• Title, Summary, Keyword: restricted maximum likelihood

Search Result 95, Processing Time 0.031 seconds

A correction of SE from penalized partial likelihood in frailty models

  • Ha, Il-Do
    • Journal of the Korean Data and Information Science Society
    • /
    • v.20 no.5
    • /
    • pp.895-903
    • /
    • 2009
  • The penalized partial likelihood based on restricted maximum likelihood method has been widely used for the inference of frailty models. However, the standard-error estimate for frailty parameter estimator can be downwardly biased. In this paper we show that such underestimation can be corrected by using hierarchical likelihood. In particular, the hierarchical likelihood gives a statistically efficient procedure for various random-effect models including frailty models. The proposed method is illustrated via a numerical example and simulation study. The simulation results demonstrate that the corrected standard-error estimate largely improves such bias.

  • PDF

Restricted maximum likelihood estimation of a censored random effects panel regression model

  • Lee, Minah;Lee, Seung-Chun
    • Communications for Statistical Applications and Methods
    • /
    • v.26 no.4
    • /
    • pp.371-383
    • /
    • 2019
  • Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

Bayes Estimation of Two Ordered Exponential Means

  • Hong, Yeon-Woong;Kwon, Yong-Mann
    • Journal of the Korean Data and Information Science Society
    • /
    • v.15 no.1
    • /
    • pp.273-284
    • /
    • 2004
  • Bayes estimation of parameters is considered for two independent exponential distributions with ordered means. Order restricted Bayes estimators for means are obtained with respect to inverted gamma, noninformative prior and uniform prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the mean are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.

  • PDF

Second-Order REML for Random Effects Models

  • Ha, Il-Do;Cho, Geon-Ho
    • Journal of the Korean Data and Information Science Society
    • /
    • v.12 no.1
    • /
    • pp.19-25
    • /
    • 2001
  • Random effects models which describe the dependence via random effects in various correlated data have recently received considerable attention in the biomedical literature. They include mixed linear models (MLMs), generatized linear mixed models (GLMMS) and hierarchical generalized linear models (HGLMs). For the inference Lee and Nelder (2000) proposed the first-and second-order REML (restricted maximum likelihood) methods based on hierarchical-likelihood of tee and Welder (1996). In this paper, for Poisson-gamma HGLMs the new methods are theoretically compared with marginal likelihood methods and both methods are illustrated by two practical examples.

  • PDF

Reliability Estimation for a Shared-Load System Based on Freund Model

  • Hong, Yeon-Woong;Lee, Jae-Man;Cha, Young-Joon
    • Journal of the Korean Data and Information Science Society
    • /
    • v.6 no.2
    • /
    • pp.1-7
    • /
    • 1995
  • This paper considers the reliability estimation of a two-component shared-load system based on Freund model. Maximum likelihood estimator, order restricted maximum likelihood estimator and uniformly minimum variance unbiased estimator of the reliability function for the system are obtained. Performance of three estimators for moderate sample sizes is studied by simulation.

  • PDF

Estimation for ordered means in normal distributions

  • Cho, Kil-Ho
    • Journal of the Korean Data and Information Science Society
    • /
    • v.21 no.5
    • /
    • pp.951-958
    • /
    • 2010
  • In this paper, we obtain the restricted maximum likelihood estimators (RMLE's) for means in normal distributions with the ordered mean constraints. The biases and mean squared errors (MSE's) of these RMLE's are approximated by Mote Carlo methods. In every case a substantial savings in MSE is obtained at the expense of a small loss in bias when using RMLE's instead of the unrestricted MLE's.

The restricted maximum likelihood estimation of a censored regression model

  • Lee, Seung-Chun
    • Communications for Statistical Applications and Methods
    • /
    • v.24 no.3
    • /
    • pp.291-301
    • /
    • 2017
  • It is well known in a small sample that the maximum likelihood (ML) approach for variance components in the general linear model yields estimates that are biased downward. The ML estimate of residual variance tends to be downwardly biased. The underestimation of residual variance, which has implications for the estimation of marginal effects and asymptotic standard error of estimates, seems to be more serious in some limited dependent variable models, as shown by some researchers. An alternative frequentist's approach may be restricted or residual maximum likelihood (REML), which accounts for the loss in degrees of freedom and gives an unbiased estimate of residual variance. In this situation, the REML estimator is derived in a censored regression model. A small sample the REML is shown to provide proper inference on regression coefficients.

ORDER RESTRICTED TESTS FOR SYMMETRY AGAINST POSITIVE BIASEDNESS

  • Oh, Myong-Sik
    • Journal of the Korean Statistical Society
    • /
    • v.36 no.3
    • /
    • pp.335-347
    • /
    • 2007
  • Two new types of positive biasedness, which are closely related to Type III positive biasedness (Yanagimoto and Sibuya, 1972), are proposed. We call these near Type III positive biasedness. Though no implication between Type II and near Type III biasedness exists, near Type III seems to be less restrictive than Type II biasedness. Constrained maximum likelihood estimates of distribution functions under near Type III positive bisedness are obtained. The likelihood ratio tests of symmetry against new positive biasedness restrictions are proposed. A small simulation study is conducted to compare the performance of the tests.

Interval Estimation in Mixed Model by Use of PROC MIXED (PROC MIXED를 활용한 혼합모형의 신뢰구간추정)

  • Park Dong-Joon
    • The Korean Journal of Applied Statistics
    • /
    • v.19 no.2
    • /
    • pp.349-360
    • /
    • 2006
  • PROC MIXED in SAS can be utilized to make inferences on parameters in a mixed model by use of Restricted Maximum Likelihood Estimation Method or Maximum Likelihood Estimation Method which has more merits than ANOVA method. A regression model with unbalanced nested error structure that belongs to a mixed model is used to construct confidence intervals on variances among groups, within groups, and regression coefficients in the model. PROC MIXED is applied to three different sample sizes for simulation. As a result of the simulation study, PROC MIXED generates confidence intervals on parameters that maintain the stated confidence coefficient in a large sample size. However, it does not generate confidence intervals that maintain the stated confidence coefficient for variance components among groups and intercept in a small sample size.

Estimation of Genetic and Phenotypic Covariance Functions for Body Weight as Longitudinal Data of SD-II Swine Line

  • Liu, Wenzhong;Cao, Guoqing;Zhou, Zhongxiao;Zhang, Guixian
    • Asian-Australasian Journal of Animal Sciences
    • /
    • v.15 no.5
    • /
    • pp.622-626
    • /
    • 2002
  • Growth records over six generations of 686 pigs in SD-II Swine Line were used to estimate the genetic and phenotypic covariance functions for body weight as longitudinal data. A random regression model with Legendre polynomials of age as independent variables was used to estimate the (co)variances among the regression coefficients, thus the coefficients of genetic and permanent environmental covariance functions by restricted maximum likelihood employing the average information algorithm. The results showed that, using litter effect as additional random effect, a reduced order of fit did not describe the data adequately. For all five orders of fit, however, the change trends of genetic and phenotypic (co)variances were very similar from ${\kappa}$=3 onwards.