Uncertainty under a multivariate nested-error regression model with logarithmic transformation

Assuming a multivariate linear regression model with one random factor, we consider the parameters defined as exponentials of mixed effects, i.e., linear combinations of fixed and random effects. Such parameters are of particular interest in prediction problems where the dependent variable is the logarithm of the variable that is the object of inference. We derive bias-corrected empirical predictors of such parameters. A second order approximation for the mean crossed product error of the predictors of two of these parameters is obtained, and an estimator is derived from it. The mean squared error is obtained as a particular case

UNCERTAINTY UNDER A MULTIVARIATE NESTED-ERROR REGRESSION MODEL WITH LOGARITHMIC TRANSFORMATION

Assuming a multivariate linear regression model with one random factor, we consider the parameters defined as exponentials of mixed effects, i.e., linear combinations of fixed and random effects. Such parameters are of particular interest in prediction problems where the dependent variable is the logarithm of the variable that is the object of inference. We derive bias-corrected empirical predictors of such parameters. A second order approximation for the mean crossed product error of the predictors of two of these parameters is obtained, and an estimator is derived from it. The mean squared error is obtained as a particular case.

Functional Structure and Approximation in Econometrics (book front matter)

This is the front matter from the book, William A. Barnett and Jane Binner (eds.), Functional Structure and Approximation in Econometrics, published in 2004 by Elsevier in its Contributions to Economic Analysis monograph series. The front matter includes the Table of Contents, Volume Introduction, and Section Introductions by Barnett and Binner and the Preface by W. Erwin Diewert. The volume contains a unified collection and discussion of W. A. Barnett's most important published papers on applied and theoretical econometric modelling.consumer demand, production, flexible functional form, functional structure, asymptotics, nonlinearity, systemwide models

Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines

Background: Multiple imputation (MI) provides an effective approach to handle missing covariate data within prognostic modelling studies, as it can properly account for the missing data uncertainty. The multiply imputed datasets are each analysed using standard prognostic modelling techniques to obtain the estimates of interest. The estimates from each imputed dataset are then combined into one overall estimate and variance, incorporating both the within and between imputation variability. Rubin's rules for combining these multiply imputed estimates are based on asymptotic theory. The resulting combined estimates may be more accurate if the posterior distribution of the population parameter of interest is better approximated by the normal distribution. However, the normality assumption may not be appropriate for all the parameters of interest when analysing prognostic modelling studies, such as predicted survival probabilities and model performance measures. Methods: Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies. Results: Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated. Conclusion: The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies

Temporal Disaggregation by State Space Methods: Dynamic Regression Methods Revisited

The paper documents and illustrates state space methods that implement time series disaggregation by regression methods, with dynamics that depend on a single autoregressive parameter. The most popular techniques for the distribution of economic flow variables, such as Chow-Lin, Fernandez and Litterman, are encompassed by this unifying framework. The state space methodology offers the generality that is required to address a variety of inferential issues, such as the role of initial conditions, which are relevant for the properties of the maximum likelihood estimates and for the the derivation of encompassing representations that nest exactly the traditional disaggregation models, and the definition of a suitable set of real time diagnostics on the quality of the disaggregation and revision histories that support model selection. The exact treatment of temporal disaggregation by dynamic regression models, when the latter are formulated in the logarithms, rather than the levels, of an economic variable, is also provided. The properties of the profile and marginal likelihood are investigated and the problems with estimating the Litterman model are illustrated. In the light of the nonstationary nature of the economic time series usually entertained in practice, the suggested strategy is to fit an autoregressive distribute lag model, which, under a reparameterisation and suitable initial conditions, nests both the Chow-Lin and the Fernandez model, thereby incorporating our uncertainty about the presence of cointegration between the aggregated series and the indicators.Autoregressive Distributed Lag Models, COMFAC, Augmented Kalman filter and smoother, Marginal Likelihood, Logarithmic Transformation.

Estimation of Linear and Non-Linear Indicators using Interval Censored Income Data

Among a variety of small area estimation methods, one popular approach for the estimation of linear and non-linear indicators is the empirical best predictor. However, parameter estimation using standard maximum likelihood methods is not possible, when the dependent variable of the underlying nested error regression model, is censored to specific intervals. This is often the case for income variables. Therefore, this work proposes an estimation method, which enables the estimation of the regression parameters of the nested error regression model using interval censored data. The introduced method is based on the stochastic expectation maximization algorithm. Since the stochastic expectation maximization method relies on the Gaussian assumptions of the error terms, transformations are incorporated into the algorithm to handle departures from normality. The estimation of the mean squared error of the empirical best predictors is facilitated by a parametric bootstrap which captures the additional uncertainty coming from the interval censored dependent variable. The validity of the proposed method is validated by extensive model-based simulations

Parametric bootstrap mean squared error of a small area multivariate EBLUP

© 2018, © 2018 Taylor & Francis Group, LLC. This article deals with mean squared error (MSE) estimation of a multivariate empirical best linear unbiased predictor (MEBLUP) under the unit-level multivariate nested-errors regression model for small area estimation via parametric bootstrap. A simulation study is designed to evaluate the performance of our algorithm and compare it with the univariate case bootstrap MSE which has been shown to be consistent to the true MSE. The simulation shows that, in line with the literature, MEBLUP provides unbiased estimates with lower MSE than EBLUP. We also provide a short empirical analysis based on real data collected from the U.S. Department of Agriculture

Generalized Multivariate Extreme Value Models for Explicit Route Choice Sets

This paper analyses a class of route choice models with closed-form probability expressions, namely, Generalized Multivariate Extreme Value (GMEV) models. A large group of these models emerge from different utility formulas that combine systematic utility and random error terms. Twelve models are captured in a single discrete choice framework. The additive utility formula leads to the known logit family, being multinomial, path-size, paired combinatorial and link-nested. For the multiplicative formulation only the multinomial and path-size weibit models have been identified; this study also identifies the paired combinatorial and link-nested variations, and generalizes the path-size variant. Furthermore, a new traveller's decision rule based on the multiplicative utility formula with a reference route is presented. Here the traveller chooses exclusively based on the differences between routes. This leads to four new GMEV models. We assess the models qualitatively based on a generic structure of route utility with random foreseen travel times, for which we empirically identify that the variance of utility should be different from thus far assumed for multinomial probit and logit-kernel models. The expected travellers' behaviour and model-behaviour under simple network changes are analysed. Furthermore, all models are estimated and validated on an illustrative network example with long distance and short distance origin-destination pairs. The new multiplicative models based on differences outperform the additive models in both tests