Algorithms for the likelihood-based estimation of the random coefficient model

The existing algorithms for fitting the random coefficient models tend to have difficulties associated with the covariance matrix parameter space. New ML and REML algorithms are developed, explicitly addressing the parameter space problem. Theoretical justification and numerical results are presented.

[1]  Rachel M. Harter,et al.  The multivariate components of variance model for small area estimation , 1986 .

[2]  D. Rubin,et al.  The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence , 1994 .

[3]  J. A. Calvin.  REML estimation in unbalanced multivariate variance components models using an EM algorithm , 1993 .

[4]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[5]  D. Bates,et al.  Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data , 1988 .

[6]  Richard Barakat.  Probability density functions of sums of sinusoidal waves having nonuniform random phases and random numbers of multipaths , 1988 .

[7]  R. Potthoff,et al.  A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[8]  N. Laird,et al.  Maximum likelihood computations with repeated measures: application of the EM algorithm , 1987 .

[9]  Yasuo Amemiya,et al.  Multivariate Mixed Model Analysis , 2019, Applied Mixed Model Analysis.

[10]  R. Jennrich,et al.  Unbalanced repeated-measures models with structured covariance matrices. , 1986, Biometrics.

[11]  James Rochon,et al.  ARMA Covariance Structures with Time Heteroscedasticity for Repeated Measures Experiments , 1992 .

[12]  Yasuo Amemiya,et al.  Asymptotic Properties of the Estimators for Multivariate Components of Variance , 1994 .

[13]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[14]  Ingram Olkin,et al.  Maximum Likelihood Estimators and Likelihood Ratio Criteria in Multivariate Components of Variance , 1986 .

[15]  Mark C. K. Yang,et al.  Large sample inference in random coefficient regression models , 1986 .

[16]  Yasuo Amemiya,et al.  What Should be Done When an Estimated between-Group Covariance Matrix is not Nonnegative Definite? , 1985 .

[17]  W. G. Hill,et al.  Probabilities of Non-Positive Definite between-Group or Genetic Covariance Matrices , 1978 .

[18]  B. Wüthrich.  AN INTERNATIONAL SYMPOSIUM , 1997 .

[19]  Calyampudi R. Rao,et al.  The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. , 1965, Biometrika.

[20]  G. Reinsel,et al.  Models for Longitudinal Data with Random Effects and AR(1) Errors , 1989 .

[21]  R W Helms,et al.  Maximum likelihood estimation for incomplete repeated-measures experiments under an ARMA covariance structure. , 1989, Biometrics.

[22]  Madan L. Puri,et al.  New perspectives in theoretical and applied statistics , 1986 .

[23]  H. Goldstein.  Multilevel mixed linear model analysis using iterative generalized least squares , 1986 .

[24]  C. Shin.  On the multivariate random and mixed coefficient analysis , 1995 .