A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models
Bibliographic record
Abstract
Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The literature on the topic has focused on conducting power analyses as well as identifying rules of thumb for deciding an appropriate sample size. Often the advice involves an assumption that sample size requirement is moderated by aspects of the model in question. In this study, an effort was undertaken to extend the findings of Gagné and Hancock (2006) Gagné, P. and Hancock, G. R. 2006. Measurement model quality, sample size, and solution propriety in confirmatory factor analysis. Multivariate Behavioral Research, 41: 65–83. [Taylor & Francis Online] , [Google Scholar] on measurement model quality and solution propriety to a broader set of confirmatory factor analysis models. As well, we examined whether Herzog, Boomsma, and Reinecke's (2007) findings for the Swain correction to the χ2 statistic for large models would generalize to models in our study. Our findings suggest that Gagné and Hancock's approach extends to large models with surprisingly little increase in sample size requirements and that the Swain correction to χ2 performs fairly well. We argue that likely rejection or model fit should be taken into account when determining sample size requirements and therefore, provide an updated table of minimum sample size that incorporates Gagné and Hancock's method and model fit.
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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 | 0.411 | 0.787 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.006 | 0.009 |
| Scholarly communication | 0.009 | 0.013 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.008 | 0.015 |
| Insufficient payload (model declined to judge) | 0.014 | 0.003 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".