| Structure | K | LogLik | AIC | BIC |
|---|---|---|---|---|
| EEI | 1 | -3671.9414001881 | 7367.8828003761 | 7415.1648554088 |
| EEI | 2 | -3345.7967597969 | 6729.5935195939 | 6804.4567733956 |
| EEI | 3 | -3261.6618444566 | 6575.3236889131 | 6677.7681414839 |
| EEI | 4 | -3218.1942882966 | 6502.3885765931 | 6632.4142279329 |
| EEI | 5 | -3170.3225449758 | 6420.6450899515 | 6578.2519400604 |
| EEI | 6 | -3151.150498259 | 6396.300996518 | 6581.4890453958 |
| VVI | 1 | -3671.9414001881 | 7367.8828003761 | 7415.1648554088 |
| VVI | 2 | -3330.9685858947 | 6711.9371717894 | 6810.4414531074 |
| VVI | 3 | -3245.0267007506 | 6566.0534015013 | 6715.7799091047 |
| VVI | 4 | -3192.3066036243 | 6486.6132072485 | 6687.5619411373 |
| VVI | 5 | -3154.4826687829 | 6436.9653375658 | 6689.1362977399 |
| VVI | 6 | -3129.0243069576 | 6412.0486139151 | 6715.4418003746 |
| EEE | 1 | -3128.9856402749 | 6311.9712805498 | 6418.3559043732 |
| EEE | 2 | -3112.2597795494 | 6292.5195590988 | 6426.4853816913 |
| EEE | 3 | -3092.1891265516 | 6266.3782531032 | 6427.9252744647 |
| EEE | 4 | -3076.420910891 | 6248.841821782 | 6437.9700419126 |
| EEE | 5 | -3068.8115375708 | 6247.6230751415 | 6464.3324940412 |
| EEE | 6 | -3061.6904981259 | 6247.3809962518 | 6491.6716139204 |
| VVV | 1 | -3128.9856402749 | 6311.9712805498 | 6418.3559043732 |
| VVV | 2 | -3075.8786080451 | 6261.7572160902 | 6478.4666349898 |
| VVV | 3 | -3043.0770243884 | 6252.1540487768 | 6579.1882627526 |
| VVV | 4 | -3014.6093935783 | 6251.2187871566 | 6688.5777962086 |
| VVV | 5 | -2963.2025748559 | 6204.4051497118 | 6752.0889538399 |
| VVV | 6 | -2942.0744084375 | 6218.148816875 | 6876.1574160793 |
Sample Latent Profile Analysis Audit
This synthetic audit compares covariance assumptions, model stability, and two ways to estimate differences in persistence. The generating model used three overlapping profiles with correlated indicators. The fitted models may recover a different structure.
Analysis sample and missingness
Of 600 simulated cases, 380 had all six indicators. The achieved missing-cell rate was 8.22%. The mask depends on observed stress by design. In a diagnostic regression, the estimated log odds of any missing indicator changed by 0.899 per unit of stress. Observed associations assess plausibility. Neither descriptive checks nor Little’s test alone establish MCAR or MAR. Complete cases provide a common comparison sample here. Deletion under MAR can change the target population and estimates.
Model fit
BIC, AIC, SABIC and classification-based ICL use the lower-is-better convention. The one-component covariance aliases are shown under both grid labels. BLRT was omitted. Bootstrap LRT interpretation depends on sample size and a mixture reference distribution.
Additional information criteria
| Structure | K | SABIC | ICL | BLRT p |
|---|---|---|---|---|
| EEI | 1 | 7377.0912017152 | 7415.1648554088 | Not computed |
| EEI | 2 | 6744.1734883808 | 6844.9572038483 | Not computed |
| EEI | 3 | 6595.2752251479 | 6768.6587425232 | Not computed |
| EEI | 4 | 6527.7116802757 | 6730.2800933335 | Not computed |
| EEI | 5 | 6451.3397610819 | 6703.6765367096 | Not computed |
| EEI | 6 | 6432.3672350961 | 6717.0052141841 | Not computed |
| VVI | 1 | 7377.0912017152 | 7415.1648554088 | Not computed |
| VVI | 2 | 6731.1213412458 | 6850.8157952359 | Not computed |
| VVI | 3 | 6595.2133390751 | 6793.8318202846 | Not computed |
| VVI | 4 | 6525.7489129397 | 6774.9165047132 | Not computed |
| VVI | 5 | 6486.0768113743 | 6796.7538062062 | Not computed |
| VVI | 6 | 6471.135855841 | 6826.5474763666 | Not computed |
| EEE | 1 | 6332.6901835627 | 6418.3559043732 | Not computed |
| EEE | 2 | 6318.6100295596 | 6504.4235887673 | Not computed |
| EEE | 3 | 6297.8402910118 | 6560.4384781843 | Not computed |
| EEE | 4 | 6285.6754271385 | 6560.6638808734 | Not computed |
| EEE | 5 | 6289.8282479458 | 6605.4625309117 | Not computed |
| EEE | 6 | 6294.9577365038 | 6670.3061411841 | Not computed |
| VVV | 1 | 6332.6901835627 | 6418.3559043732 | Not computed |
| VVV | 2 | 6303.9623888944 | 6554.0040769165 | Not computed |
| VVV | 3 | 6315.8454913723 | 6690.3971694429 | Not computed |
| VVV | 4 | 6336.3964995433 | 6747.770119415 | Not computed |
| VVV | 5 | 6311.0691318898 | 6837.5013023752 | Not computed |
| VVV | 6 | 6346.2990688441 | 6947.246740102 | Not computed |
Classification and stability
Entropy of 0.80 and minimum AvePP of 0.70 are contextual guides to classification precision. Entropy is undefined for one profile. Class size is based on modal assignment. Each multi-profile fit starts from a hierarchical initialization and eight seeded random-center partitions. A repeat is a converged solution within 0.001 log likelihood units of the best converged fit. Repeated likelihoods do not establish a global optimum.
| Covariance | K | Entropy | Min AvePP | Min class % | Min class n |
|---|---|---|---|---|---|
| EEI | 1 | Not computed | 1 | 100 | 380 |
| EEI | 2 | 0.84336536128 | 0.93664481555 | 40 | 152 |
| EEI | 3 | 0.78604750633 | 0.87281755327 | 20.5263157895 | 78 |
| EEI | 4 | 0.80585193631 | 0.81385626042 | 12.1052631579 | 46 |
| EEI | 5 | 0.79272222469 | 0.83128616323 | 12.1052631579 | 46 |
| EEI | 6 | 0.79286316318 | 0.82770953784 | 7.1052631579 | 27 |
| VVI | 1 | Not computed | 1 | 100 | 380 |
| VVI | 2 | 0.84975606304 | 0.93933922402 | 39.2105263158 | 149 |
| VVI | 3 | 0.81205548109 | 0.89713166672 | 18.6842105263 | 71 |
| VVI | 4 | 0.81719562481 | 0.86533643929 | 11.3157894737 | 43 |
| VVI | 5 | 0.80880583222 | 0.84634823355 | 11.0526315789 | 42 |
| VVI | 6 | 0.82344021898 | 0.85419838964 | 5.7894736842 | 22 |
| EEE | 1 | Not computed | 1 | 100 | 380 |
| EEE | 2 | 0.70134017873 | 0.85389341063 | 27.3684210526 | 104 |
| EEE | 3 | 0.66951151896 | 0.83040589665 | 28.1578947368 | 107 |
| EEE | 4 | 0.75168272041 | 0.84735855793 | 11.0526315789 | 42 |
| EEE | 5 | 0.75475829683 | 0.74327904024 | 8.4210526316 | 32 |
| EEE | 6 | 0.72569445157 | 0.7228740252 | 9.4736842105 | 36 |
| VVV | 1 | Not computed | 1 | 100 | 380 |
| VVV | 2 | 0.70915176812 | 0.90356905043 | 42.1052631579 | 160 |
| VVV | 3 | 0.72411254992 | 0.76190091094 | 22.6315789474 | 86 |
| VVV | 4 | 0.88086935488 | 0.88041638589 | 4.2105263158 | 16 |
| VVV | 5 | 0.85336117088 | 0.81979071088 | 6.8421052632 | 26 |
| VVV | 6 | 0.89095471982 | 0.79497897342 | 4.7368421053 | 18 |
Start replication and flags
| Model | K | Starts | OK | Repeats | Flags |
|---|---|---|---|---|---|
| EEI | 1 | 1 | 1 | 1 | Clear |
| EEI | 2 | 9 | 9 | 9 | Clear |
| EEI | 3 | 9 | 9 | 9 | Clear |
| EEI | 4 | 9 | 9 | 3 | Clear |
| EEI | 5 | 9 | 9 | 9 | Clear |
| EEI | 6 | 9 | 9 | 1 | Best likelihood not replicated |
| VVI | 1 | 1 | 1 | 1 | Clear |
| VVI | 2 | 9 | 9 | 9 | Clear |
| VVI | 3 | 9 | 9 | 8 | Clear |
| VVI | 4 | 9 | 9 | 5 | Clear |
| VVI | 5 | 9 | 9 | 3 | Clear |
| VVI | 6 | 9 | 9 | 1 | Best likelihood not replicated; Small modal class |
| EEE | 1 | 1 | 1 | 1 | Clear |
| EEE | 2 | 9 | 9 | 6 | Clear |
| EEE | 3 | 9 | 9 | 5 | Clear |
| EEE | 4 | 9 | 9 | 2 | Clear |
| EEE | 5 | 9 | 9 | 1 | Best likelihood not replicated |
| EEE | 6 | 9 | 9 | 1 | Best likelihood not replicated |
| VVV | 1 | 1 | 1 | 1 | Clear |
| VVV | 2 | 9 | 9 | 4 | Clear |
| VVV | 3 | 9 | 9 | 2 | Clear |
| VVV | 4 | 9 | 9 | 1 | Best likelihood not replicated; Small modal class |
| VVV | 5 | 9 | 9 | 1 | Best likelihood not replicated |
| VVV | 6 | 9 | 9 | 1 | Best likelihood not replicated; Small modal class |
Review flagged candidates before interpretation.
- Some candidates contain a class below 5% or 25 modal assignments. Assess stability in resamples or independent data.
Covariance sensitivity
The table gives the lowest BIC among candidates with no stability flags in each structure. Interpret the comparison alongside the full grid.
| covariance | K | BIC |
|---|---|---|
| EEI | 5 | 6578.2519400604 |
| VVV | 1 | 6418.3559043732 |
Distal outcome comparison
The demonstration fixes the three-profile VVV solution in advance and orders classes by their average indicator mean. The naive OLS estimates use modal classes and conventional standard errors. BCH inverts the posterior-estimated modal classification matrix and applies the resulting signed weights to class means. Its case bootstrap re-estimates that matrix with the indicator fit fixed. The resulting SE is conditional on that fit and excludes model selection uncertainty. The correction assumes modal assignment and persistence are independent within the true profile. Error is the estimate minus the generating contrast in this one simulation. Sampling and classification both contribute to the difference.
| Contrast | Target | Modal OLS | OLS SE | OLS error |
|---|---|---|---|---|
| 2 vs 1 | 0.65 | 0.46644843556 | 0.13262823771 | -0.18355156444 |
| 3 vs 1 | 1.35 | 0.93865078055 | 0.1214126777 | -0.41134921945 |
Corrected contrasts
| Contrast | BCH estimate | Conditional SE | BCH error |
|---|---|---|---|
| 2 vs 1 | 0.5725108129 | 0.18864748999 | -0.077489187103 |
| 3 vs 1 | 1.0512551835 | 0.13320325234 | -0.29874481646 |
Profiles describe patterns of indicators in an analysis sample. Causal mechanisms and discrete latent types require separate evidence.
Method reference Bakk and Vermunt (2016).