×

zbMATH — the first resource for mathematics

The derivation of BLUP, ML, REML estimation methods for generalised linear mixed models. (English) Zbl 0875.62341
Summary: This paper presents a unified derivation of BLUP, ML and REML estimation procedures for normally distributed response variables with possibly correlated random components occurring in the mixed model for the mean. The theory is extended to generalised linear mixed models, where the response variable is not necessarily normally distributed but the model may be fitted using a penalised quasi-likelihood approach which mirrors the development in normal theory models. The method is applied to binomially distributed response variables with logit link to a mixed model containing a random component distributed as an AR(1) process.

MSC:
62J12 Generalized linear models (logistic models)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.2307/2290687 · Zbl 0775.62195
[2] DOI: 10.2307/1269603 · Zbl 0597.62018
[3] DOI: 10.1080/03610918708812599 · Zbl 0665.62069
[4] DOI: 10.2307/2286796 · Zbl 0373.62040
[5] Henderson C.R., Statistical Genetics and PlantBreeding 982 pp 141– (1963)
[6] Henderson, C.R. Sire evaluation and genetic trends. Proceedings of the Animal Breeding and Genetics Symposium in Honor of Dr Jay Lush. Champaign, Illinois. pp.10–41. Amer. Soc. Animal Science.
[7] DOI: 10.2307/2529430 · Zbl 0335.62048
[8] DOI: 10.2307/2527669 · Zbl 0128.40301
[9] Mccullagh P., Generalised linear models (1989) · Zbl 0588.62104
[10] DOI: 10.2307/2532615
[11] Mcgilchrist C.A., J.R. Statist. Soc. B 56 pp 61– (1994)
[12] DOI: 10.1002/bimj.4710330202 · Zbl 0729.62566
[13] DOI: 10.2307/2532138
[14] DOI: 10.1002/bimj.4710320505 · Zbl 04500861
[15] DOI: 10.1093/biomet/58.3.545 · Zbl 0228.62046
[16] DOI: 10.1214/ss/1177011926 · Zbl 0955.62500
[17] DOI: 10.1093/biomet/78.4.719 · Zbl 0850.62561
[18] Searle S.R., Linear models (1971)
[19] DOI: 10.1214/ss/1177011930
[20] Thompson R., Math. Operforsch. Statist. Ser. Statist 11 pp 545– (1980)
[21] DOI: 10.1093/biomet/80.4.791 · Zbl 0800.62351
[22] DOI: 10.1080/00949659308811554 · Zbl 0833.62067
[23] DOI: 10.1016/0025-5564(92)90017-Q
[24] DOI: 10.1002/bimj.4710340607 · Zbl 0850.62497
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.