smoothed piecewise regression

This study addresses the limitation of traditional regression adjustment methods, which can only estimate average treatment effects and fail to capture the dynamic evolution of treatment effects over time. The authors propose a novel longitudinal treatment effect estimation framework that, for the first time, incorporates time-varying covariate transition mechanisms into regression adjustment. By modeling post-treatment covariate trajectories through transition kernels, the method enables a fine-grained characterization of effect heterogeneity across time. The proposed estimator is theoretically shown to achieve the semiparametric efficiency bound and possesses asymptotic normality. Both simulation studies and empirical analysis using A/B test data from a Japanese streaming platform demonstrate that the approach substantially reduces estimation variance and enhances statistical inference efficiency.

This paper addresses the joint selection of the number and continuity type (continuous vs. discontinuous) of change-points in segmented regression models. We derive, for the first time, model-specific information criteria rigorously grounded in the original Akaike Information Criterion (AIC) definition. Theoretical analysis reveals distinct penalty terms for change-point parameters: 6 for discontinuous models and 2 for continuous ones, with derivative discontinuities leaving the penalty structure unchanged. Our method integrates statistical asymptotic theory, the AIC information-theoretic framework, and Monte Carlo simulation, and is validated on real epidemiological datasets—including COVID-19 incidence series. Results demonstrate that the proposed AIC-type criterion more effectively minimizes the Kullback–Leibler divergence between true and estimated model structures than the Bayesian Information Criterion (BIC). It frequently yields different model selections from BIC, offering a more robust and theoretically coherent tool for longitudinal trend analysis.

Traditional piecewise regression models often assume abrupt change points and ignore population heterogeneity, limiting their ability to capture smooth transitions and systematic differences observed in real-world data. This work proposes the smoothbp R package, which implements a Bayesian hierarchical framework incorporating a logistic smooth transition mechanism and Kuo–Mallick spike-and-slab priors to enable automatic selection of the number of breakpoints. The model accommodates random intercepts, random breakpoints, and covariate effects. Computational efficiency is substantially enhanced through a custom Metropolis-within-Gibbs sampler implemented in Rust, which integrates conjugate updates with Hamiltonian Monte Carlo (HMC). Simulation studies demonstrate that the method yields accurate parameter estimates and well-calibrated posterior inference, outperforming existing tools such as brms and mcp in both modeling flexibility and computational performance.

Standard hidden Markov models (HMMs) lack flexibility in incorporating covariates to elucidate drivers of state transitions or to construct Markov-switching regression models. Method: We develop the R package `hmmTMB`, the first framework to unify automatic smoothness-selection multivariate penalized splines, hierarchical random effects, and generalized response distributions within the HMM paradigm. It enables nonlinear covariate effects in both transition probabilities and observation parameters, and supports extensions such as semi-Markov and higher-order Markov structures. Inference leverages the Template Model Builder (TMB), Laplace approximation, and ADMB’s automatic differentiation for efficient Bayesian estimation. Contribution/Results: Applied to complex time-series data—including animal movement tracking—`hmmTMB` significantly improves state decoding accuracy and interpretability of covariate effects. It broadens the applicability and flexibility of HMMs in ecology, medicine, and finance by enabling rich, interpretable, and computationally scalable modeling of dynamic processes.

To address low covariate efficiency and poor scalability to high-dimensional settings in regression discontinuity (RD) designs, this paper proposes a novel class of covariate-adjusted estimators. The method achieves efficient adjustment by subtracting from the outcome variable an optimal nonparametric prediction function of the covariates. Crucially, it preserves the intrinsic robustness of RD estimation while enabling flexible, data-driven estimation of the adjustment function via modern machine learning tools—including Lasso and random forests. Notably, it is the first RD adjustment framework that simultaneously attains asymptotic variance minimization and compatibility with machine learning estimators. Theoretical analysis confirms that the estimator’s first-order asymptotic properties remain unchanged. Empirical re-analyses demonstrate average standard error reductions of 15–30%. The approach is plug-in, computationally lightweight, and broadly applicable across diverse RD settings.

Traditional likelihood-based approaches struggle to flexibly accommodate complex structures in nonlinear longitudinal data, such as random change points, multiple latent classes, and multivariate associations. This work proposes a unified Bayesian piecewise random-effects modeling framework and introduces BEND, an open-source R package that integrates core models—including Bayes_PREM, Bayes_BPREM, and Bayes_CREM—for the first time. The framework enables data-driven change point detection, latent class discovery, bivariate joint modeling, and covariate integration. Leveraging Markov chain Monte Carlo (MCMC) algorithms, the proposed method substantially enhances model flexibility, practical utility, and interpretability. Empirical analyses demonstrate its effectiveness in handling complex longitudinal data structures.

This study addresses the challenges in traditional change-plane regression—namely, non-differentiability of the objective function, weak boundary identifiability, and unstable large-sample inference caused by hard-threshold boundaries. To overcome these issues, the authors propose a Bayesian inference framework based on a probit-gated smooth likelihood, which employs a controllable smoothing approximation to handle non-smoothness while asymptotically recovering the true hard-threshold boundary as the smoothing scale approaches zero. The work innovatively incorporates a misspecification-robust Bernstein–von Mises theorem to characterize the trade-off between smoothing scale and Gaussian approximation error, and introduces a decision-theoretic mechanism that disentangles evidence for heterogeneity from boundary reporting. Simulation studies and empirical analyses demonstrate that the proposed method outperforms existing frequentist approaches in both estimation accuracy and uncertainty quantification, successfully uncovering heterogeneous treatment effects in lifestyle interventions.

This study addresses the identification of dynamic, evolving patterns in longitudinal, multidimensional women’s health symptoms that are associated with subsequent fall risk. To this end, the authors propose a heterogeneous latent transition analysis framework: individuals are first stratified into latent classes based on symptom response profiles, and then multilevel clustering is applied to sequences of class transitions, jointly modeling their association with fall outcomes. The method integrates Bayesian inference, latent transition modeling, and longitudinal categorical data analysis, and demonstrates strong performance in parameter estimation and cluster recovery, as validated through Monte Carlo simulations. Empirical analysis successfully uncovers several symptom trajectories that significantly predict fall risk, offering an effective tool for pattern discovery in complex longitudinal health data.

This study addresses the challenge that existing statistical methods struggle to effectively estimate average treatment effects in experiments involving both randomly assigned treatments and fixed covariates. The authors develop a unified theoretical framework that, for the first time, establishes a general estimating equation theory for misspecified linear regression models with mixed regressors—combining random treatment indicators and fixed covariates—and extends this framework to clustered data settings. By integrating estimating equations, misspecification-robust analysis, and causal inference techniques, the proposed approach yields valid causal interpretations of regression coefficients and their standard errors even under model misspecification. This methodology is broadly applicable to practical experimental designs, including completely randomized trials.

This study addresses the challenge of simultaneously unknown jump locations and segment levels in piecewise constant regression. The authors propose an integrated estimation framework that combines least squares with Bayesian inference and introduce two novel information criteria—AJIC and BJIC—specifically designed for selecting the number of change points in jump models. Theoretical analysis establishes a convergence rate of order $n$ for jump locations and $\sqrt{n}$ for level parameters. The proposed Bayesian approach demonstrates superior estimation accuracy compared to conventional methods, while the new criteria effectively identify the optimal jump configuration, enabling both efficient parameter estimation and reliable statistical inference.