Four-Factor Model. Path Diagram I
Model the WAIS-III IQ Scale (Wechsler Adult Intelligence Scale version III)
Path Diagram I
Any Heywood Cases?
A Heywood case occurs a) when the estimation of the correlation between variables is over the absolute value of 1, or out of bounds, or b) when negative variances are estimated for the model. Generally, correlation errors happen on the latent variables and negative variances occur in the error terms.
The output summary indicates a problem with the correlation between perceptual organization and processing speed (Std.all = 1.031).
lavaan 0.6-12 ended normally after 153 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 30
Number of observations 300
Model Test User Model:
Test statistic 233.268
Degrees of freedom 48
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 1042.916
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.810
Tucker-Lewis Index (TLI) 0.739
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9939.800
Loglikelihood unrestricted model (H1) -9823.166
Akaike (AIC) 19939.599
Bayesian (BIC) 20050.713
Sample-size adjusted Bayesian (BIC) 19955.570
Root Mean Square Error of Approximation:
RMSEA 0.113
90 Percent confidence interval - lower 0.099
90 Percent confidence interval - upper 0.128
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.073
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
verbalcomp =~
vocab 1.000
simil 0.296 0.031 9.470 0.000
inform 0.450 0.043 10.483 0.000
compreh 0.315 0.035 8.986 0.000
workingmemory =~
arith 1.000
digspan 0.875 0.137 6.373 0.000
lnseq 0.225 0.106 2.130 0.033
perceptorg =~
piccomp 1.000
block 3.988 0.421 9.477 0.000
matrixreason 0.909 0.127 7.171 0.000
processing =~
digsym 1.000
symbolsearch 1.065 0.300 3.547 0.000
Std.lv Std.all
6.282 0.879
1.859 0.581
2.825 0.645
1.979 0.551
2.530 0.845
2.213 0.561
0.570 0.142
1.391 0.596
5.546 0.719
1.264 0.494
2.809 0.239
2.990 0.724
Covariances:
Estimate Std.Err z-value P(>|z|)
verbalcomp ~~
workingmemory 6.120 1.232 4.969 0.000
perceptorg 5.644 0.868 6.503 0.000
processing 10.050 3.150 3.190 0.001
workingmemory ~~
perceptorg 2.437 0.371 6.561 0.000
processing 2.701 0.984 2.745 0.006
perceptorg ~~
processing 4.027 1.200 3.356 0.001
Std.lv Std.all
0.385 0.385
0.646 0.646
0.570 0.570
0.693 0.693
0.380 0.380
1.031 1.031
Variances:
Estimate Std.Err z-value P(>|z|)
.vocab 11.573 2.656 4.357 0.000
.simil 6.792 0.620 10.951 0.000
.inform 11.201 1.084 10.330 0.000
.compreh 8.969 0.804 11.157 0.000
.arith 2.560 0.901 2.842 0.004
.digspan 10.653 1.102 9.666 0.000
.lnseq 15.750 1.294 12.173 0.000
.piccomp 3.505 0.323 10.851 0.000
.block 28.761 3.207 8.968 0.000
.matrixreason 4.957 0.431 11.509 0.000
.digsym 130.314 10.847 12.014 0.000
.symbolsearch 8.127 2.480 3.277 0.001
verbalcomp 39.459 4.757 8.294 0.000
workingmemory 6.399 1.122 5.703 0.000
perceptorg 1.934 0.371 5.211 0.000
processing 7.889 4.309 1.831 0.067
Std.lv Std.all
11.573 0.227
6.792 0.663
11.201 0.584
8.969 0.696
2.560 0.286
10.653 0.685
15.750 0.980
3.505 0.644
28.761 0.483
4.957 0.756
130.314 0.943
8.127 0.476
1.000 1.000
1.000 1.000
1.000 1.000
1.000 1.000
R-Square:
Estimate
vocab 0.773
simil 0.337
inform 0.416
compreh 0.304
arith 0.714
digspan 0.315
lnseq 0.020
piccomp 0.356
block 0.517
matrixreason 0.244
digsym 0.057
symbolsearch 0.524Model Update I. Three-Factor Model
In order to fix a highly correlated set of latent variables, you should collapse those two variables into one latent variable. This makes the original Four-Factor Model a Three-Factor Model without Heywood Cases, as you can verify in the summary output.
lavaan 0.6-12 ended normally after 110 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 27
Number of observations 300
Model Test User Model:
Test statistic 252.809
Degrees of freedom 51
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 1042.916
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.793
Tucker-Lewis Index (TLI) 0.733
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9949.570
Loglikelihood unrestricted model (H1) -9823.166
Akaike (AIC) 19953.141
Bayesian (BIC) 20053.143
Sample-size adjusted Bayesian (BIC) 19967.515
Root Mean Square Error of Approximation:
RMSEA 0.115
90 Percent confidence interval - lower 0.101
90 Percent confidence interval - upper 0.129
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.076
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
verbalcomp =~
vocab 1.000
simil 0.296 0.031 9.483 0.000
inform 0.449 0.043 10.481 0.000
compreh 0.315 0.035 8.999 0.000
workingmemory =~
arith 1.000
digspan 0.881 0.152 5.786 0.000
lnseq 0.205 0.107 1.920 0.055
performance =~
piccomp 1.000
block 3.739 0.390 9.583 0.000
matrixreason 0.832 0.117 7.099 0.000
digsym 1.603 0.507 3.160 0.002
symbolsearch 1.880 0.204 9.236 0.000
Std.lv Std.all
6.281 0.879
1.861 0.581
2.822 0.644
1.981 0.552
2.528 0.844
2.227 0.565
0.518 0.129
1.517 0.650
5.672 0.735
1.262 0.493
2.431 0.207
2.852 0.690
Covariances:
Estimate Std.Err z-value P(>|z|)
verbalcomp ~~
workingmemory 6.132 1.234 4.970 0.000
performance 5.892 0.886 6.647 0.000
workingmemory ~~
performance 2.227 0.362 6.149 0.000
Std.lv Std.all
0.386 0.386
0.618 0.618
0.581 0.581
Variances:
Estimate Std.Err z-value P(>|z|)
.vocab 11.577 2.651 4.367 0.000
.simil 6.787 0.620 10.950 0.000
.inform 11.218 1.085 10.342 0.000
.compreh 8.962 0.803 11.155 0.000
.arith 2.571 1.014 2.535 0.011
.digspan 10.590 1.161 9.121 0.000
.lnseq 15.807 1.297 12.183 0.000
.piccomp 3.138 0.317 9.913 0.000
.block 27.343 3.226 8.476 0.000
.matrixreason 4.960 0.441 11.243 0.000
.digsym 132.291 10.925 12.109 0.000
.symbolsearch 8.936 0.957 9.333 0.000
verbalcomp 39.455 4.754 8.299 0.000
workingmemory 6.388 1.215 5.259 0.000
performance 2.301 0.408 5.646 0.000
Std.lv Std.all
11.577 0.227
6.787 0.662
11.218 0.585
8.962 0.696
2.571 0.287
10.590 0.681
15.807 0.983
3.138 0.577
27.343 0.459
4.960 0.757
132.291 0.957
8.936 0.524
1.000 1.000
1.000 1.000
1.000 1.000
R-Square:
Estimate
vocab 0.773
simil 0.338
inform 0.415
compreh 0.304
arith 0.713
digspan 0.319
lnseq 0.017
piccomp 0.423
block 0.541
matrixreason 0.243
digsym 0.043
symbolsearch 0.476Path Diagram II
The plot shows that some of the loadings are not very strong (lighter shading), which indicate some of the manifest variables not measuring their latent variable as expected.
Path Diagram II
Model Update II
Once the model is stable, you can look for potential areas to improve the model by exploring the loadings and fit indices.
Overall, the model fit is poor, as the goodness-of-fit measures with CFI and TLI are lower than 0.8, while the RMSEA is higher than 0.1, and SRMR is OK (lower than 0.1).
Fit Statistics
lavaan 0.6-12 ended normally after 110 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 27
Number of observations 300
Model Test User Model:
Test statistic 252.809
Degrees of freedom 51
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 1042.916
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.793
Tucker-Lewis Index (TLI) 0.733
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9949.570
Loglikelihood unrestricted model (H1) -9823.166
Akaike (AIC) 19953.141
Bayesian (BIC) 20053.143
Sample-size adjusted Bayesian (BIC) 19967.515
Root Mean Square Error of Approximation:
RMSEA 0.115
90 Percent confidence interval - lower 0.101
90 Percent confidence interval - upper 0.129
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.076
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
verbalcomp =~
vocab 1.000
simil 0.296 0.031 9.483 0.000
inform 0.449 0.043 10.481 0.000
compreh 0.315 0.035 8.999 0.000
workingmemory =~
arith 1.000
digspan 0.881 0.152 5.786 0.000
lnseq 0.205 0.107 1.920 0.055
performance =~
piccomp 1.000
block 3.739 0.390 9.583 0.000
matrixreason 0.832 0.117 7.099 0.000
digsym 1.603 0.507 3.160 0.002
symbolsearch 1.880 0.204 9.236 0.000
Std.lv Std.all
6.281 0.879
1.861 0.581
2.822 0.644
1.981 0.552
2.528 0.844
2.227 0.565
0.518 0.129
1.517 0.650
5.672 0.735
1.262 0.493
2.431 0.207
2.852 0.690
Covariances:
Estimate Std.Err z-value P(>|z|)
verbalcomp ~~
workingmemory 6.132 1.234 4.970 0.000
performance 5.892 0.886 6.647 0.000
workingmemory ~~
performance 2.227 0.362 6.149 0.000
Std.lv Std.all
0.386 0.386
0.618 0.618
0.581 0.581
Variances:
Estimate Std.Err z-value P(>|z|)
.vocab 11.577 2.651 4.367 0.000
.simil 6.787 0.620 10.950 0.000
.inform 11.218 1.085 10.342 0.000
.compreh 8.962 0.803 11.155 0.000
.arith 2.571 1.014 2.535 0.011
.digspan 10.590 1.161 9.121 0.000
.lnseq 15.807 1.297 12.183 0.000
.piccomp 3.138 0.317 9.913 0.000
.block 27.343 3.226 8.476 0.000
.matrixreason 4.960 0.441 11.243 0.000
.digsym 132.291 10.925 12.109 0.000
.symbolsearch 8.936 0.957 9.333 0.000
verbalcomp 39.455 4.754 8.299 0.000
workingmemory 6.388 1.215 5.259 0.000
performance 2.301 0.408 5.646 0.000
Std.lv Std.all
11.577 0.227
6.787 0.662
11.218 0.585
8.962 0.696
2.571 0.287
10.590 0.681
15.807 0.983
3.138 0.577
27.343 0.459
4.960 0.757
132.291 0.957
8.936 0.524
1.000 1.000
1.000 1.000
1.000 1.000
R-Square:
Estimate
vocab 0.773
simil 0.338
inform 0.415
compreh 0.304
arith 0.713
digspan 0.319
lnseq 0.017
piccomp 0.423
block 0.541
matrixreason 0.243
digsym 0.043
symbolsearch 0.476Modification Indices
The modification indices also show a good place to start to improve the model, but think about the implications of what you are adding to the model. Correlated error terms are normal estimates to add, as the variance of the manifest variables on the same factor can be related to each other. Such is the case with Similarity and information, two subscales on the verbal comprehension factor, so it is logical that they might have correlated error terms.
lhs op rhs mi epc sepc.lv
66 simil ~~ inform 35.879 -3.757 -3.757
56 vocab ~~ inform 28.377 9.783 9.783
48 performance =~ vocab 21.865 -2.077 -3.151
115 block ~~ matrixreason 16.209 -3.622 -3.622
96 arith ~~ block 15.061 3.679 3.679
117 block ~~ symbolsearch 13.144 5.725 5.725
47 workingmemory =~ symbolsearch 12.272 -0.467 -1.181
81 inform ~~ block 12.269 4.358 4.358
64 vocab ~~ digsym 11.578 -11.261 -11.261
40 workingmemory =~ simil 11.383 0.278 0.703
72 simil ~~ block 10.605 -3.084 -3.084
45 workingmemory =~ matrixreason 9.685 0.267 0.675
95 arith ~~ piccomp 9.463 -0.892 -0.892
60 vocab ~~ lnseq 9.425 -3.486 -3.486
67 simil ~~ compreh 9.356 1.587 1.587
44 workingmemory =~ block 9.258 0.765 1.933
51 performance =~ compreh 9.177 0.601 0.912
62 vocab ~~ block 8.712 -5.377 -5.377
73 simil ~~ matrixreason 8.672 1.065 1.065
106 lnseq ~~ piccomp 8.620 1.298 1.298
91 compreh ~~ digsym 8.155 5.908 5.908
59 vocab ~~ digspan 8.127 2.849 2.849
37 verbalcomp =~ digsym 7.803 -0.464 -2.917
68 simil ~~ arith 7.534 1.064 1.064
99 arith ~~ symbolsearch 7.468 -1.391 -1.391
57 vocab ~~ compreh 7.107 -3.508 -3.508
87 compreh ~~ lnseq 7.001 1.887 1.887
97 arith ~~ matrixreason 6.391 0.848 0.848
107 lnseq ~~ block 5.677 3.289 3.289
34 verbalcomp =~ piccomp 5.507 0.071 0.447
78 inform ~~ digspan 5.435 -1.649 -1.649
33 verbalcomp =~ lnseq 5.250 -0.104 -0.652
54 performance =~ lnseq 4.644 0.512 0.777
39 workingmemory =~ vocab 4.638 -0.406 -1.025
102 digspan ~~ block 4.564 -2.689 -2.689
35 verbalcomp =~ block 4.551 -0.218 -1.371
88 compreh ~~ piccomp 4.455 0.728 0.728
112 piccomp ~~ matrixreason 4.306 0.568 0.568
101 digspan ~~ piccomp 4.218 0.808 0.808
46 workingmemory =~ digsym 4.139 -0.852 -2.152
71 simil ~~ piccomp 4.029 0.607 0.607
76 inform ~~ compreh 3.789 -1.367 -1.367
70 simil ~~ lnseq 3.693 -1.200 -1.200
50 performance =~ inform 3.487 0.444 0.673
58 vocab ~~ arith 3.451 -1.457 -1.457
55 vocab ~~ simil 3.393 2.239 2.239
113 piccomp ~~ digsym 3.375 2.419 2.419
93 arith ~~ digspan 3.274 7.960 7.960
86 compreh ~~ digspan 3.234 -1.110 -1.110
80 inform ~~ piccomp 2.871 -0.672 -0.672
104 digspan ~~ digsym 2.754 -3.822 -3.822
114 piccomp ~~ symbolsearch 2.677 -0.731 -0.731
89 compreh ~~ block 2.551 1.725 1.725
90 compreh ~~ matrixreason 2.342 -0.632 -0.632
74 simil ~~ digsym 2.021 -2.575 -2.575
43 workingmemory =~ piccomp 1.899 -0.104 -0.262
49 performance =~ simil 1.675 0.227 0.345
92 compreh ~~ symbolsearch 1.646 0.764 0.764
111 piccomp ~~ block 1.591 -1.084 -1.084
85 compreh ~~ arith 1.350 -0.514 -0.514
32 verbalcomp =~ digspan 1.224 0.058 0.365
79 inform ~~ lnseq 0.998 -0.815 -0.815
69 simil ~~ digspan 0.996 0.540 0.540
53 performance =~ digspan 0.942 -0.710 -1.077
77 inform ~~ arith 0.890 0.480 0.480
116 block ~~ digsym 0.805 3.770 3.770
120 digsym ~~ symbolsearch 0.724 1.948 1.948
100 digspan ~~ lnseq 0.703 -0.688 -0.688
83 inform ~~ digsym 0.667 1.935 1.935
36 verbalcomp =~ matrixreason 0.543 0.025 0.159
61 vocab ~~ piccomp 0.529 0.414 0.414
105 digspan ~~ symbolsearch 0.481 -0.475 -0.475
52 performance =~ arith 0.478 -0.694 -1.052
98 arith ~~ digsym 0.474 -1.135 -1.135
94 arith ~~ lnseq 0.430 -0.496 -0.496
31 verbalcomp =~ arith 0.237 -0.029 -0.182
103 digspan ~~ matrixreason 0.226 0.221 0.221
42 workingmemory =~ compreh 0.190 -0.041 -0.103
75 simil ~~ symbolsearch 0.188 -0.227 -0.227
63 vocab ~~ matrixreason 0.143 -0.253 -0.253
109 lnseq ~~ digsym 0.128 -0.951 -0.951
38 verbalcomp =~ symbolsearch 0.077 0.015 0.094
118 matrixreason ~~ digsym 0.060 -0.380 -0.380
41 workingmemory =~ inform 0.037 0.021 0.053
119 matrixreason ~~ symbolsearch 0.031 -0.085 -0.085
108 lnseq ~~ matrixreason 0.017 0.069 0.069
110 lnseq ~~ symbolsearch 0.009 0.072 0.072
65 vocab ~~ symbolsearch 0.005 -0.068 -0.068
84 inform ~~ symbolsearch 0.004 -0.045 -0.045
82 inform ~~ matrixreason 0.004 0.029 0.029
sepc.all sepc.nox
66 -0.431 -0.431
56 0.858 0.858
48 -0.441 -0.441
115 -0.311 -0.311
96 0.439 0.439
117 0.366 0.366
47 -0.286 -0.286
81 0.249 0.249
64 -0.288 -0.288
40 0.220 0.220
72 -0.226 -0.226
45 0.264 0.264
95 -0.314 -0.314
60 -0.258 -0.258
67 0.203 0.203
44 0.251 0.251
51 0.254 0.254
62 -0.302 -0.302
73 0.184 0.184
106 0.184 0.184
91 0.172 0.172
59 0.257 0.257
37 -0.248 -0.248
68 0.255 0.255
99 -0.290 -0.290
57 -0.344 -0.344
87 0.159 0.159
97 0.237 0.237
107 0.158 0.158
34 0.192 0.192
78 -0.151 -0.151
33 -0.163 -0.163
54 0.194 0.194
39 -0.143 -0.143
102 -0.158 -0.158
35 -0.178 -0.178
88 0.137 0.137
112 0.144 0.144
101 0.140 0.140
46 -0.183 -0.183
71 0.132 0.132
76 -0.136 -0.136
70 -0.116 -0.116
50 0.154 0.154
58 -0.267 -0.267
55 0.253 0.253
113 0.119 0.119
93 1.526 1.526
86 -0.114 -0.114
80 -0.113 -0.113
104 -0.102 -0.102
114 -0.138 -0.138
89 0.110 0.110
90 -0.095 -0.095
74 -0.086 -0.086
43 -0.113 -0.113
49 0.108 0.108
92 0.085 0.085
111 -0.117 -0.117
85 -0.107 -0.107
32 0.092 0.092
79 -0.061 -0.061
69 0.064 0.064
53 -0.273 -0.273
77 0.089 0.089
116 0.063 0.063
120 0.057 0.057
100 -0.053 -0.053
83 0.050 0.050
36 0.062 0.062
61 0.069 0.069
105 -0.049 -0.049
52 -0.352 -0.352
98 -0.062 -0.062
94 -0.078 -0.078
31 -0.061 -0.061
103 0.030 0.030
42 -0.029 -0.029
75 -0.029 -0.029
63 -0.033 -0.033
109 -0.021 -0.021
38 0.023 0.023
118 -0.015 -0.015
41 0.012 0.012
119 -0.013 -0.013
108 0.008 0.008
110 0.006 0.006
65 -0.007 -0.007
84 -0.004 -0.004
82 0.004 0.004Model Update III
Fit Statistics
lavaan 0.6-12 ended normally after 114 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 28
Number of observations 300
Model Test User Model:
Test statistic 212.813
Degrees of freedom 50
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 1042.916
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.833
Tucker-Lewis Index (TLI) 0.780
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9929.572
Loglikelihood unrestricted model (H1) -9823.166
Akaike (AIC) 19915.144
Bayesian (BIC) 20018.850
Sample-size adjusted Bayesian (BIC) 19930.051
Root Mean Square Error of Approximation:
RMSEA 0.104
90 Percent confidence interval - lower 0.090
90 Percent confidence interval - upper 0.119
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.071
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
verbalcomp =~
vocab 1.000
simil 0.361 0.035 10.184 0.000
inform 0.525 0.048 10.857 0.000
compreh 0.334 0.036 9.349 0.000
workingmemory =~
arith 1.000
digspan 0.857 0.149 5.768 0.000
lnseq 0.193 0.104 1.850 0.064
performance =~
piccomp 1.000
block 3.737 0.390 9.581 0.000
matrixreason 0.843 0.118 7.176 0.000
digsym 1.615 0.508 3.181 0.001
symbolsearch 1.875 0.203 9.218 0.000
Std.lv Std.all
5.888 0.824
2.125 0.664
3.090 0.706
1.965 0.547
2.565 0.857
2.199 0.558
0.495 0.123
1.515 0.650
5.662 0.734
1.278 0.499
2.446 0.208
2.841 0.688
Covariances:
Estimate Std.Err z-value P(>|z|)
.simil ~~
.inform -3.738 0.606 -6.169 0.000
verbalcomp ~~
workingmemory 6.278 1.181 5.315 0.000
performance 5.654 0.859 6.583 0.000
workingmemory ~~
performance 2.237 0.363 6.172 0.000
Std.lv Std.all
-3.738 -0.503
0.416 0.416
0.634 0.634
0.576 0.576
Variances:
Estimate Std.Err z-value P(>|z|)
.vocab 16.365 2.375 6.892 0.000
.simil 5.734 0.610 9.399 0.000
.inform 9.635 1.095 8.801 0.000
.compreh 9.026 0.791 11.413 0.000
.arith 2.380 1.037 2.294 0.022
.digspan 10.715 1.154 9.282 0.000
.lnseq 15.830 1.298 12.193 0.000
.piccomp 3.143 0.316 9.937 0.000
.block 27.457 3.220 8.527 0.000
.matrixreason 4.921 0.439 11.216 0.000
.digsym 132.218 10.920 12.108 0.000
.symbolsearch 8.996 0.958 9.393 0.000
verbalcomp 34.667 4.408 7.865 0.000
workingmemory 6.579 1.239 5.309 0.000
performance 2.296 0.407 5.643 0.000
Std.lv Std.all
16.365 0.321
5.734 0.560
9.635 0.502
9.026 0.700
2.380 0.266
10.715 0.689
15.830 0.985
3.143 0.578
27.457 0.461
4.921 0.751
132.218 0.957
8.996 0.527
1.000 1.000
1.000 1.000
1.000 1.000
R-Square:
Estimate
vocab 0.679
simil 0.440
inform 0.498
compreh 0.300
arith 0.734
digspan 0.311
lnseq 0.015
piccomp 0.422
block 0.539
matrixreason 0.249
digsym 0.043
symbolsearch 0.473Comparing Models
You can conduct a likelihood ratio test to see whether the models fit significantly differently. The significant result indicates that the three-factor model with the added correlated error term fits significantly better than the original model.
Chi-Squared Difference Test
Df AIC BIC Chisq Chisq diff Df diff
wais.fit1.1 50 19915 20019 212.81
wais.fit1 51 19953 20053 252.81 39.996 1
Pr(>Chisq)
wais.fit1.1
wais.fit1 2.545e-10 ***
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Signif. codes:
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Moreover, you can compare fit statistics for both models. both AIC and ECVI are smaller. The revised model’s AIC is lower, indicating a better fit.
aic ecvi
19953.141 1.023 ECVI, or Expected Cross Validation Index, indicates the likelihood this model will replicate with the same sample size and population. The revised model’s ECVI is also lower, indicating a better fit.
aic ecvi
19915.144 0.896 Path Diagram III
Path Diagram of the Final Model
