Jinsong Chen

Shi-Ting Chen, Jinsong Chen

Newly developed items must ordinarily be field tested before their psychometric properties are known, creating a cold start problem for item calibration. Predicting item parameters from features is a long standing measurement problem dating back to the Linear Logistic Test Model; modern text embeddings now automate the design matrices traditionally specified by hand. We propose an evaluation framework combining regularized regression on item text embeddings, repeated cross validated R squared reported with its resampling standard deviation, and two performance upper bounds: a reliability ceiling derived from parameter standard errors, and a design ceiling derived from simulation based power calibration. Applying this framework to a mathematics item bank (EEDI) and a medical licensure benchmark (BEA 2024), we find that item difficulty is highly predictable from text (repeated cross validated R squared = 0.53, or about 57% of its reliability ceiling), whereas discrimination and pseudo guessing appear less predictable. However, evaluating these results against our ceilings reveals that this apparent hierarchy stems from target reliability rather than text signal strength: text uniformly recovers 57 to 63% of the reliable variance across difficulty targets, whereas the 3PL pseudo guessing parameter has a reliability ceiling near zero, making it an unviable target at current precision. On BEA, embedding based regression matches leaderboard RMSE despite explaining almost no variance, highlighting the critical need for scale free metrics and explicit ceilings in benchmarking. Finally, we show that a single train and test split can inflate apparent accuracy by 0.1 to 0.15 in R squared, underscoring the necessity of repeated cross validation for calibration support applications and future benchmark construction.

Jinsong Chen, Yi Jin

In partially exploratory factor analysis (PEFA), the loading structure and factor numbers are weakly specified. The regularized variational approximation for partially confirmatory factor analysis (PCFA VA) recovers this structure via Bayesian variable selection, using spike and slab priors to assign inclusion probabilities to unspecified loadings. This research introduces a post selection assessment framework for this approach. We convert converged solutions into covariance models using either hard selection (thresholding probabilities into a sparse pattern) or soft selection (retaining them as weights for effective parameter counts). We derive the resulting degrees of freedom, absolute fit diagnostics (RMSEA, SRMR, CFI, TLI), and relative criteria (AIC, BIC, ELBO). To determine factor numbers, we propose a scale free gain rule with a sustained drop guard. Simulations show absolute indices successfully track loading recovery and flag under factoring. While raw criteria over factor, our gain rule accurately recovers true dimensionality, with the ELBO variant proving most robust. Finally, a 100 item PID 5 example demonstrates that our model fits better than a confirmatory 25 facet model and concordantly recovers major structures across disjoint specifications.