Noel Cadigan | Searcharxiv

arXiv2026

A unifying theory for the evaluation of conditional Akaike information for mixed-effects models

We propose two methods to evaluate the conditional Akaike information (cAI) for mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed and random effects estimators with respect to observations. Method 2, compatible with any type of observation, requires modeling the marginal (or prior) distribution of random effects as a multivariate normal distribution. Simulations show that Method 1 performs well with Gaussian data but struggles with skewed continuous distributions, whereas Method 2 consistently performs well across various distributions, including normal, gamma, negative binomial, and Tweedie, with flexible link functions. A case study demonstrates the differences in model selection for real-world data between the conventional AIC and the conditional AIC. Based on our findings, we recommend Method 2 as a distributionally robust cAI criterion for model selection in mixed-effects models.

stat.ME↗

arXiv2024

Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models

Statistical inference for high dimensional parameters (HDPs) can be based on their intrinsic correlation; that is, parameters that are close spatially or temporally tend to have more similar values. This is why nonlinear mixed-effects models (NMMs) are commonly (and appropriately) used for models with HDPs. Conversely, in many practical applications of NMM, the random effects (REs) are actually correlated HDPs that should remain constant during repeated sampling for frequentist inference. In both scenarios, the inference should be conditional on REs, instead of marginal inference by integrating out REs. In this paper, we first summarize recent theory of conditional inference for NMM, and then propose a bias-corrected RE predictor and confidence interval (CI). We also extend this methodology to accommodate the case where some REs are not associated with data. Simulation studies indicate that this new approach leads to substantial improvement in the conditional coverage rate of RE CIs, including CIs for smooth functions in generalized additive models, as compared to the existing method based on marginal inference.

stat.ME↗