| Title:
|
Bayesian estimation of the intraclass correlation coefficients in the mixed linear model (English) |
| Author:
|
Jelenkowska, Teresa H. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
103-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The method of determining Bayesian estimators for the special ratios of variance components called the intraclass correlation coefficients is presented. The exact posterior distribution for these ratios of variance components is obtained. The approximate posterior mean of this distribution is also derived. All computations are non-iterative and avoid numerical integration. (English) |
| Keyword:
|
Bayesian estimation |
| Keyword:
|
standard random linear model |
| Keyword:
|
posterior distribution |
| Keyword:
|
inverted multidimensional Dirichlet distribution |
| Keyword:
|
intraclass correlation coefficients |
| MSC:
|
62A15 |
| MSC:
|
62H12 |
| idZBL:
|
Zbl 0937.62026 |
| idMR:
|
MR1609170 |
| DOI:
|
10.1023/A:1023210900467 |
| . |
| Date available:
|
2009-09-22T17:57:05Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134378 |
| . |
| Reference:
|
[1] Box, G.E.P. and Tiao G.C.: Bayesian Inference in Statistical Analysis.Massachusetts: Addison Wesley, 1973. MR 0418321 |
| Reference:
|
[2] Broemeling, L.D.: Bayesian Analysis of Linear Models.Marcel Dekker, New York, 1985. Zbl 0564.62020, MR 0772380 |
| Reference:
|
[3] Cook, P., Broemeling, L.D. and Gharraf, M.: A Bayesian analysis of the mixed linear model.Communications in Statistics A19, No 3 (1990), 987–1002. MR 1075481 |
| Reference:
|
[4] De Groot, M.H.: Optimal Statistical Decisions.McGraw-Hill Co, New York, 1970. MR 0356303 |
| Reference:
|
[5] Gharraf, M.: General Solution to Making Inference about the Parameters of Mixed Linear Models.Ph.D. dissertation, Oklahoma State University, Stillwater, Oklahoma, 1979. |
| Reference:
|
[6] Hill, B.M.: Inference about variance components in the one-way model.Jour. of the American Statistical Association 60 (1979), 806–825. MR 0187319, 10.1080/01621459.1965.10480829 |
| Reference:
|
[7] Hill, B.M.: Correlated errors in the random model.Journal of the American Statistical Association 62 (1967), 1387–1400. Zbl 0158.37504, MR 0223010, 10.1080/01621459.1967.10500941 |
| Reference:
|
[8] Jelenkowska, T.H.: Bayesian estimation of the variance components in a general random linear model, Bayesian Statistics 3.Oxford Sci. Publ. Oxford Univ. Press, New York (1988), 653–656. MR 1008076 |
| Reference:
|
[9] Press, J.S.: Applied Multivariate Analysis.Holt, Reinhart and Winston, Inc., 1972. Zbl 0276.62051, MR 0420970 |
| Reference:
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[10] Rajagopal, M. and Broemeling L.D.: Bayesian inference for the variance components of the general mixed model.Communications in Statistics 12, No 6 (1983), 701–724. MR 0696816, 10.1080/03610928308828490 |
| Reference:
|
[11] Searle, S.R.: A Summary of Recently Developed Methods of Estimation of Variance Components.Technical Report, BU-388, Biometrics Unit., Cornell University, Ithaca, New York, 1991. |
| Reference:
|
[12] Stone, M. and Springer, B.G.F.: A paradox involving quasi-prior distributions.Biometrika 52 (1965), 623–627. MR 0210233, 10.1093/biomet/52.3-4.623 |
| Reference:
|
[13] Tiao, G.C. and Tan, W.Y.: Bayesian analysis of random-effect models in the analysis of variance—I: Posterior distribution of variance components.Biometrika 52 (1965), 37–53. MR 0208765, 10.1093/biomet/52.1-2.37 |
| . |
