A Computationally Efficient State Space Approach to Estimating Multilevel Regression Models and Multilevel Confirmatory Factor Models
Bibliographic record
Abstract
Although the state space approach for estimating multilevel regression models has been well established for decades in the time series literature, it does not receive much attention from educational and psychological researchers. In this article, we (a) introduce the state space approach for estimating multilevel regression models and (b) extend the state space approach for estimating multilevel factor models. A brief outline of the state space formulation is provided and then state space forms for univariate and multivariate multilevel regression models, and a multilevel confirmatory factor model, are illustrated. The utility of the state space approach is demonstrated with either a simulated or real example for each multilevel model. It is concluded that the results from the state space approach are essentially identical to those from specialized multilevel regression modeling and structural equation modeling software. More importantly, the state space approach offers researchers a computationally more efficient alternative to fit multilevel regression models with a large number of Level 1 units within each Level 2 unit or a large number of observations on each subject in a longitudinal study.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.007 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".