2,324 research outputs found
A geoadditive Bayesian latent variable model for Poisson indicators
We introduce a new latent variable model with count variable indicators, where usual linear parametric effects of covariates, nonparametric effects of continuous covariates and spatial effects on the continuous latent variables are modelled through a geoadditive predictor. Bayesian modelling of nonparametric functions and spatial effects is based on penalized spline and Markov random field priors. Full Bayesian inference is performed via an auxiliary variable Gibbs sampling technique, using a recent suggestion of Frühwirth-Schnatter and Wagner (2006). As an advantage, our Poisson indicator latent variable model can be combined with semiparametric latent variable models for mixed binary, ordinal and continuous indicator variables within an unified and coherent framework for modelling and inference. A simulation study investigates performance, and an application to post war human security in Cambodia illustrates the approach
Inference on Categorical Survey Response: A Predictive Approach
We consider the estimation of finite population proportions of categorical survey responses obtained by probability sampling. The customary design-based estimator does not make use of the auxiliary data available for all the population units at the estimation stage. We adopt a model-based predictive approach to incorporate this information and make the estimates more efficient. In the first part of our paper we consider a multinomial logit type model when logit function is a known parametric function of the covariates. We then use it for the prediction of non-sampled responses. This together with sampled responses is used to obtain the estimates of the proportions. The asymptotic biases and variances of these estimators are obtained. The main drawback of this approach is, being a parametric model it may suffer from model misspecification and thus, may lose it’s efficiencies over the usual design-based estimates. To overcome this drawback, in the next part of this paper we replace the multinomial logit type model by a nonparametric model using recently developed random coefficients splines models. Finally, we carry out a simulation study. It shows that the nonparametric approach may lead to an appreciable improvement over both parametric and design-based approaches when the regression function is quite different from multinomial logit.
Inference on Counterfactual Distributions
Counterfactual distributions are important ingredients for policy analysis
and decomposition analysis in empirical economics. In this article we develop
modeling and inference tools for counterfactual distributions based on
regression methods. The counterfactual scenarios that we consider consist of
ceteris paribus changes in either the distribution of covariates related to the
outcome of interest or the conditional distribution of the outcome given
covariates. For either of these scenarios we derive joint functional central
limit theorems and bootstrap validity results for regression-based estimators
of the status quo and counterfactual outcome distributions. These results allow
us to construct simultaneous confidence sets for function-valued effects of the
counterfactual changes, including the effects on the entire distribution and
quantile functions of the outcome as well as on related functionals. These
confidence sets can be used to test functional hypotheses such as no-effect,
positive effect, or stochastic dominance. Our theory applies to general
counterfactual changes and covers the main regression methods including
classical, quantile, duration, and distribution regressions. We illustrate the
results with an empirical application to wage decompositions using data for the
United States.
As a part of developing the main results, we introduce distribution
regression as a comprehensive and flexible tool for modeling and estimating the
\textit{entire} conditional distribution. We show that distribution regression
encompasses the Cox duration regression and represents a useful alternative to
quantile regression. We establish functional central limit theorems and
bootstrap validity results for the empirical distribution regression process
and various related functionals.Comment: 55 pages, 1 table, 3 figures, supplementary appendix with additional
results available from the authors' web site
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