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Lectures 5 and 6: Inference for Categorical Data

romF Raw Data to Tabular Data oT study the relationship between two categorical ariablesv we usually rst create a contingency table from the raw data In the previous chapter we studied the relationship between mortality rate and water hardness both numeric Now let us rede ne them ascategoricalariablesv and cross-classify the data data water;

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Categorical Data Analysis

This course is designed as a broad applied introduction to the statistical analysis of categorical data with an emphasis on: Course outline Textbooks Main texts Friendly & Meyer (2016) Discrete Data Analysis with R: Visualizing & Modeling Techniques for Categorical & Count Data 30 discount on Routledge web site (code: ADC22)

PDF	Categorical DataAnalysis 1 ✪ Methods for response (dependent) variable Y scale that is a set of categories having Explanatory variables may be categorical or contin-uous or both Example = vote in election (Democrat Republican Indepen-dent) x’s - income education gender race

How specialized statistical methods are used for categorical data?
Random Effects: Generalized Linear Mixed Models In recent years, the use of specialized statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. Partly this reflects the development during the past few decades of sophisticated methods for analyzing categorical data.

Introduction

1. ✪ Methods for response (dependent) variable Y scale that is a set of categories having Explanatory variables may be categorical or contin-uous or both Example = vote in election (Democrat, Republican, Indepen-dent) x’s - income, education, gender, race users.stat.ufl.edu

Ordinal

patient condition (excellent, good, fair, poor) government spending (too high, about right, too low) users.stat.ufl.edu

Nominal

transport to work (car, bus, bicycle, walk, ) favorite music (rock, classical, jazz, country, folk, pop) We pay special attention to binary variables (success - fail) for which nominal - ordinal distinction unimportant. users.stat.ufl.edu

Probability Distributions for Categorical Data

✪ The binomial distribution (and its multinomial dis-tribution generalization) plays the role that the normal distribution does for continuous response. Binomial Distribution Bernoulli trials - two possible outcomes for each (success, failure) users.stat.ufl.edu

) P (Y

y = jX = no) We can estimate P (X jY ), so can estimate . users.stat.ufl.edu

Chapter 5: Building Logistic Regression Models

✪ Model selection Model checking Be careful with “sparse” categorical data (infinite estimates possible). users.stat.ufl.edu

Sparse data

Caution: Parameter estimates in logistic re-gression can be infinite. Ex. users.stat.ufl.edu

✪ (Y1 Y 2

No likelihood function No LR inference (LR test, LR CI) users.stat.ufl.edu

Y T ).

T times, we con-sider marginal model that describes each For responses users.stat.ufl.edu

Cumulative Logit Modeling of Repeated Or-dinal Responses

For multicategory responses, recall popular logit models use logits of cumulative probabilities (ordinal response) log[P (Y users.stat.ufl.edu

Statistics 101: Describing a Categorical Variable

Types of Data: Categorical(Nominal Ordinal) Numerical(Discrete Continues) Stats: part-1

PDF	An Introduction to Categorical Data Analysis - Second Edition Probability Distributions for Categorical Data 3. 1.2.1. Binomial Distribution

PDF	3rd-ed-alan_agresti_categorical_data_analysis.pdf Categorical data analysis / Alan Agresti. – 3rd ed. p. cm. - (Wiley series in probability and statistics; 792). Includes bibliographical references and index

PDF	Categorical data Categorical data. So far we've focused on analyzing numerical data. This section focuses on data that's categorical (e.g.

PDF	Introduction to Categorical Data Analysis Procedures There are two approaches to performing categorical data analyses. Reference documentation delivered in HTML and PDF – free on the Web.

PDF	Parallel Sets: Visual Analysis of Categorical Data Figure 1: A visualization of a CRM data set which contains 93.872 data records; three categorical dimensions are displayed as Parallel Sets.

PDF	9. Categorical data analysis It tests whether an observed frequency distribution of a nominal variable matches an expected frequency distribution. For example suppose a group of patients

PDF	Parallel Sets: Interactive Exploration and Visual Analysis of Visual Analysis of Categorical Data. Robert Kosara Member

PDF	Similarity Measure Selection for Categorical Data Clustering 9 déc. 2019 We propose a strategy to automatically select similarity measures for clustering categorical data. Organization of the Paper. This paper is ...

PDF	Chapter 5 - Introduction to Categorical Data Analysis Procedures data: CATMOD fits linear models to functions of categorical data facilitating such analyses as regression

PDF	An Introduction to Categorical Data Analysis - Second Edition Probability Distributions for Categorical Data 3. 1.2.1. Binomial Distribution

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PDF	Introduction to Categorical Data Analysis “ffirs” — 2007/1/31 — page iii — #3 An Introduction to Categorical Data Analysis Second Edition ALAN AGRESTI Department of Statistics University of Florida

PDF	Introduction to Categorical Data Analysis Procedures - SAS Support There are two approaches to performing categorical data analyses The first Reference documentation delivered in HTML and PDF – free on the Web

PDF	Categorical Data Analysis Related topics/headings: Categorical data analysis; or, Nonparametric statistics; or, chi-square tests for the analysis of categorical data For our hypothesis testing

PDF	Introduction to Categorical Data Analysis Procedures Categorical data result from observations on multiple subjects where one or more categorical variables are observed for each subject If there is only one

PDF	Introduction to Categorical Data Analysis - e-Disciplinas Library of Congress Cataloging-in-Publication Data Agresti, Alan An introduction to categorical data analysis / Alan Agresti p cm Includes bibliographical

PDF	STA 4504 - 5503: Outline of Lecture Notes, c Alan Agresti Categorical Data Analysis 1 Introduction • Methods for response (dependent) variable Y having scale that is a set of categories • Explanatory variables may be

PDF	Categorical data - MIT Categorical data So far, we've focused on analyzing numerical data This section focuses on data that's categorical (e g , with values like 'red' or 'blue' that don't

PDF	Categorical data analysis - Stanford NLP Group - Stanford University Categorical Data Analysis: Away from ANOVAs (transformation or not) and towards Logit Mixed Models In the psychological sciences, training in the statistical