The performance of unweighted least squares and regularized unweighted least squares in estimating factor loadings in structural equation modeling
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Bibliographic record
Abstract
In a confirmatory study, researchers are expected to employ the covariance-based structural equation modeling (CB-SEM). One of the key presumptions when utilizing CB-SEM is that the data is multivariate normal. Nevertheless, a perfect normal distribution is rarely observed in real-life data. To resolve this, the unweighted least square (ULS) is designed to specifically deal with non-normal data in SEM. However, ULS often yields improper solutions like negative, or boundary estimates of unique variances since it considers measurement errors in observed variables. The disturbance in SEM is reflected in unique variance, which is random error due to unreliability or measurement error and reliable variation in the item that indicates unknown latent causes. Consequently, this can generate bias in indicator loadings estimates. As an action to disentangle this issue, the present study proposes the implementation of regularization parameters by adding small positive values to the variance-covariance matrix. The ratio of bias to variance in a model can be improved to obtain the best estimation performance. Pro-Active Monte Carlo simulation was used to produce multivariate non-normal data with designated sample sizes and population characteristics. The data were analyzed using R Programming Environment by employing “psych”, “MASS”, “foreign”, “mvrnonnorm”, “purr”, and “semTools” packages with 1000 replications to produce multivariate non-normal data. Next, the “lavaan” package was used for SEM and regularized SEM analyses. The outcome of this study proves the capability of regularized ULS to improve parameter estimation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it