Model-averaged Estimates Research Articles

Model averaging by jackknife criterion for varying-coefficient partially linear models

This paper is concerned with model averaging procedure for varying-coefficient partially linear models. We proposed a jackknife model averaging method that involves minimizing a leave-one-out cross-validation criterion, and developed a computational shortcut to optimize the cross-validation criterion for weight choice. The resulting model average estimator is shown to be asymptotically optimal in terms of achieving the smallest possible squared error. The simulation studies have provided evidence of the superiority of the proposed procedures. Our approach is further applied to a real data.

IS BUSINESS CYCLE ASYMMETRY INTRINSIC IN INDUSTRIALIZED ECONOMIES?

We consider a model-averaged forecast-based estimate of the output gap to measure economic slack in 10 industrialized economies. Our measure takes changes in the long-run growth rate into account and, by addressing model uncertainty using equal weights on different forecast-based estimates, is robust to different assumptions about the underlying structure of the economy. For all 10 countries in the sample, we find that the estimated output gap has much larger negative movements during recessions than positive movements in expansions, suggesting business cycle asymmetry is an intrinsic characteristic of industrialized economies. Furthermore, the estimated output gap is always strongly negatively correlated with future output growth and unemployment and positively correlated with capacity utilization. It also implies a convex Phillips Curve in many cases. The model-averaged output gap is reliable in real time in the sense of being subject to relatively small revisions.

New Internal Model Average Consensus Estimators with Light Communication Load

The dynamic average consensus problem for a group of agents is considered. Each agent in the group is supposed to estimate the average of inputs applied to all agents and the estimation should be done in a distributed way. By reinterpreting the proportional integral type estimator, a new structure for the average estimator which can embed the internal model of inputs is proposed and conditions which result in the zero estimation error in the steady state are derived. We present constructive design procedures for the cases of constant inputs and time-varying inputs employing the root locus for the former and LQR-based design for the latter. The theory is validated through numerical simulations.

Model averaging for M-estimation

ABSTRACTM-estimation is a widely used technique for robust statistical inference. In this paper, we study model selection and model averaging for M-estimation to simultaneously improve the coverage probability of confidence intervals of the parameters of interest and reduce the impact of heavy-tailed errors or outliers in the response. Under general conditions, we develop robust versions of the focused information criterion and a frequentist model average estimator for M-estimation, and we examine their theoretical properties. In addition, we carry out extensive simulation studies as well as two real examples to assess the performance of our new procedure, and find that the proposed method produces satisfactory results.

Weighted-averaging estimator for possible threshold in segmented linear regression model

This paper proposes two types of weighted-averaging estimators of coefficients in segmented linear regressions with a possible threshold. We construct an approximate Mallows criterion which can be looked as an average of limit cases with corresponding threshold effect zero and infinite. Following Hansen (2007) we propose to weightedly average two estimators of coefficients separately with and without threshold effect where weights can be selected by minimizing the Mallows criterion. Further we construct another type of Mallows criterion which is an estimate of the squared error from the model average fit and is used to obtain the new weights for averaging. Under the second Mallows criterion, we find that the new weights make Mallows Model Average (MMA) estimator to be asymptotically optimal in the sense of achieving a lower squared error. Specially in the case of a possible abrupt change, new weights are proved to tend to either one or zero under the true model with only one threshold or tend to 1∕2 under the true model without a threshold. Numerical results demonstrate that the proposed MMA estimator performs better under different complicated changes and does choose the true model under one possible abrupt change.

Composite versus model-averaged quantile regression

The composite quantile estimator is a robust and efficient alternative to the least-squares estimator in linear models. However, it is computationally demanding when the number of quantiles is large. We consider a model-averaged quantile estimator as a computationally cheaper alternative. We derive its asymptotic properties in high-dimensional linear models and compare its performance to the composite quantile estimator in both low- and high-dimensional settings. We also assess the effect on efficiency of using equal weights, theoretically optimal weights, and estimated optimal weights for combining the different quantiles. None of the estimators dominates in all settings under consideration, thus leaving room for both model-averaged and composite estimators, both with equal and estimated optimal weights in practice.

High levels of human infection with Trypanosoma cruzi associated with the domestic density of infected vectors and hosts in a rural area of northeastern Argentina

BackgroundInsecticide spraying campaigns designed to suppress the principal vectors of the Chagas disease usually lack an active surveillance system that copes with house reinvasion. Following an insecticide campaign with no subsequent surveillance over a 12-year period, we implemented a longitudinal intervention programme including periodic surveys for Triatoma infestans, full-coverage house spraying with insecticides, and selective control in a well-defined rural area of the Argentinean Chaco inhabited by Creoles and one indigenous group (Qom). Here, we conducted a cross-sectional study and report the age-specific seroprevalence of human T. cruzi infection by group, and examine the association between human infection, the onset of the intervention, the relative density of infected domestic bugs, and the household number of infected people, dogs, or cats.ResultsThe seroprevalence of infection among 691 residents examined was 39.8% and increased steadily with age, reaching 53–70% in those older than 20 years. The mean annual force of infection was 2.5 per 100 person-years (95% CI: 1.8–3.3%). Infection in children younger than 16 years born before the intervention programme was two to four times higher in houses with infected T. infestans than in houses without them and was six times higher when there were both infected dogs or cats and bugs than when they were absent. The model-averaged estimate of the intervention effect suggests that the odds of seropositivity were about nine times smaller for those born after the onset of the intervention than for those born before it, regardless of ethnic background, age, gender, household wealth, and cohabitation with T. cruzi-infected vectors or human hosts. Human infection was also closely associated with the baseline abundance of infected domestic triatomines and the number of infected cohabitants. Two of 43 children born after interventions were T. cruzi-seropositive; since their mothers were seropositive and both resided in apparently uninfested houses they were attributed to vertical transmission. Alternatively, these cases could be due to non-local vector-borne transmission.ConclusionsOur study reveals high levels of human infection with T. cruzi in the Argentinean Chaco, and the immediate impact of sustained vector surveillance and selective control actions on transmission.

Optimizing Prediction Using Bayesian Model Averaging: Examples Using Large-Scale Educational Assessments.

This article provides a review of Bayesian model averaging as a means of optimizing the predictive performance of common statistical models applied to large-scale educational assessments. The Bayesian framework recognizes that in addition to parameter uncertainty, there is uncertainty in the choice of models themselves. A Bayesian approach to addressing the problem of model uncertainty is the method of Bayesian model averaging. Bayesian model averaging searches the space of possible models for a set of submodels that satisfy certain scientific principles and then averages the coefficients across these submodels weighted by each model's posterior model probability (PMP). Using the weighted coefficients for prediction has been shown to yield optimal predictive performance according to certain scoring rules. We demonstrate the utility of Bayesian model averaging for prediction in education research with three examples: Bayesian regression analysis, Bayesian logistic regression, and a recently developed approach for Bayesian structural equation modeling. In each case, the model-averaged estimates are shown to yield better prediction of the outcome of interest than any submodel based on predictive coverage and the log-score rule. Implications for the design of large-scale assessments when the goal is optimal prediction in a policy context are discussed.

Estimating abundance without recaptures of marked pallid sturgeon in the Mississippi River.

Abundance estimates are essential for assessing the viability of populations and the risks posed by alternative management actions. An effort to estimate abundance via a repeated mark-recapture experiment may fail to recapture marked individuals. We devised a method for obtaining lower bounds on abundance in the absence of recaptures for both panmictic and spatially structured populations. The method assumes few enough recaptures were expected to be missed by random chance. The upper Bayesian credible limit on expected recaptures allows probabilistic statements about the minimum number of individuals present in the population. We applied this method to data from a 12-year survey of pallid sturgeon (Scaphirhynchus albus) in the lower and middle Mississippi River (U.S.A.). None of the 241 individuals marked was recaptured in the survey. After accounting for survival and movement, our model-averaged estimate of the total abundance of pallid sturgeon ≥3 years old in the study area had a 1%, 5%, or 25% chance of being <4,600, 7,000, or 15,000, respectively. When we assumed fish were distributed in proportion to survey catch per unit effort, the farthest downstream reach in the survey hosted at least 4.5-15 fish per river kilometer (rkm), whereas the remainder of the reaches in the lower and middle Mississippi River hosted at least 2.6-8.5 fish/rkm for all model variations examined. The lower Mississippi River had an average density of pallid sturgeon ≥3 years old of at least 3.0-9.8 fish/rkm. The choice of Bayesian prior was the largest source of uncertainty we considered but did not alter the order of magnitude of lower bounds. Nil-recapture estimates of abundance are highly uncertain and require careful communication but can deliver insights from experiments that might otherwise be considered a failure.

Weighted-average least squares estimation of generalized linear models

The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model-averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework, and the finite-sample properties of this estimator by a Monte Carlo experiment the design of which is based on a real empirical analysis of attrition in the first two waves of the Survey of Health, Aging and Retirement in Europe (SHARE).

Model selection and model averaging for semiparametric partially linear models with missing data

ABSTRACTWe study model selection and model averaging in semiparametric partially linear models with missing responses. An imputation method is used to estimate the linear regression coefficients and the nonparametric function. We show that the corresponding estimators of the linear regression coefficients are asymptotically normal. Then a focused information criterion and frequentist model average estimators are proposed and their theoretical properties are established. Simulation studies are performed to demonstrate the superiority of the proposed methods over the existing strategies in terms of mean squared error and coverage probability. Finally, the approach is applied to a real data case.

Identifiability of parameters of three-phase oil relative permeability models under simultaneous water and gas (SWAG) injection

We assess the relative performance of a suite of selected models to interpret three-phase oil relative permeability data and provide a procedure to determine identifiability of the model parameters. We ground our analysis on observations of Steady-State two- and three-phase relative permeabilities we collect on a water-wet Sand-Pack sample through series of core-flooding experiments. Three-phase experiments are characterized by simultaneous injection of water and gas into the core sample initiated at irreducible water saturation, a scenario which is relevant for modern enhanced oil recovery techniques. The selected oil relative permeability models include classical and recent formulations and we consider their performance when (i) solely two-phase data are employed and/or (ii) two- and three-phase data are jointly used to render predictions of three-phase oil relative permeability, kro. We assess identifiability of model parameters through the Profile Likelihood (PL) technique. We rely on formal model discrimination criteria for a quantitative evaluation of the interpretive skill of each of the candidate models tested. We also evaluate the relative degree of likelihood associated with the competing models through a posterior probability weight and use Maximum Likelihood Bayesian model averaging to provide model-averaged estimate of kro and the associated uncertainty bounds. Results show that assessing identifiability of uncertain model parameters on the basis of the available dataset can provide valuable information about the quality of the parameter estimates and can reduce computational costs by selecting solely identifiable models among available candidates.

Model averaging for multivariate multiple regression models

ABSTRACTThe theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.

OUP accepted manuscript

We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf.

Is Business Cycle Asymmetry Intrinsic in Industrialized Economies?

We consider a model-averaged forecast-based estimate of the output gap to measure economic slack for ten industrialized economies. Our measure takes changes in the long-run growth rate into account and, by accounting for model uncertainty using equal weights on different forecast-based estimates, is robust to different assumptions about the underlying structure of the economy. For each country, we find that the estimated output gap is highly asymmetric, with much larger negative movements during recessions than positive movements in expansions, suggesting that this particular form of business cycle asymmetry is an intrinsic characteristic of industrialized economies. Furthermore, the estimated output gap is strongly negatively correlated with future output growth and unemployment and positively correlated with capacity utilization in each case. It also implies a convex Phillips Curve in many cases.

Determinants of Distribution Patterns and Management Needs in a Critically Endangered Lion Panthera leo Population

The lion Panthera leo is Critically Endangered in West Africa and is known to occupy only four protected areas within the region. The largest population persists in the trans-boundary W-Arly-Pendjari (WAP) ecosystem, in the border region of Benin, Burkina Faso, and Niger. WAP harbors an estimated 350 individuals, or 90% of West Africa’s lions. We modeled lion occupancy across WAP using systematic, vehicle-based spoor counts to assess how landscape variables related to biotic factors, management and human impact influence lion distribution across WAP. We surveyed 1110 km of roads across WAP in 2012, obtaining 79 lion detections in 32 of our 167 15 x 15 km sampling units (naive occupancy = 0.41). Overall occupancy (Ψ) was 0.71 (95% SE = 0.56-0.83) when accounting for imperfect detection (p = 0.22, 95% SE = 0.18-0.27). The best predictors of lion occupancy were numbers of permanent protected area staff and mean monthly dry season precipitation. Model-averaged estimates suggest greatest lion occupancy in the Arly and Pendjari management blocks, with lowest occupancy in the tri-national W National Park. Our results suggest that lions in WAP are equally limited by management and biotic factors, and demonstrate how unevenly distributed protection effort limits the distribution of an apex predator across a protected landscape. We strongly recommend increased funding and better protection to increase lion occupancy in WAP, most urgently in the W National Park.

Patterns of Snow Leopard Site Use in an Increasingly Human-Dominated Landscape

Human population growth and concomitant increases in demand for natural resources pose threats to many wildlife populations. The landscapes used by the endangered snow leopard (Panthera uncia) and their prey is increasingly subject to major changes in land use. We aimed to assess the influence of 1) key human activities, as indicated by the presence of mining and livestock herding, and 2) the presence of a key prey species, the blue sheep (Pseudois nayaur), on probability of snow leopard site use across the landscape. In Gansu Province, China, we conducted sign surveys in 49 grid cells, each of 16 km2 in size, within a larger area of 3392 km2. We analysed the data using likelihood-based habitat occupancy models that explicitly account for imperfect detection and spatial auto-correlation between survey transect segments. The model-averaged estimate of snow leopard occupancy was high [0.75 (SE 0.10)], but only marginally higher than the naïve estimate (0.67). Snow leopard segment-level probability of detection, given occupancy on a 500 m spatial replicate, was also high [0.68 (SE 0.08)]. Prey presence was the main determinant of snow leopard site use, while human disturbances, in the form of mining and herding, had low predictive power. These findings suggest that snow leopards continue to use areas very close to such disturbances, as long as there is sufficient prey. Improved knowledge about the effect of human activity on large carnivores, which require large areas and intact prey populations, is urgently needed for conservation planning at the local and global levels. We highlight a number of methodological considerations that should guide the design of such research.

Local and landscape metrics identify opportunities for conserving cavity-nesting birds in a rapidly urbanizing ecoregion

Urban centers are rapidly expanding globally, resulting in regional forest-cover transformations that shift from temperate forest biomes to a heterogeneous mix of urban development, forest patches, and agriculture. Data on habitat use within remaining forest patches embedded across land use types, particularly in urban land use, are needed to optimize conservation strategies as urban growth continues. In the rapidly urbanizing southern Piedmont, USA, small pine patches have become more frequent across the landscape and are found embedded within second-growth forest, agricultural, and urban land use matrices. We used point-count surveys and N-mixture models to determine the effect of patch- and landscape-scale drivers on cavity-nesting bird abundance, including the threatened Brown-headed Nuthatch ( Sitta pusilla ), in pine forest patches. Model-averaged estimates suggest Brown-headed Nuthatches are more abundant in large patches in a heterogeneous matrix that includes urban residential development. Three other cavity-nesting species declined in abundance as a function of reduced canopy cover. White-breasted Nuthatches increased and Tufted Titmice decreased in abundance in response to patch area. By identifying factors that predict abundance at local and landscape scales for ecologically sensitive and generalist species, we can more effectively contribute to regional conservation efforts in urban ecosystems, extending conservation in practice beyond protected areas.

A semiparametric generalized ridge estimator and link with model averaging

ABSTRACTIn recent years, the suggestion of combining models as an alternative to selecting a single model from a frequentist prospective has been advanced in a number of studies. In this article, we propose a new semiparametric estimator of regression coefficients, which is in the form of a feasible generalized ridge estimator by Hoerl and Kennard (1970b) but with different biasing factors. We prove that after reparameterization such that the regressors are orthogonal, the generalized ridge estimator is algebraically identical to the model average estimator. Further, the biasing factors that determine the properties of both the generalized ridge and semiparametric estimators are directly linked to the weights used in model averaging. These are interesting results for the interpretations and applications of both semiparametric and ridge estimators. Furthermore, we demonstrate that these estimators based on model averaging weights can have properties superior to the well-known feasible generalized ridge estimator in a large region of the parameter space. Two empirical examples are presented.

Diversified learning for continuous hidden Markov models with application to fault diagnosis

The learning problem of continuous hidden Markov models (CHMMs) is the most critical and challenging one for the application of CHMMs. This paper aims to attack the learning problem of CHMMs by using the diversified gradient descent (DGD) algorithm. The novel learning formula of CHMM parameters, requiring no special form of the objective function and yielding various parameter estimates with different degree of diversity, is derived through dynamically adjusting the iterative procedure according to the gradient change of each parameter. It is the first work for standard CHMM attempting to obtain more local maxima so that the global maximum of the likelihood function of CHMM can be better approximated or even discovered. Hence this paper takes an important step forward in solving the learning problem of CHMM. Furthermore, a likelihood-based model averaging (LBMA) estimator is developed to achieve robust parameter estimation of CHMM based upon the diversiform models attained by the DGD algorithm. The proposed methods are tested on simulation and real-life bearing fault diagnosis problem. The results show that proposed methods perform better in parameter estimation and bearing fault diagnosis compared to the conventional methods.