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Register a new userIdentifying latent groups in spatial panel data using a Markov random field constrained product partition model
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Added by
Tianyu Pan
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.
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This paper describes a data reduction technique in case of a markov chain of specified order. Instead of observing all the transitions in a markov chain we record only a few of them and treat the remaining part as missing. The decision about which transitions to be filtered is taken before the observation process starts. Based on the filtered chain we try to estimate the parameters of the markov model using EM algorithm. In the first half of the paper we characterize a class of filtering mechanism for which all the parameters remain identifiable. In the later half we explain methods of estimation and testing about the transition probabilities of the markov chain based on the filtered data. The methods are first developed assuming a simple markov model with each probability of transition positive, but then generalized for models with structural zeroes in the transition probability matrix. Further extension is also done for multiple markov chains. The performance of the developed method of estimation is studied using simulated data along with a real life data.
In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust nonlinear iteration scheme based on the least squares method to estimate the coefficient functions of interest. We also establish the asymptotic theory of the resulting estimators under certain regularity assumptions, including the consistency, the convergence rate and the asymptotic distribution. Furthermore, we develop a least squares dummy variable method to study an important special case of the proposed model: the varying coefficient panel data model with additive fixed effects. To construct the pointwise confidence intervals for the coefficient functions, a residual-based block bootstrap method is proposed to reduce the computational burden as well as to avoid the accumulative errors. Simulation studies and a real data analysis are also carried out to assess the performance of our proposed methods.
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed covariates modeling the mean of the response are correlated with the spatial random effect. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive results. In this paper, we develop a computationally efficient spatial model in a Bayesian framework integrating novel prior structure that reduces spatial confounding. Starting from the univariate case, we extend our prior structure to case of multiple spatially confounded covariates. In a simulation study, we show that our novel model flexibly detects and reduces spatial confounding in spatial datasets, and it performs better than typically used methods such as restricted spatial regression. These results are promising for any applied researcher who wishes to interpret covariate effects in spatial regression models. As a real data illustration, we study the effect of elevation and temperature on the mean of daily precipitation in Germany.
Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic Gaussian processes. The partition is created using a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The Markov chain Monte Carlo algorithm is made possible through a Laplace approximation on the latent variables of the logistic Gaussian process model. This approximation marginalizes the parameters in each partition element, allowing an efficient search of the posterior distribution of the tessellation. The method has desirable consistency properties. In simulation and applications, the model successfully estimates the partition structure and conditional distribution of y.
We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinees latent state. Using topic transition probabilities along with response times enables us to capture examinees learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem solving item in 2012 Programme for International Student Assessment (PISA 2012).
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