# Course detail

### LCE5861 - Linear Models I

__Credit hours__

In-class work per week |
Practice per week |
Credits |
Duration |
Total |

3 |
1 |
8 |
15 weeks |
120 hours |

__Instructor__

Carlos Tadeu dos Santos Dias

Cesar Goncalves de Lima

__Objective__

At the end of the course the students should be able to: (1) To interpret and solve problems involving modeling the Gauss-Markov´s linear model in its various characterizations. (2) Identify estimable functions and build point, interval and region estimates. (3) Perform analysis of variance and interpret concepts of orthogonal projection and orthogonal decomposition of sums of squares. (4) Discuss the quadratic forms of interest and identify situations in the presence of imbalance with or without missing plots. (5) Use with competence the glm procedure of SAS and modules of the statistical system R.

__Content__

(1) Matrix algebra review: generalized inverse matrices, inconsistent systems, orthogonal projection. (2) Linear model of Gauss-Markov: multiple linear regression model; overparameterized models of incomplete non-full-rank with parametric constraints and equivalent models. (3) Estimability and point estimation. "BLUE" of estimable functions. Gauss-Markov´s theorem. Practical rules for estimability. (4) Analysis of variance and sums of squares. Projection and orthogonal decomposition, orthogonal contrasts, notation R (.). Mean, distribution and independence of quadratic forms of interest. (5) Confidence interval and region. (6) Hypothesis testing: sums of squares of hypotheses, equivalent assumptions ratio test of likelihood and other criteria. (7) Constraints on parameters and solutions. Reparametrization and equivalent models. (8) Generalized linear model of Gauss-Markov: weighted and generalized least squares, estimation and testing. (9) Unbalanced experiments and missing plots. Interpretation of hypothesis. (10) Introduction to the mixed effect models. (11) Introduction to the longitudinal data analysis.

__Bibliography__

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14. Little, R.J.A., Rubin, D.B. (2002). Statistical Analysis with Missing Data. Hoboken, NJ: Wiley.

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25. Searle, S.R., (2006). Linear models for unbalanced data. New York : Wiley-Interscience.

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