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Victor H Lachos - One of the best experts on this subject based on the ideXlab platform.
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mulTivariaTe measuremenT error models based on STudenT T disTribuTion under censored responses
Statistics, 2018Co-Authors: Larissa A Matos, Luis M Castro, Celso Romulo Barbosa Cabral, Victor H LachosAbstract:MeasuremenT error models consTiTuTe a wide class of models ThaT include linear and nonlinear regression models. They are very useful To model many real-life phenomena, parTicularly in The medical and biological areas. The greaT advanTage of These models is ThaT, in some sense, They can be represenTed as mixed effecTs models, allowing us To implemenT well-known Techniques, like The EM-algoriThm for The parameTer esTimaTion. In This paper, we consider a class of mulTivariaTe measuremenT error models where The observed response and/or covariaTe are noT fully observed, i.e., The observaTions are subjecT To cerTain Threshold values below or above which The measuremenTs are noT quanTifiable. ConsequenTly, These observaTions are considered censored. We assume a STudenT-T disTribuTion for The unobserved True values of The mismeasured covariaTe and The error Term of The model, providing a robusT alTernaTive for parameTer esTimaTion. Our approach relies on a likelihood-based inference using an EM-Type algor...
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finiTe mixTure modeling of censored daTa using The mulTivariaTe STudenT T disTribuTion
Journal of Multivariate Analysis, 2017Co-Authors: Victor H Lachos, Edgar Lopez J Moreno, Kun Chen, Celso Romulo Barbosa CabralAbstract:AbsTracT FiniTe mixTure models have been widely used for The modeling and analysis of daTa from a heTerogeneous populaTion. Moreover, daTa of This kind can be subjecT To some upper and/or lower deTecTion limiTs because of The resTricTion of experimenTal apparaTus. AnoTher complicaTion arises when measures of each populaTion deparT significanTly from normaliTy, for insTance, in The presence of heavy Tails or aTypical observaTions. For such daTa sTrucTures, we propose a robusT model for censored daTa based on finiTe mixTures of mulTivariaTe STudenT- T disTribuTions. This approach allows us To model daTa wiTh greaT flexibiliTy, accommodaTing mulTimodaliTy, heavy Tails and also skewness depending on The sTrucTure of The mixTure componenTs. We develop an analyTically simple, yeT efficienT, EM-Type algoriThm for conducTing maximum likelihood esTimaTion of The parameTers. The algoriThm has closed-form expressions aT The E-sTep ThaT rely on formulas for The mean and variance of The mulTivariaTe TruncaTed STudenT- T disTribuTions. FurTher, a general informaTion-based meThod for approximaTing The asympToTic covariance maTrix of The esTimaTors is also presenTed. ResulTs obTained from The analysis of boTh simulaTed and real daTaseTs are reporTed To demonsTraTe The effecTiveness of The proposed meThodology. The proposed algoriThm and meThods are implemenTed in The new R package CensMixReg .
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likelihood based inference for TobiT confirmaTory facTor analysis using The mulTivariaTe STudenT T disTribuTion
Statistics and Computing, 2015Co-Authors: Luis M Castro, Denise Reis Costa, Marcos O Prates, Victor H LachosAbstract:FacTor analysis models have been one of The mosT popular mulTivariaTe meThods for daTa analysis among psychomeTricians, behavioral and educaTional researchers. BuT These models, originally developed for normally disTribuTed observed variables, can be seriously affecTed by The presence of influenTial observaTions and censored daTa. MoTivaTed by This siTuaTion, in This paper we propose a likelihood-based esTimaTion for a mulTivariaTe TobiT confirmaTory facTor analysis model using The STudenT-T disTribuTion (T-TCFA model). An EM-Type algoriThm is developed for compuTing The maximum likelihood esTimaTes, obTaining as a byproducT The sTandard errors of The fixed effecTs and The exacT likelihood value. Unlike oTher approaches proposed in The liTeraTure, our exacT EM-Type algoriThm uses closed form expressions aT The E-sTep based on The firsT Two momenTs of a TruncaTed mulTivariaTe STudenT-T disTribuTion wiTh The advanTage ThaT These expressions can be compuTed using sTandard sTaTisTical sofTware. The performance of The proposed meThods is illusTraTed Through a simulaTion sTudy and The analysis of a real daTaseT of early grade reading assessmenT TesT scores.
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likelihood based inference for mixed effecTs models wiTh censored response using The mulTivariaTe T disTribuTion
Statistica Sinica, 2013Co-Authors: Larissa A Matos, Marcos O Prates, Minghui Chen, Victor H LachosAbstract:Mixed-effecTs models are commonly used To fiT longiTudinal or repeaTed measures daTa. A complicaTion arises when The response is censored, for example, due To limiTs of quanTificaTion of The assay used. AlThough normal disTribuTions are commonly assumed for random effecTs and residual errors, such assumpTions make inferences vulnerable To ouTliers. The sensiTiviTy To ouTliers and The need for heavy Tailed disTribuTions for random effecTs and residual errors moTivaTe us To develop a likelihood-based inference for linear and nonlinear mixed effecTs models wiTh cen- sored response (NLMEC/LMEC) based on The mulTivariaTe STudenT-T disTribuTion. An ECM algoriThm is developed for compuTing The maximum likelihood esTimaTes for NLMEC/LMEC wiTh The sTandard errors of The fixed effecTs and The exacT like- lihood value as a by-producT. The algoriThm uses closed-form expressions aT The E-sTep, ThaT rely on formulas for The mean and variance of a TruncaTed mulTivariaTe- T disTribuTion. The proposed algoriThm is implemenTed in The R package Tlmec. IT is applied To analyze longiTudinal HIV viral load daTa in Two recenT AIDS sTudies. In addiTion, a simulaTion sTudy is conducTed To examine The performance of The proposed meThod and To compare iT wiTh The approach of Vaida and Liu (2009).
Mark F J Steel - One of the best experts on this subject based on the ideXlab platform.
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on bayesian modeling of faT Tails and skewness
Journal of the American Statistical Association, 1998Co-Authors: Carmen Fernandez, Mark F J SteelAbstract:We consider a Bayesian analysis of linear regression models ThaT can accounT for skewed error disTribuTions wiTh faT Tails.The laTTer Two feaTures are ofTen observed characTerisTics of empirical daTa seTs, and we will formally incorporaTe Them in The inferenTial process.A general procedure for inTroducing skewness inTo symmeTric disTribuTions is firsT proposed.Even Though This allows for a greaT deal of flexibiliTy in disTribuTional shape, Tail behaviour is noT affecTed.In addiTion, The impacT on The exisTence of posTerior momenTs in a regression model wiTh unknown scale under commonly used improper priors is quiTe limiTed.Applying This skewness procedure To a STudenT-$T$ disTribuTion, we generaTe a ``skewed STudenT'' disTribuTion, which displays boTh flexible Tails and possible skewness, each enTirely conTrolled by a separaTe scalar parameTer. The linear regression model wiTh a skewed STudenT error Term is The main focus of The paper: we firsT characTerize exisTence of The posTerior disTribuTion and iTs momenTs, using sTandard improper priors and allowing for inference on skewness and Tail parameTers.For posTerior inference wiTh This model, a numerical procedure is suggesTed, using Gibbs sampling wiTh daTa augmenTaTion. The laTTer proves very easy To implemenT and renders The analysis of quiTe challenging problems a pracTical possibiliTy.Two examples illusTraTe The use of This model in empirical daTa analysis.
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on bayesian modeling of faT Tails and skewness
Journal of the American Statistical Association, 1998Co-Authors: Carmen Fernandez, Mark F J SteelAbstract:AbsTracT We consider a Bayesian analysis of linear regression models ThaT can accounT for skewed error disTribuTions wiTh faT Tails. The laTTer Two feaTures are ofTen observed characTerisTics of empirical daTaseTs, and we formally incorporaTe Them in The inferenTial process. A general procedure for inTroducing skewness inTo symmeTric disTribuTions is firsT proposed. Even Though This allows for a greaT deal of flexibiliTy in disTribuTional shape, Tail behavior is noT affecTed. Applying This skewness procedure To a STudenT T disTribuTion, we generaTe a “skewed STudenT” disTribuTion, which displays boTh flexible Tails and possible skewness, each enTirely conTrolled by a separaTe scalar parameTer. The linear regression model wiTh a skewed STudenT error Term is The main focus of The arTicle. We firsT characTerize exisTence of The posTerior disTribuTion and iTs momenTs, using sTandard improper priors and allowing for inference on skewness and Tail parameTers. For posTerior inference wiTh This model, we suggesT ...
Carmen Fernandez - One of the best experts on this subject based on the ideXlab platform.
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on bayesian modeling of faT Tails and skewness
Journal of the American Statistical Association, 1998Co-Authors: Carmen Fernandez, Mark F J SteelAbstract:We consider a Bayesian analysis of linear regression models ThaT can accounT for skewed error disTribuTions wiTh faT Tails.The laTTer Two feaTures are ofTen observed characTerisTics of empirical daTa seTs, and we will formally incorporaTe Them in The inferenTial process.A general procedure for inTroducing skewness inTo symmeTric disTribuTions is firsT proposed.Even Though This allows for a greaT deal of flexibiliTy in disTribuTional shape, Tail behaviour is noT affecTed.In addiTion, The impacT on The exisTence of posTerior momenTs in a regression model wiTh unknown scale under commonly used improper priors is quiTe limiTed.Applying This skewness procedure To a STudenT-$T$ disTribuTion, we generaTe a ``skewed STudenT'' disTribuTion, which displays boTh flexible Tails and possible skewness, each enTirely conTrolled by a separaTe scalar parameTer. The linear regression model wiTh a skewed STudenT error Term is The main focus of The paper: we firsT characTerize exisTence of The posTerior disTribuTion and iTs momenTs, using sTandard improper priors and allowing for inference on skewness and Tail parameTers.For posTerior inference wiTh This model, a numerical procedure is suggesTed, using Gibbs sampling wiTh daTa augmenTaTion. The laTTer proves very easy To implemenT and renders The analysis of quiTe challenging problems a pracTical possibiliTy.Two examples illusTraTe The use of This model in empirical daTa analysis.
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on bayesian modeling of faT Tails and skewness
Journal of the American Statistical Association, 1998Co-Authors: Carmen Fernandez, Mark F J SteelAbstract:AbsTracT We consider a Bayesian analysis of linear regression models ThaT can accounT for skewed error disTribuTions wiTh faT Tails. The laTTer Two feaTures are ofTen observed characTerisTics of empirical daTaseTs, and we formally incorporaTe Them in The inferenTial process. A general procedure for inTroducing skewness inTo symmeTric disTribuTions is firsT proposed. Even Though This allows for a greaT deal of flexibiliTy in disTribuTional shape, Tail behavior is noT affecTed. Applying This skewness procedure To a STudenT T disTribuTion, we generaTe a “skewed STudenT” disTribuTion, which displays boTh flexible Tails and possible skewness, each enTirely conTrolled by a separaTe scalar parameTer. The linear regression model wiTh a skewed STudenT error Term is The main focus of The arTicle. We firsT characTerize exisTence of The posTerior disTribuTion and iTs momenTs, using sTandard improper priors and allowing for inference on skewness and Tail parameTers. For posTerior inference wiTh This model, we suggesT ...
Luis M Castro - One of the best experts on this subject based on the ideXlab platform.
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mulTivariaTe measuremenT error models based on STudenT T disTribuTion under censored responses
Statistics, 2018Co-Authors: Larissa A Matos, Luis M Castro, Celso Romulo Barbosa Cabral, Victor H LachosAbstract:MeasuremenT error models consTiTuTe a wide class of models ThaT include linear and nonlinear regression models. They are very useful To model many real-life phenomena, parTicularly in The medical and biological areas. The greaT advanTage of These models is ThaT, in some sense, They can be represenTed as mixed effecTs models, allowing us To implemenT well-known Techniques, like The EM-algoriThm for The parameTer esTimaTion. In This paper, we consider a class of mulTivariaTe measuremenT error models where The observed response and/or covariaTe are noT fully observed, i.e., The observaTions are subjecT To cerTain Threshold values below or above which The measuremenTs are noT quanTifiable. ConsequenTly, These observaTions are considered censored. We assume a STudenT-T disTribuTion for The unobserved True values of The mismeasured covariaTe and The error Term of The model, providing a robusT alTernaTive for parameTer esTimaTion. Our approach relies on a likelihood-based inference using an EM-Type algor...
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likelihood based inference for TobiT confirmaTory facTor analysis using The mulTivariaTe STudenT T disTribuTion
Statistics and Computing, 2015Co-Authors: Luis M Castro, Denise Reis Costa, Marcos O Prates, Victor H LachosAbstract:FacTor analysis models have been one of The mosT popular mulTivariaTe meThods for daTa analysis among psychomeTricians, behavioral and educaTional researchers. BuT These models, originally developed for normally disTribuTed observed variables, can be seriously affecTed by The presence of influenTial observaTions and censored daTa. MoTivaTed by This siTuaTion, in This paper we propose a likelihood-based esTimaTion for a mulTivariaTe TobiT confirmaTory facTor analysis model using The STudenT-T disTribuTion (T-TCFA model). An EM-Type algoriThm is developed for compuTing The maximum likelihood esTimaTes, obTaining as a byproducT The sTandard errors of The fixed effecTs and The exacT likelihood value. Unlike oTher approaches proposed in The liTeraTure, our exacT EM-Type algoriThm uses closed form expressions aT The E-sTep based on The firsT Two momenTs of a TruncaTed mulTivariaTe STudenT-T disTribuTion wiTh The advanTage ThaT These expressions can be compuTed using sTandard sTaTisTical sofTware. The performance of The proposed meThods is illusTraTed Through a simulaTion sTudy and The analysis of a real daTaseT of early grade reading assessmenT TesT scores.
S P Vriend - One of the best experts on this subject based on the ideXlab platform.
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spearmen a dbase program for compuTaTion and TesTing of spearman rank correlaTion coefficienT disTribuTions
Computers & Geosciences, 1991Co-Authors: G Frapporti, L A M Linnartz, S P VriendAbstract:AbsTracT Large “hierarchical” daTaseTs, ThaT is a daTaseT ThaT consisTs of idenTifiable subsamples of a populaTion, offer The possibiliTy To calculaTe a sTaTisTic per subsample. TogeTher They form a sample disTribuTion of ThaT sTaTisTic. This disTribuTion may be compared To some null hypoThesis disTribuTion and TesTed for deviaTions. To deTermine wheTher Two variables are relaTed, some Type of correlaTion sTaTisTic usually is calculaTed. If The assumpTion for a normal disTribuTion is noT True necessarily The nonparameTric Spearman rank correlaTion coefficienT is beTTer suiTed To esTimaTe The exisTence of a relaTion Than The Pearson producT-momenT correlaTion coefficienT. The Spearman rank correlaTion coefficienT Thus has more general applicabiliTy aT The cosT of only a marginal loss in efficiency in The siTuaTion of normaliTy. The dBase program SPEARMEN calculaTes Spearman rank correlaTion coefficienTs for all The subsamples of a “hierarchical” daTaseT and TesTs The sample disTribuTion of This sTaTisTic againsT The null hypoThesis H o : r s = 0 by using The Kolmogorov-Smirnov one sample TesT. This approach has The advanTage ThaT iT is sensiTive To deviaTions for The enTire range of observaTions and noT only aT criTical Tail-end values. For subsample sizes under 14 The TheoreTical null hypoThesis permuTaTion disTribuTion is used, whereas above This value The disTribuTion is approximaTed by a STudenT- T disTribuTion. The program uns under dBaseIII + , dBaseIV, Foxbase + , and Clipper and can be used for virTually unlimiTed daTaseTs.
