DSpace Angular :: Browsing by Author "Castro, Luis M."

Browsing by Author "Castro, Luis M."

Now showing 1 - 16 of 16

A Bayesian approach for mixed effects state-space models under skewness and heavy tails
(2023) Hernandez-Velasco, Lina L.; Abanto-Valle, Carlos A.; Dey, Dipak K.; Castro, Luis M.
Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.
A Censored Time Series Analysis for Responses on the Unit Interval: An Application to Acid Rain Modeling
(2024) Schumacher, Fernanda L.; Matos, Larissa A.; Lachos, Victor H.; Abanto-Valle, Carlos A.; Castro, Luis M.
In this paper, we propose an autoregressive model for time series in which the variable of interest lies in the unit interval and is subject to certain threshold values below or above which the measurements are not quantifiable. The model includes an independent beta regression (Ferrari and Cribari-Neto, J. Appl. Stat., 31, 799-815 2004) as a special case. A Markov chain Monte Carlo (MCMC) algorithm is tailored to obtain Bayesian posterior distributions of unknown quantities of interest. The likelihood function was used to compute Bayesian model selection measures. We discuss the construction of the proposed model and compare it with alternative models by using simulated data. Finally, we illustrate the use of our proposal by modeling a left-censored weekly series of acid rain data.
Bayesian analysis of survival data with missing censoring indicators
(WILEY, 2021) Brownstein, Naomi C.; Bunn, Veronica; Castro, Luis M.; Sinha, Debajyoti
In some large clinical studies, it may be impractical to perform the physical examination to every subject at his/her last monitoring time in order to diagnose the occurrence of the event of interest. This gives rise to survival data with missing censoring indicators where the probability of missing may depend on time of last monitoring and some covariates. We present a fully Bayesian semi-parametric method for such survival data to estimate regression parameters of the proportional hazards model of Cox. Theoretical investigation and simulation studies show that our method performs better than competing methods. We apply the proposed method to analyze the survival data with missing censoring indicators from the Orofacial Pain: Prospective Evaluation and Risk Assessment study.
Bayesian Inference for Shape Mixtures of Skewed Distributions, with Application to Regression Analysis
(INT SOC BAYESIAN ANALYSIS, 2008) Arellano Valle, Reinaldo B.; Castro, Luis M.; Genton, Marc G.; Gomez, Hector W.
We introduce a class of shape mixtures of skewed distributions and study some of its main properties. We discuss a Bayesian interpretation and some invariance results of the proposed class. We develop a Bayesian analysis of the skew-normal, skew-generalized-normal, skew-normal-t and skew-t-normal linear regression models under some special prior specifications for the model parameters. In particular, we show that the full posterior of the skew-normal regression model parameters is proper under an arbitrary proper prior for the shape parameter and noninformative prior for the other parameters. We implement a convenient hierarchical representation in order to obtain the corresponding posterior analysis. We illustrate our approach with an application to a real dataset on characteristics of Australian male athletes.
Bayesian inference on multivariate-t nonlinear mixed-effects models for multiple longitudinal data with missing values
(2018) Wang, Wan-Lun; Castro, Luis M.
The multivariate-t nonlinear mixed-effects model (MtNLMM) has been shown to be a promising robust tool for analyzing multiple longitudinal trajectories following arbitrary growth patterns in the presence of outliers and possible missing responses. Owing to intractable likelihood function of the model, we devise a fully Bayesian estimating procedure to account for the uncertainties of model parameters, random effects, and missing responses via the Markov chain Monte Carlo method. Posterior predictive inferences for the future values and missing responses are also investigated. We conduct a simulation study to demonstrate the feasibility of our Bayesian sampling schemes. The proposed techniques are illustrated through applications to two case studies.
Bayesian Modeling of Censored Partial Linear Models using Scale-Mixtures of Normal Distributions
(AMER INST PHYSICS, 2012) Castro, Luis M.; Lachos, Victor H.; Ferreira, Guillermo P.; Arellano Valle, Reinaldo B.; Stern, JM; Lauretto, MD; Polpo, A; Diniz, MA
Regression models where the dependent variable is censored (limited) are usually considered in statistical analysis. Particularly, the case of a truncation to the left of zero and a normality assumption for the error terms is studied in detail by [1] in the well known Tobit model. In the present article, this typical censored regression model is extended by considering a partial linear model with errors belonging to the class of scale mixture of normal distributions. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. We evaluate the performances of the proposed methods with simulated data. In addition, we present an application in order to know what type of variables affect the income of housewives.
Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness
(2019) Castro, Luis M.; Wang, Wan-Lun; Lachos, Victor H.; de Carvalho, Vanda Inacio; Bayes, Cristian L.
In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.
Bregman divergence to generalize Bayesian influence measures for data analysis
(2021) De Oliveira, Melaine C.; Castro, Luis M.; Dey, Dipak K.; Sinha, Debajyoti
For existing Bayesian cross-validated measure of influence of each observation on the posterior distribution, this paper considers a generalization using the Bregman Divergence (BD). We investigate various practically useful and desirable properties of these BD based measures to demonstrate the superiority of these measures compared to existing Bayesian measures of influence and Bayesian residual based diagnostics. We provide a practical and easily comprehensible method for calibrating these BD based measures. Also, we show how to compute our BD based measure via Markov chain Monte Carlo (MCMC) samples from a single posterior based on the full data. Using a Bayesian meta-analysis of clinical trials, we illustrate how our new measures of influence of observations have more useful practical roles for data analysis than popular Bayesian residual analysis tools. (c) 2020 Elsevier B.V. All rights reserved.
Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results
(2013) San Martin, Ernesto; Rolin, Jean-Marie; Castro, Luis M.
In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution G generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution G is not identified. It is finally shown that, after introducing two identification restrictions, either on the distribution G or on the item parameters, the distribution G and the item parameters are identified provided an infinite quantity of items is available.
Joint Random Partition Models for Multivariate Change Point Analysis
(2024) Quinlan, Jose J.; Page, Garritt L.; Castro, Luis M.
Change point analyses are concerned with identifying positions of an ordered stochastic process that undergo abrupt local changes of some underly-ing distribution. When multiple processes are observed, it is often the case that information regarding the change point positions is shared across the different processes. This work describes a method that takes advantage of this type of infor-mation. Since the number and position of change points can be described through a partition with contiguous clusters, our approach develops a joint model for these types of partitions. We describe computational strategies associated with our ap-proach and illustrate improved performance in detecting change points through a small simulation study. We then apply our method to a financial data set of emerging markets in Latin America and highlight interesting insights discovered due to the correlation between change point locations among these economies.
Mixtures of t factor analysers with censored responses and external covariates: An application to educational data from Peru
(2024) Wang, Wan-Lun; Castro, Luis M.; Li, Huei-Jyun; Lin, Tsung-, I
Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures of t factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.
Modeling Point Referenced Spatial Count Data: A Poisson Process Approach
(2024) Morales-Navarrete, Diego; Bevilacqua, Moreno; Caamano-Carrillo, Christian; Castro, Luis M.
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and mathematical tractability. However, this assumption seems to be restrictive when dealing with counting data. To deal with this situation, we propose a random field with a Poisson marginal distribution considering a sequence of independent copies of a random field with an exponential marginal distribution as "inter-arrival times " in the counting renewal processes framework. Our proposal can be viewed as a spatial generalization of the Poisson counting process. Unlike the classical hierarchical Poisson Log-Gaussian model, our proposal generates a (non)-stationary random field that is mean square continuous and with Poisson marginal distributions. For the proposed Poisson spatial random field, analytic expressions for the covariance function and the bivariate distribution are provided. In an extensive simulation study, we investigate the weighted pairwise likelihood as a method for estimating the Poisson random field parameters. Finally, the effectiveness of our methodology is illustrated by an analysis of reindeer pellet-group survey data, where a zero-inflated version of the proposed model is compared with zero-inflated Poisson Log-Gaussian and Poisson Gaussian copula models. for this article, including technical proofs and R code for reproducing the work, are available as an online supplement.
Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution
(ELSEVIER INC, 2022) Galarza, Christian E.; Matos, Larissa A.; Castro, Luis M.; Lachos, Victor H.
In this paper, we compute doubly truncated moments for the selection elliptical class of distributions, including some multivariate asymmetric versions of well-known elliptical distributions, such as the normal, Student's t, slash, among others. We address the moments for doubly truncated members of this family, establishing neat formulation for high-order moments and its first two moments. We establish sufficient and necessary conditions for the existence of these truncated moments. Further, we propose optimized methods to handle the extreme setting of the parameters, partitions with almost zero volume or no truncation, which are validated with numerical studies. All results have been particularized to the unified skew-t distribution, a complex multivariate asymmetric heavy-tailed distribution which includes the extended skew-t, extended skew-normal, skew-t, and skew-normal distributions as particular and limiting cases. (C) 2021 Elsevier Inc. All rights reserved.
Partially linear censored regression models using heavy-tailed distributions: A Bayesian approach
(ELSEVIER SCIENCE BV, 2014) Castro, Luis M.; Lachos, Victor H.; Ferreira, Guillermo P.; Arellano Valle, Reinaldo B.
Linear regression models where the response variable is censored are often considered in statistical analysis. A parametric relationship between the response variable and covariates and normality of random errors are assumptions typically considered in modeling censored responses. In this context, the aim of this paper is to extend the normal censored regression model by considering on one hand that the response variable is linearly dependent on some covariates whereas its relation to other variables is characterized by nonparametric functions, and on the other hand that error terms of the regression model belong to a class of symmetric heavy-tailed distributions capable of accommodating outliers and/or influential observations in a better way than the normal distribution. We achieve a fully Bayesian inference using pth-degree spline smooth functions to approximate the nonparametric functions. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. The newly developed procedures are illustrated with an application and simulated data. (C) 2013 Elsevier B.V. All rights reserved.
Student-t censored regression model: properties and inference
(2012) Arellano-Valle, Reinaldo B.; Castro, Luis M.; Gonzalez-Farias, Graciela; Munoz-Gajardo, Karla A.
In statistical analysis, particularly in econometrics, it is usual to consider regression models where the dependent variable is censored (limited). In particular, a censoring scheme to the left of zero is considered here. In this article, an extension of the classical normal censored model is developed by considering independent disturbances with identical Student-t distribution. In the context of maximum likelihood estimation, an expression for the expected information matrix is provided, and an efficient EM-type algorithm for the estimation of the model parameters is developed. In order to know what type of variables affect the income of housewives, the results and methods are applied to a real data set. A brief review on the normal censored regression model or Tobit model is also presented.
The skew-t censored regression model: parameter estimation via an EM-type algorithm
(KOREAN STATISTICAL SOC, 2022) Lachos, Victor H.; Bazan, Jorge L.; Castro, Luis M.; Park, Jiwon
The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.

Browsing by Author "Castro, Luis M."

Results Per Page

Sort Options