LCE5861 - Linear Models

Credit hours

Instructor
Cesar Goncalves de Lima
Edwin Moises Marcos Ortega
Idemauro Antonio Rodrigues de Lara
Renata Alcarde Sermarini

Objective
Interpret and solve problems involving full-rank and nonfull-rank linear models, in their various
characterizations, using statistical software. Identify estimable functions and construct point, interval,
and region estimates. Perform analyses of variance and interpret concepts of orthogonal projection and
orthogonal decomposition of sums of squares. Discuss quadratic forms of interest and identify
hypotheses in the presence of imbalance with or without empty cells.

Content
(1) Matrix algebra review: basic operations, matrix rank, usual and generalized inverses, linear systems,
linear dependence, orthogonal projection, classification of quadratic forms. (2) Multivariate normal
distribution; non-central T, chi-square, and F distributions. Distribution, expectation and independence
of quadratic forms of interest. (3) Gauss-Markov linear model: multiple linear regression model;
overparameterized models of incomplete rank, cell mean, with parametric constraints, and equivalent
models. (4) Ordinary least squares method. Estimability and estimation by point, interval, and region.
"BLUE" of estimable functions. Gauss-Markov theorem. Practical rules of estimability. (5) Analysis of
variance and sums of squares. Orthogonal projection and decomposition, orthogonal contrasts. (6)
Hypothesis testing: sums of squares of hypotheses, equivalent hypotheses, likelihood ratio test and
other criteria. (7) Constraints on parameters and constraints on solutions. Reparameterizations and
equivalent models. (8) Generalized linear Gauss-Markov model: weighted and generalized least squares,
estimation and tests. (9) Unbalanced experiments and experiments with empty cells. Interpretation of
hypotheses.

Bibliography
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