# Analysis of Discrete Data

## Objectives

1. To develop a critical approach to the analysis of contingency tables
2. To examine the basic ideas and methods of generalized linear models
3. To link logit and log-linear methods with generalized linear models
4. To develop skills on analysis of discrete data using R

## General characterization

200198

4.0

##### Responsible teacher

Docente a designar

##### Hours

Weekly - Available soon

Total - Available soon

##### Teaching language

Portuguese. If there are Erasmus students, classes will be taught in English

### Bibliography

- Agresti, A. (2013). Categorical Data Analysis, 3rd Edition, Wiley.

### Teaching method

The curricular unit is based on theoretical and practical lessons. A variety of instructional strategies will be applied, including lectures, slide show demonstrations, step-by-step applications (with and without software), questions and answers. The sessions include presentation of concepts and methodologies, solving examples, discussion and interpretation of results. The practical component is geared towards solving problems and exercises, including discussion and interpretation of results. A set of exercises to be completed independently in extra-classroom context is also proposed.

### Evaluation method

Evaluation:
1st call: pro ject (40%), first round exam (60%)
2nd call: final exam (100%)

## Subject matter

1. Review of discrete probability distributions: binomial, multinomial, and Poisson. The concept of likelihood.
2. Tests for one-way tables using Pearson¿s X^2 and likelihood-ratio G^2 statistics.
3. Contingency tables including 2 × 2 and r × c tables, tests for independence and homogeneity of proportions, Fishers exact test, odds ratio and logit, other measures of association.
4. Three-way tables in full independence and conditional independence contexts.
5. Generalized linear models in Poisson regression and logistic regression contexts for dichotomous response, including interpretation of coefficients, main effects and interactions, model selection, diagnostics, and assessing goodness of fit.
6. Polytomous logit models for ordinal and nominal response.
7. Loglinear models (and graphical models) for multi-way tables.
8. Repeated measures generalized least squares, mixed models
9. Latent-class models and missing data.

## Programs

Programs where the course is taught: