LINEAR,GENERALIZED AND MIXED MODELS

Specialization / Direction

Specific Foundation / Core

Upon successful completion of the course, students will: 1) understand the importance of statistical models, the exponential family of distributions, and specifically the normal distribution and distributions derived from it. 2) apply the theory of special matrices and quadratic forms of random variables in statistical models. 3) know and be able to apply the basic theory of linear models, generalized linear models, and mixed models, including the assumptions and limitations of each type of model. 4) handle the metric scale of data and variables, clustered or hierarchical data, fixed and random effects factors, interactions, and missing values, and apply the best statistical model for each design and data generation process. 5) handle the R programming language and its libraries and be able to modify existing code according to the requirements of each theoretical model. 6) apply fundamental concepts of maximum likelihood, restricted maximum likelihood, best linear unbiased estimator, and best linear unbiased predictor, and their properties. 7) apply analysis of variance methods and estimate variance components. 8) be able to evaluate the assumptions of each type of model and apply variable transformations when necessary 9) be able to generate appropriate hypothesis tests, confidence intervals, and use statistical models for predictions. 10) be able to develop statistical methodology, critically interpret the results of statistical analyses, and communicate statistical results by creating appropriate graphical representations and tables. 11) be able to collaborate in teams to solve complex theoretical problems and modeling problems.

Introduction to Statistical Models, Observational Studies and Experimental Studies, Orthogonal Matrices, Projection Matrices, Quadratic Forms, Cochran-Fisher Theorem, The Full-Rank Homoscedastic Linear Model, Least Squares Estimators Gauss-Markov Theorem, Properties of Least Squares Estimators, Analysis of Variance, Frisch–Waugh–Lovell Theorem, Hypothesis Tests, Confidence Intervals, Goodness-of-Fit Tests, Coefficient of Determination, Model Selection, Prediction, Checking Assumption, Residuals, Outliers, Multicollinearity, Box-Cox Transformation, The General Linear Model, Non-Full-Rank Linear Model, Analysis of Variance with Fixed Effects Factors, Goodness-of-Fit Tests, Generalized Inverse of the "Hat" Matrix and Adaptation of Basic Theorems, Main Effect, Interaction, Contrasts, Pairwise Comparisons or Multiple; Comparisons, Generalized Linear Models, Exponential Family of Distributions, Link Function, Maximum Likelihood Estimator Score Function and Information Matrices, Iteratively Reweighted Least Squares Algorithm, Estimators and Their Properties Goodness-of-Fit Tests, Dispersion Parameter φ, Quasi-likelihood Method, Hypothesis Testing, Prediction, Deviance Residuals, Logistic Regression, Poisson Regression, Clustered, Hierarchical, or Longitudinal Data, Random Effects Factors, (Normal) Linear Mixed Model, Intraclass Correlation Coefficient (ICC), Maximum Likelihood and Restricted Maximum Likelihood, Best Linear Unbiased Estimator (BLUE) and Best Linear Unbiased Predictor (BLUP), Multiple Comparisons, Generalized Linear Mixed Models Applications in the Laboratory using R

Projection Matrix, Linear Model, General Linear Model, Analysis of Variance, Generalized Linear Model, Linear Mixed Mode, Generalized Linear Mixed Model

18-05-2025