Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke

In the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for strokes, we apply Bayesian model averaging to the selection of variables in Cox proportional hazard models. We use an extension of the leaps-and-bounds algorithm for locating the models that are to be averaged over and make available S-PLUS software to implement the methods. Bayesian model averaging provides a posterior probability that each variable belongs in the model, a more directly interpretable measure of variable importance than a P -value. P -values from models preferred by stepwise methods tend to overstate the evidence for the predictive value of a variable and do not account for model uncertainty. We introduce the partial predictive score to evaluate predictive performance. For the Cardiovascular Health Study, Bayesian model averaging predictively outperforms standard model selection and does a better job of assessing who is at high risk for a stroke.     

Bayesian Nonlinear Regression for the Air Pollution Effects on Daily Clinic Visits in Small Areas of Taiwan

We consider the complete clinic visit records and environmental monitoring data at 50 townships and city districts where ambient air monitoring stations of Taiwan Air Quality Monitoring Stations are located. A Bayesian analysis is carried out using regression spline model on principal components obtained from several pollutant covariables. The appropriate model is selected using Bayesian model averaging. A brief account of our results is provided for the elderly patients group.     

The Changing Transmission of Uncertainty Shocks in the U.S.

This article investigates if the impact of uncertainty shocks on the U.S. economy has changed over time. To this end, we develop an extended factor augmented vector autoregression (VAR) model that simultaneously allows the estimation of a measure of uncertainty and its time-varying impact on a range of variables. We find that the impact of uncertainty shocks on real activity and financial variables has declined systematically over time. In contrast, the response of inflation and the short-term interest rate to this shock has remained fairly stable. Simulations from a nonlinear dynamic stochastic general equilibrium (DSGE) model suggest that these empirical results are consistent with an increase in the monetary authorities’ antiinflation stance and a “flattening” of the Phillips curve. Supplementary materials for this article are available online.     

Wavelet-based Bayesian nonlinear regression for the air pollution effects on clinic visits in small areas of Taiwan

We revisit the complete clinic visit records and environmental monitoring data at 50 townships and city districts of Taiwan. Extending the earlier analyses, here we consider a Bayesian analysis using Daubechies wavelet. Appropriate model selection is also considered using Bayesian model averaging. Temperature, dew point, and NO₂ and CO of the current day and the previous day are identified as the pollutants in different areas of the island following some spatial pattern.     

Finite-Sample Properties of the Maximum Likelihood Estimator for the Poisson Regression Model With Random Covariates

We examine the small-sample behaviour of the maximum likelihood estimator for the Poisson regression model with random covariates. Analytic expressions for the second-order bias and mean squared error are derived, and we undertake some numerical evaluations to illustrate these results for the single covariate case. The properties of the bias-adjusted maximum likelihood estimator are investigated in a Monte Carlo experiment. Correcting the estimator for its second-order bias is found to be effective in the cases considered, and we recommend its use when the Poisson regression model is estimated by maximum likelihood with small samples.     

Bias Correction in the Dynamic Panel Data Model with a Nonscalar Disturbance Covariance Matrix

Approximation formulae are developed for the bias of ordinary and generalized Least Squares Dummy Variable (LSDV) estimators in dynamic panel data models. Results from Kiviet [Kiviet, J. F. (1995), on bias, inconsistency, and efficiency of various estimators in dynamic panel data models, J. Econometrics68:53-78; Kiviet, J. F. (1999), Expectations of expansions for estimators in a dynamic panel data model: some results for weakly exogenous regressors, In: Hsiao, C., Lahiri, K., Lee, L-F., Pesaran, M. H., eds., Analysis of Panels and Limited Dependent Variables, Cambridge: Cambridge University Press, pp. 199-225] are extended to higher-order dynamic panel data models with general covariance structure. The focus is on estimation of both short- and long-run coefficients. The results show that proper modelling of the disturbance covariance structure is indispensable. The bias approximations are used to construct bias corrected estimators which are then applied to quarterly data from 14 European Union countries. Money demand functions for M1, M2 and M3 are estimated for the EU area as a whole for the period 1991: I-1995: IV. Significant spillovers between countries are found reflecting the dependence of domestic money demand on foreign developments. The empirical results show that in general plausible long-run effects are obtained by the bias corrected estimators. Moreover, finite sample bias, although of moderate magnitude, is present underlining the importance of more refined estimation techniques. Also the efficiency gains by exploiting the heteroscedasticity and cross-correlation patterns between countries are sometimes considerable.     

Bias Correction in the Dynamic Panel Data Model with a Nonscalar Disturbance Covariance Matrix

Abstract

Approximation formulae are developed for the bias of ordinary and generalized Least Squares Dummy Variable (LSDV) estimators in dynamic panel data models. Results from Kiviet [Kiviet, J. F. (1995), on bias, inconsistency, and efficiency of various estimators in dynamic panel data models, J. Econometrics68:53–78; Kiviet, J. F. (1999), Expectations of expansions for estimators in a dynamic panel data model: some results for weakly exogenous regressors, In: Hsiao, C., Lahiri, K., Lee, L‐F., Pesaran, M. H., eds., Analysis of Panels and Limited Dependent Variables, Cambridge: Cambridge University Press, pp. 199–225] are extended to higher‐order dynamic panel data models with general covariance structure. The focus is on estimation of both short‐ and long‐run coefficients. The results show that proper modelling of the disturbance covariance structure is indispensable. The bias approximations are used to construct bias corrected estimators which are then applied to quarterly data from 14 European Union countries. Money demand functions for M1, M2 and M3 are estimated for the EU area as a whole for the period 1991: I–1995: IV. Significant spillovers between countries are found reflecting the dependence of domestic money demand on foreign developments. The empirical results show that in general plausible long‐run effects are obtained by the bias corrected estimators. Moreover, finite sample bias, although of moderate magnitude, is present underlining the importance of more refined estimation techniques. Also the efficiency gains by exploiting the heteroscedasticity and cross‐correlation patterns between countries are sometimes considerable.     

Model of Combined Prevision: An Application of the Monthly Series of Dengue Notifications in the State of Pernambuco

In this paper we state and justify a two-stage sampling procedure for selecting a subset of size m containing the t best of k independent normal populations, when the ranking parameters are the population means. We do not assume that the variances of the populations are known or equal. Discrete event simulation studies are often concerned with choosing one or more system designs which are best in some sense. We present empirical results from a typical simulation application for which the observations are not normally distributed.     

Permutation Methods for Comparing the Accuracy of Nested Prediction Models in Survival Analysis

When making patient-specific prediction, it is important to compare prediction models to evaluate the gain in prediction accuracy for including additional covariates. We propose two statistical testing methods, the complete data permutation (CDP) and the permutation cross-validation (PCV) for comparing prediction models. We simulate clinical trial settings extensively and show that both methods are robust and achieve almost correct test sizes; the methods have comparable power in moderate to large sample situations, while the CDP is more efficient in computation. The methods are also applied to ovarian cancer clinical trial data.     

Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section

This article proposes a Bayesian estimation framework for a typical multi-factor model with time-varying risk exposures to macroeconomic risk factors and corresponding premia to price U.S. publicly traded assets. The model assumes that risk exposures and idiosyncratic volatility follow a break-point latent process, allowing for changes at any point on time but not restricting them to change at all points. The empirical application to 40 years of U.S. data and 23 portfolios shows that the approach yields sensible results compared to previous two-step methods based on naive recursive estimation schemes, as well as a set of alternative model restrictions. A variance decomposition test shows that although most of the predictable variation comes from the market risk premium, a number of additional macroeconomic risks, including real output and inflation shocks, are significantly priced in the cross-section. A Bayes factor analysis massively favors the proposed change-point model. Supplementary materials for this article are available online.