Model-averaged Estimates Research Articles

Investigating Causal Associations between the Gut Microbiota and Dementia: A Mendelian Randomization Study.

Background: The causal association of specific gut microbiota with dementia remains incompletely understood. We aimed to access the causal relationships in which one or more gut microbiota account for dementia. Method: Using data from the MiBioGen and FinnGen consortia, we employed multiple Mendelian randomization (MR) approaches including two-sample MR (TSMR), multivariable MR (MVMR), and Bayesian model averaging MR to comprehensively evaluate the causal associations between 119 genera and dementia, and to prioritize the predominant bacterium. Result: We identified 21 genera that had causal effects on dementia and suggested Barnesiella (OR = 0.827, 95%CI = 0.722-0.948, marginal inclusion probability [MIP] = 0.464; model-averaged causal estimate [MACE] = -0.068) and Allisonella (OR = 0.770, 95%CI = 0.693-0.855, MIP = 0.898, MACE = -0.204) as the predominant genera for AD and all-cause dementia. Conclusions: These findings confirm the causal relationships between specific gut microbiota and dementia, highlighting the necessity of multiple MR approaches in gut microbiota analysis, and provides promising genera as potential novel biomarkers for dementia risk.

A Subsampling Strategy for AIC-based Model Averaging with Generalized Linear Models

Subsampling is an effective approach to address computational challenges associated with massive datasets. However, existing subsampling methods do not consider model uncertainty. In this paper, we investigate the subsampling technique for the Akaike information criterion (AIC) and extend the subsampling method to the smoothed AIC model-averaging framework in the context of generalized linear models. By correcting the asymptotic bias of the maximized subsample objective function used to approximate the Kullback–Leibler divergence, we derive the form of the AIC based on the subsample. We then provide a subsampling strategy for the smoothed AIC model-averaging estimator and study the corresponding asymptotic properties of the loss and the resulting estimator. A practically implementable algorithm is developed, and its performance is evaluated through numerical experiments on both real and simulated datasets.

Optimal Instrument Selection Using Bayesian Model Averaging for Model Implied Instrumental Variable Two Stage Least Squares Estimators

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, noniterative estimator for latent variable models. Associated with this estimator are equation-specific tests of model misspecification. One issue with equation-specific tests is that they lack specificity, in that they indicate that some instruments are problematic without revealing which specific ones. Instruments that are poor predictors of their target variables (“weak instruments”) is a second potential problem. We propose a novel extension to detect instrument-specific tests of misspecification and weak instruments. We term this the Model-Implied Instrumental Variable Two-Stage Bayesian Model Averaging (MIIV-2SBMA) estimator. We evaluate the performance of MIIV-2SBMA against MIIV-2SLS in a simulation study and show that it has comparable performance in terms of parameter estimation. Additionally, our instrument-specific overidentification tests developed within the MIIV-2SBMA framework show increased power to detect specific problematic and weak instruments. Finally, we demonstrate MIIV-2SBMA using an empirical example.

Model Averaging for Accelerated Failure Time Models with Missing Censoring Indicators

Model averaging has become a crucial statistical methodology, especially in situations where numerous models vie to elucidate a phenomenon. Over the past two decades, there has been substantial advancement in the theory of model averaging. However, a gap remains in the field regarding model averaging in the presence of missing censoring indicators. Therefore, in this paper, we present a new model-averaging method for accelerated failure time models with right censored data when censoring indicators are missing. The model-averaging weights are determined by minimizing the Mallows criterion. Under mild conditions, the calculated weights exhibit asymptotic optimality, leading to the model-averaging estimator achieving the lowest squared error asymptotically. Monte Carlo simulations demonstrate that the method proposed in this paper has lower mean squared errors compared to other model-selection and model-averaging methods. Finally, we conducted an empirical analysis using the real-world Acute Myeloid Leukemia (AML) dataset. The results of the empirical analysis demonstrate that the method proposed in this paper outperforms existing approaches in terms of predictive performance.

Determinants of Military Spending in Africa: Do Institutions Matter?

Abstract This paper focuses on the determinants of military spending in Africa by considering the role played by institutions. With data obtained between the years 1996–2019, the Driscoll and Kraay fixed effects, the Generalised Method of Moments (GMM), and the Bayesian Model Averaging (BMA) estimators are used. The findings suggest that government size, trade freedom, economic risk, and political risk decrease military spending, whereas government stability and military involvement in politics are found to raise it. Using alternative institutional variables, we find that corruption, government effectiveness, political stability, regulatory quality, the rule of law, and voice and accountability significantly diminish military spending in Africa. In addition, concerning the economic determinants, the results reveal that trade openness and total natural resource rents reduce military spending, while GDP per capita, inflation, and foreign debt stocks increase it. Looking at strategic determinants, arms imports, urban population, and ethnic tensions positively affect African military expenditures. Robustness checks show that these results change once regional specificities are considered. The study concludes that institutional factors could be an engine for evolution in Africa’s military spending.

Optimal model averaging for semiparametric partially linear models with measurement errors

This paper is concerned with optimal model averaging procedure for semiparametric partially linear models where some covariates are subject to measurement error. We proposed a corrected semiparametric generalized least squares estimation for unknown parameters and nonparametric function, and developed a Mallows-type criterion for weight choice. The resulting model average estimator is shown to be asymptotically optimal in terms of achieving the smallest possible squared error under some regularity conditions. The simulation studies demonstrate that the proposed procedure is superior to traditional model selection and model averaging methods. Our approach is further applied to Ragweed Pollen Level data.

Effectiveness of the mindfulness–acceptance–commitment approach: a meta-analysis

ABSTRACT The presented study evaluates the evidence base underpinning the use of the Mindfulness–Acceptance–Commitment approach (MAC) in applied sport psychology. To assess the effectiveness of the MAC protocol on improving mindfulness and psychological flexibility, and on enhancing sport performance and well-being among athletes, we used Robust Bayesian Meta-Analysis with Publication Selection Model-Averaging (RoBMAPSMA). In total, there were eleven controlled trials included in the meta-analysis. Results of the RoBMAPSMA show: a moderate model-averaged effect size estimate for developing mindfulness with strong evidence (g = 0.64, 95% CI 0.00–0.91, BFes = 25.35); a small model-averaged effect size estimate for experiential acceptance with anecdotal evidence (g = 0.36, 95% CI 0.00–0.92, BFes = 2.32); and a small model-averaged effect size estimate for improving sport performance with moderate evidence (g = 0.37, 95% CI 0.00–0.79, BFes = 3.27). Only one study assessed the effectiveness of the MAC protocol on well-being and averaged effect sizes ranged from 0.01 to 0.82. Based on the results of the meta-analysis, the Mindfulness–Acceptance–Commitment protocol can be effective in improving mindfulness. In addition, results suggest that the MAC protocol might be effective in improving sport performance. Currently available trials, however, do not provide sufficient evidence supporting the MAC protocol's effectiveness in developing psychological flexibility, experiential acceptance, and promoting well-being among athletes.

Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data

In the past few decades, model averaging has received extensive attention, and has been regarded as a feasible alternative to model selection. However, this work is mainly based on parametric model framework and complete dataset. This paper develops a frequentist model-averaging estimation for semiparametric partially linear models with censored responses. The nonparametric function is approximated by B-spline, and the weights in model-averaging estimator are picked up via minimizing a leave-one-out cross-validation criterion. The resulting model-averaging estimator is proved to be asymptotically optimal in the sense of achieving the lowest possible squared error. A simulation study demonstrates that the method in this paper is superior to traditional model-selection and model-averaging methods. Finally, as an illustration, the proposed procedure is further applied to analyze two real datasets.

Phenome-wide Mendelian randomisation analysis identifies causal factors for age-related macular degeneration.

Age-related macular degeneration (AMD) is a leading cause of blindness in the industrialised world and is projected to affect >280 million people worldwide by 2040. Aiming to identify causal factors and potential therapeutic targets for this common condition, we designed and undertook a phenome-wide Mendelian randomisation (MR) study. We evaluated the effect of 4591 exposure traits on early AMD using univariable MR. Statistically significant results were explored further using: validation in an advanced AMD cohort; MR Bayesian model averaging (MR-BMA); and multivariable MR. Overall, 44 traits were found to be putatively causal for early AMD in univariable analysis. Serum proteins that were found to have significant relationships with AMD included S100-A5 (odds ratio [OR] = 1.07, p-value = 6.80E-06), cathepsin F (OR = 1.10, p-value = 7.16E-05), and serine palmitoyltransferase 2 (OR = 0.86, p-value = 1.00E-03). Univariable MR analysis also supported roles for complement and immune cell traits. Although numerous lipid traits were found to be significantly related to AMD, MR-BMA suggested a driving causal role for serum sphingomyelin (marginal inclusion probability [MIP] = 0.76; model-averaged causal estimate [MACE] = 0.29). The results of this MR study support several putative causal factors for AMD and highlight avenues for future translational research. This project was funded by the Wellcome Trust (224643/Z/21/Z; 200990/Z/16/Z); the University of Manchester's Wellcome Institutional Strategic Support Fund (Wellcome ISSF) grant (204796/Z/16/Z); the UK National Institute for Health Research (NIHR) Academic Clinical Fellow and Clinical Lecturer Programmes; Retina UK and Fight for Sight (GR586); the Australian National Health and Medical Research Council (NHMRC) (1150144).

Mallows Model Averaging Estimator for the MIDAS Model with Almon Polynomial Weight

Mallows Model Averaging Estimator for the MIDAS Model with Almon Polynomial Weight

Frequentist model averaging for zero‐inflated Poisson regression models

AbstractThis paper considers frequentist model averaging for estimating the unknown parameters of the zero‐inflated Poisson regression model. Our proposed weight choice procedure is based on the minimization of an unbiased estimator of a conditional quadratic loss function. We prove that the resulting model average estimator enjoys optimal asymptotic property and improves finite sample properties over the two commonly used information‐based model selection estimators and their model average estimators via simulation studies. The proposed method is illustrated by a real data example.

GMM Model Averaging Using Higher Order Approximations

Moment conditions model averaging (MA) estimators in the GMM framework are considered. Under finite sample considerations, MA estimators with optimal weights are proposed, in the sense that weights minimize the corresponding higher-order asymptotic mean squared error (AMSE). It is shown that the higher-order AMSE objective function has a closed-form expression, which makes this procedure applicable in practice. In addition, and as an alternative, different averaging schemes based on moment selection criteria are considered, in which weights for averaging across GMM estimates can be obtained by direct smoothing or by numerical minimization of a specific criterion. Asymptotic properties assuming correctly specified models are derived and the performance of the proposed averaging approaches is contrasted with existing model selection alternatives i) analytically, for a simple IV example, and ii) by means of Monte Carlo experiments in a nonlinear setting, showing that MA compares favourably in many relevant setups. The usefulness of MA methods is illustrated by studying the effect of institutions on economic performance.

Model averaging estimation of panel data models with many instruments and boosting

Applied researchers often confront two issues when using the fixed effect-two-stage least squares (FE-2SLS) estimator for panel data models. One is that it may lose its consistency due to too many instruments. The other is that the gain of using FE-2SLS may not exceed its loss when the endogeneity is weak. In this paper, an L 2 Boosting regularization procedure for panel data models is proposed to tackle the many instruments issue. We then construct a Stein-like model-averaging estimator to take advantage of FE and FE-2SLS-Boosting estimators. Finite sample properties are examined in Monte Carlo and an empirical application is presented.

Bayesian Model Averaging in Modeling of State Specific Failure Rates in HIV/AIDS Progression

In modeling HIV/AIDS progression, we carried out a comprehensive investigation into the risk factors for state-specific-failure rates to identify the influential co-variates using Bayesian Model averaging method (BMA). BMA provides a posterior probability via Markov Chain Monte Carlo (MCMC) for each variable that belongs to the model. It accounts for model uncertainty by averaging all plausible models using their posterior probabilities as the weights for model-averaged predictions and estimates of the required parameters. Patients' age, and gender, among other co-variates, have been found to influence the state-specific-failure rates highly. However, the impact of each of the factors on the state specific-failure was not quantified. This paper seeks to evaluate and quantify the contribution of the patient's age and gender, CD4 cell count during any two consecutive visits, and state movement on the state-specific-failure rates for patients transiting either to the same, better or worse state. We used R Studio statistical Programming software to implement the method by applying BMS and BMA packages. State movement had a comparatively large coefficient with a posterior inclusion probability (PIP) of 0.8788 (87.88%). Hence, the most critical variable followed by observation-two-CD4-cell-count with a PIP of 0.1416 (14.16%), age and gender were the last with a PIP of 0.0556 (5.56%) and 0.0510 (5.10%) respectively for patients transiting to the same state. For patients transiting to a better state, the patients' age group dominated with a PIP of 0.9969 (99.69%), followed by patients' gender with a PIP of 0.0608 (6.08%). Patients' CD4 cell count during the second observation had the least PIP of 0.0399 (3.99%). For patients transiting to a worse disease state, patients CD4 cell count during the second observation proved to be the most important, with a PIP of 0.6179(61.79%) followed by state movement with a PIP of 0.2599 (25.99%), patients gender tailed with a PIP of 0.0467 (4.67%).

Frequentist model averaging under inequality constraints

Motivated by the inability of the Akaike information criterion to distinguish between statistical models with inequality constraints on parameters, a series of papers have considered alternative model selection criteria for models under inequality constraints. Among the criteria proposed, the order-restricted information criterion and its generalised version have received the most attention. This paper considers the alternative approach of model averaging, where estimates are obtained based not on one single linear model, but a weighted ensemble of linear models each subject to a distinct set of linear inequality constraints. We develop a J-fold cross validation criterion for choosing model weights that reflect the support of the models by the data, and prove that the resultant model average estimator has an optimal asymptotic property. We further prove that for the special case of a finite number of regressors, the sum of the weights obtained by the proposed method for models with the correct inequality constraints converges to one in probability. In our limited simulation study and real data analysis, it is observed that the proposed model average estimator frequently outperforms the estimator that arises from the generalised order-restricted information-based model selection criterion in terms of average MSE and median MSE.

Model selection and model averaging for matrix exponential spatial models

In this paper, we focus on a model specification problem in spatial econometric models when an empiricist needs to choose from a pool of candidates for the spatial weights matrix. We propose a model selection (MS) procedure for the matrix exponential spatial specification (MESS), when the true spatial weights matrix may not be in the set of candidate spatial weights matrices. We show that the selection estimator is asymptotically optimal in the sense that asymptotically it is as efficient as the infeasible estimator that uses the best candidate spatial weights matrix. The proposed selection procedure is also consistent in the sense that when the data generating process involves spatial effects, it chooses the true spatial weights matrix with probability approaching one in large samples. We also propose a model averaging (MA) estimator that compromises across a set of candidate models. We show that it is asymptotically optimal. We further flesh out how to extend the proposed selection and averaging schemes to higher order specifications and to the MESS with heteroscedasticity. Our Monte Carlo simulation results indicate that the MS and MA estimators perform well in finite samples. We also illustrate the usefulness of the proposed MS and MA schemes in a spatially augmented economic growth model.

Survival of rehabilitated and released red-tailed hawks (Buteo jamaicensis)

Wildlife rehabilitation provides responsible care for sick, injured or orphaned wild animals with the goal of releasing fully recovered individuals back into the environment. Post-release survival data for these animals remain sparse but necessary to measure and assess the impact of wildlife rehabilitation as a conservation strategy. This study used national banding data to quantitatively compare annual survival of wild-caught (non-rehabilitated) and rehabilitated red-tailed hawks (Buteo jamaicensis). In addition, 13 rehabilitated and released red-tailed hawks from Dane County Humane Society’s Wildlife Center (DCHS, Madison, WI) were monitored using radio telemetry. Annual survival of rehabilitated and radio-tagged red-tailed hawks from DCHS was 36% over 85 weeks of monitoring. Nationally, wild red-tailed hawk annual survival (0.777; 95% CI [0.768, 0.777]) was largely equivalent to estimates reported in other published studies. These estimates reflect average survival over 40 years in a fully time-dependent model (variance component estimated using the Delta Method; Powell 2007). Rehabilitated red-tailed hawks had an annual survival of 0.549 (95% CI: 0.523, 0.575]) over 43 years. These values reflect model-averaged estimates from time-independent survival models (recovery was time dependent) that were equivalent in terms of likelihood (Brownie = Seber = wi = 0.50). Consequently, survival of rehabilitated red-tailed hawks was approximately 22% lower than wild-caught individuals. Furthermore, young (hatch-year) red-tailed hawks experienced increased mortality (34%) relative to those rehabilitated as adults (0.255; 95% CI [0.199, 0.321] versus 0.598; 95% CI [0.571, 0.624], respectfully). The results of this study demonstrate the need for additional post-release monitoring and may guide future management decisions regarding wildlife rehabilitative criteria, practice and viability.

Model Averaging Estimation Method by Kullback–Leibler Divergence for Multiplicative Error Model

In this paper, we propose the model averaging estimation method for multiplicative error model and construct the corresponding weight choosing criterion based on the Kullback–Leibler divergence with a hyperparameter to avoid the problem of overfitting. The resulting model average estimator is proved to be asymptotically optimal. It is shown that the Kullback–Leibler model averaging (KLMA) estimator asymptotically minimizes the in‐sample Kullback–Leibler divergence and improves the forecast accuracy of out‐of‐sample even under different loss functions. In simulations, we show that the KLMA estimator compares favorably with smooth‐AIC estimator (SAIC), smooth‐BIC estimator (SBIC), and Mallows model averaging estimator (MMA), especially when some nonlinear noise is added to the data generation process. The empirical applications in the daily range of S&P500 and price duration of IBM show that the out‐of‐sample forecasting capacity of the KLMA estimator is better than that of other methods.

Bayesian learning with Wasserstein barycenters

We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first show how this estimator, termed Bayesian Wasserstein barycenter (BWB), arises naturally in a general, parameter-free Bayesian model-selection framework, when the considered Bayesian risk is the Wasserstein distance. Examples are given, illustrating how the BWB extends some classic parametric and non-parametric selection strategies. Furthermore, we also provide explicit conditions granting the existence and statistical consistency of the BWB, and discuss some of its general and specific properties, providing insights into its advantages compared to usual choices, such as the model average estimator. Finally, we illustrate how this estimator can be computed using the stochastic gradient descent (SGD) algorithm in Wasserstein space introduced in a companion paper, and provide a numerical example for experimental validation of the proposed method.

Model averaging for interval-valued data

In recent years, model averaging, by which estimates are obtained based on not one single model but a weighted ensemble of models, has received growing attention as an alternative to model selection. To-date, methods for model averaging have been developed almost exclusively for point-valued data, despite the fact that interval-valued data are commonplace in many applications and the substantial body of literature on estimation and inference methods for interval-valued data. This paper focuses on the special case of interval time series data, and assumes that the mid-point and log-range of the interval values are modelled by a two-equation vector autoregressive with exogenous covariates (VARX) model. We develop a methodology for combining models of varying lag orders based on a weight choice criterion that minimises an unbiased estimator of the squared error risk of the model average estimator. We prove that this method yields predictors of mid-points and ranges with an optimal asymptotic property. In addition, we develop a method for correcting the range forecasts, taking into account the forecast error variance. An extensive simulation experiment examines the performance of the proposed model averaging method in finite samples. We apply the method to an interval-valued data series on crude oil future prices.