Sahai H., Ojeda M. Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis

Birkhäuser, 2005. — 480 p. — ISBN: 0817632298, 978-0817632298.Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs with a detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level. It also includes numerical examples to analyze data from a wide variety of disciplines as well as any worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example.Matrix Preliminaries and General Linear Model
Some General Methods for Making Inferences about Variance Components
One-Way Classification
Two-Way Crossed Classification without Interaction
Two-Way Crossed Classification with Interaction
Three-Way and Higher-Order Crossed Classifications
Two-Way Nested Classification
Three-Way Nested Classification
General r-Way Nested Classification
Appendices:
A Two Useful Lemmas in Distribution Theory
B Some Useful Lemmas for a Certain Matrix
C Incomplete Beta Function
D Incomplete Inverted Dirichlet Function
E Inverted Chi-Square Distribution
F The Satterthwaite Procedure
G Maximum Likelihood Estimation
H Some Useful Lemmas on the Invariance Property of the ML Estimators
I Complete Sufficient Statistics and the Rao–Blackwell and Lehmann–Sheffé Theorems
J Point Estimators and the MSE Criterion
K Likelihood Ratio Test
L Definition of Interaction
M Some Basic Results on Matrix Algebra
N Newton–Raphson, Fisher Scoring, and EM Algorithms
O Software for Variance Component Analysis