Data Analysis and Power Simulations with General Linear Mixed Modelling for Psychophysical Data – A Practical, R-Based Guide
Bibliographic record
Abstract
Sample size planning is not straight-forward for the complex designs that are usually employed in psychophysical (two-alternative forced-choice) experiments: characteristics such as binary response variables and nested data structures where responses may be correlated differently within participants and experimental sessions than across participants and experimental sessions make it harder to estimate the necessary number of participants and trials with traditional means. In this practical R-based guide, we first show in detail how we can simulate verisimilar psychophysical data. We then use these simulations to compare two different methods by which two-alternative forced-choice data can be analyzed: (1) the “two-step” approach, where first psychometric functions are fitted and then statistical tests are performed over the parameters of these fitted psychometric functions; (2) an approach based on Generalized Linear Mixed Modeling (GLMM) that does not require the intermediary step of fitting psychometric functions. We argue that the GLMM approach enhances statistical validity and show that it can increase statistical power. Finally, we provide a sample implementation of a simulation-based power analysis that can be used as-is for many simple designs, but is also easily adaptable for more complex designs. Overall, we show that a GLMM-based approach can be beneficial for data analysis and sample size planning for typical (two-alternative forced-choice) psychophysical designs.
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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 | 0.033 | 0.159 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.065 | 0.028 |
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".