Expected versus observed information in SEM with incomplete normal and nonnormal data.
Bibliographic record
Abstract
Maximum likelihood is the most common estimation method in structural equation modeling. Standard errors for maximum likelihood estimates are obtained from the associated information matrix, which can be estimated from the sample using either expected or observed information. It is known that, with complete data, estimates based on observed or expected information are consistent. The situation changes with incomplete data. When the data are missing at random (MAR), standard errors based on expected information are not consistent, and observed information should be used. A less known fact is that in the presence of nonnormality, the estimated information matrix also enters the robust computations (both standard errors and the test statistic). Thus, with MAR nonnormal data, the use of the expected information matrix can potentially lead to incorrect robust computations. This article summarizes the results of 2 simulation studies that investigated the effect of using observed versus expected information estimates of standard errors and test statistics with normal and nonnormal incomplete data. Observed information is preferred across all conditions. Recommendations to researchers and software developers are outlined.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.131 | 0.544 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".