1.000 1.000 1.000
CSH_M5a 1.000 1.000 1.000
CSH_M2a 1.000 1.000 1.000