• Title, Summary, Keyword: random effects

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Bayesian modeling of random effects precision/covariance matrix in cumulative logit random effects models

  • Kim, Jiyeong;Sohn, Insuk;Lee, Keunbaik
    • Communications for Statistical Applications and Methods
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    • v.24 no.1
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    • pp.81-96
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    • 2017
  • Cumulative logit random effects models are typically used to analyze longitudinal ordinal data. The random effects covariance matrix is used in the models to demonstrate both subject-specific and time variations. The covariance matrix may also be homogeneous; however, the structure of the covariance matrix is assumed to be homoscedastic and restricted because the matrix is high-dimensional and should be positive definite. To satisfy these restrictions two Cholesky decomposition methods were proposed in linear (mixed) models for the random effects precision matrix and the random effects covariance matrix, respectively: modified Cholesky and moving average Cholesky decompositions. In this paper, we use these two methods to model the random effects precision matrix and the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. The methods are illustrated by a lung cancer data set.

An Analysis on Vehicle Accident Factors of Intersections using Random Effects Tobit Regression Model (Random Effects Tobit 회귀모형을 이용한 교차로 교통사고 요인 분석)

  • Lee, Sang Hyuk;Lee, Jung-Beom
    • The Journal of The Korea Institute of Intelligent Transport Systems
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    • v.16 no.1
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    • pp.26-37
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    • 2017
  • The study is to develop safety performance functions(SPFs) for urban intersections using random effects Tobit regression model and to analyze correlations between crashes and factors. Also fixed effects Tobit regression model was estimated to compare and analyze model validation with random effects model. As a result, AADT, speed limits, number of lanes, land usage, exclusive right turn lanes and front traffic signal were found to be significant. For comparing statistical significance between random and fixed effects model, random effects Tobit regression model of total crash rate could be better statistical significance with $R^2_p$ : 0.418, log-likelihood at convergence: -3210.103, ${\rho}^2$: 0.056, MAD: 19.533, MAPE: 75.725, RMSE: 26.886 comparing with $R^2_p$ : 0.298, log-likelihood at convergence: -3276.138, ${\rho}^2$: 0.037, MAD: 20.725, MAPE: 82.473, RMSE: 27.267 for the fixed model. Also random effects Tobit regression model of injury crash rate has similar results of model statistical significant with random effects Tobit regression model.

Matching Conditions for Predicting the Random Effects in ANOVA Models

  • Chang, In-Hong
    • 한국데이터정보과학회:학술대회논문집
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    • pp.1-6
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    • 2006
  • We consider the issue of Bayesian prediction of the unobservable random effects, And we characterize priors that ensure approximate frequentist validity of posterior quantiles of unobservable random effects. Finally we show that the probability matching criteria for prediction of unobservable random effects in one-way random ANOVA model.

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On prediction of random effects in log-normal frailty models

  • Ha, Il-Do;Cho, Geon-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.1
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    • pp.203-209
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    • 2009
  • Frailty models are useful for the analysis of correlated and/or heterogeneous survival data. However, the inferences of fixed parameters, rather than random effects, have been mainly studied. The prediction (or estimation) of random effects is also practically useful to investigate the heterogeneity of the hospital or patient effects. In this paper we propose how to extend the prediction method for random effects in HGLMs (hierarchical generalized linear models) to log-normal semiparametric frailty models with nonparametric baseline hazard. The proposed method is demonstrated by a simulation study.

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Random Effects Models for Multivariate Survival Data: Hierarchical-Likelihood Approach

  • Ha Il Do;Lee Youngjo;Song Jae-Kee
    • Proceedings of the Korean Statistical Society Conference
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    • pp.193-200
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    • 2000
  • Modelling the dependence via random effects in censored multivariate survival data has recently received considerable attention in the biomedical literature. The random effects models model not only the conditional survival times but also the conditional hazard rate. Systematic likelihood inference for the models with random effects is possible using Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). The purpose of this presentation is to introduce Ha et al.'s (2000a,b) inferential methods for the random effects models via the h-likelihood, which provide a conceptually simple, numerically efficient and reliable inferential procedures.

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Modeling of random effects covariance matrix in marginalized random effects models

  • Lee, Keunbaik;Kim, Seolhwa
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.3
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    • pp.815-825
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    • 2016
  • Marginalized random effects models (MREMs) are often used to analyze longitudinal categorical data. The models permit direct estimation of marginal mean parameters and specify the serial correlation of longitudinal categorical data via the random effects. However, it is not easy to estimate the random effects covariance matrix in the MREMs because the matrix is high-dimensional and must be positive-definite. To solve these restrictions, we introduce two modeling approaches of the random effects covariance matrix: partial autocorrelation and the modified Cholesky decomposition. These proposed methods are illustrated with the real data from Korean genomic epidemiology study.

Bayesian baseline-category logit random effects models for longitudinal nominal data

  • Kim, Jiyeong;Lee, Keunbaik
    • Communications for Statistical Applications and Methods
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    • v.27 no.2
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    • pp.201-210
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    • 2020
  • Baseline-category logit random effects models have been used to analyze longitudinal nominal data. The models account for subject-specific variations using random effects. However, the random effects covariance matrix in the models needs to explain subject-specific variations as well as serial correlations for nominal outcomes. In order to satisfy them, the covariance matrix must be heterogeneous and high-dimensional. However, it is difficult to estimate the random effects covariance matrix due to its high dimensionality and positive-definiteness. In this paper, we exploit the modified Cholesky decomposition to estimate the high-dimensional heterogeneous random effects covariance matrix. Bayesian methodology is proposed to estimate parameters of interest. The proposed methods are illustrated with real data from the McKinney Homeless Research Project.

Review and discussion of marginalized random effects models (주변화 변량효과모형의 조사 및 고찰)

  • Jeon, Joo Yeong;Lee, Keunbaik
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.6
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    • pp.1263-1272
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    • 2014
  • Longitudinal categorical data commonly occur from medical, health, and social sciences. In these data, the correlation of repeated outcomes is taken into account to explain the effects of covariates exactly. In this paper, we introduce marginalized random effects models that are used for the estimation of the population-averaged effects of covariates. We also review how these models have been developed. Real data analysis is presented using the marginalized random effects.

Autoregressive Cholesky Factor Modeling for Marginalized Random Effects Models

  • Lee, Keunbaik;Sung, Sunah
    • Communications for Statistical Applications and Methods
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    • v.21 no.2
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    • pp.169-181
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    • 2014
  • Marginalized random effects models (MREM) are commonly used to analyze longitudinal categorical data when the population-averaged effects is of interest. In these models, random effects are used to explain both subject and time variations. The estimation of the random effects covariance matrix is not simple in MREM because of the high dimension and the positive definiteness. A relatively simple structure for the correlation is assumed such as a homogeneous AR(1) structure; however, it is too strong of an assumption. In consequence, the estimates of the fixed effects can be biased. To avoid this problem, we introduce one approach to explain a heterogenous random effects covariance matrix using a modified Cholesky decomposition. The approach results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The interpretation of the parameters is sensible. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using this method.

A Cumulative Logit Mixed Model for Ordered Response Data

  • Choi, Jae-Sung
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.1
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    • pp.123-130
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    • 2006
  • This paper discusses about how to build up a mixed-effects model using cumulative logits when some factors are fixed and others are random. Location effects are considered as random effects by choosing them randomly from a population of locations. Estimation procedure for the unknown parameters in a suggested model is also discussed by an illustrated example.

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