### Categorical Data Analysis (STAT-411)

Introduction:

Categorical data analysis is the analysis of data where the response variable has been grouped into a set of mutually exclusive ordered (such as age group) or unordered (such as eye color) categories.This course surveys theory and methods for the analysis of categorical response and count data.

Course objectives:

Prescribed course is concerned with the applicable knowledge about statistics in the field of categorical nature of variables. Course aimed at providing students with a formal treatment of categorical data specifically in the social sciences and decision making theories based on behavioral and attributional variables. This course also explores the basic concepts of advanced categorical methodologies with their mathematical derivations. Course communicate the high skills to play the major role in statistics by using the knowledge of categorical data. The course is heavily oriented with tools for analyzing categorical data with practical applications.

Learning outcomes:

Upon successful completion, students will have the knowledge and skills to:

• Construct R by C tables when given counts
• Calculate joint, marginal and conditional probabilities
• Test for independence, and equality of proportions
• Fit logistic models
• Fit Poisson models for count data
• Check model assumptions and analyze residuals and goodness-of-fit
• Conduct inference for model parameters
• Interpret the output of logistic models

Recommended Books:

1. Agresti, A. (1990). “Categorical Data Analysis”. John Wiley & Sons.
2. Bishop, Y. V. V. Fienberg, S.E and Holland, P.W. (1975). “Discrete Multivariate Analysis”. MA: MIT Press Cambridge.
3. Agresti, A. (2018). "An Introduction to Categorical Data Analysis". John Wiley & Sons.

Course Plan:

 Week Topics and Readings Books 1 Categorical Data and its Types, Probability Distributions for Categorical Data. An Introduction to Categorical Data Analysis (1-16) 2 Two-Way Contingency Tables, Probability Structure for Contingency Tables. An Introduction to Categorical Data Analysis (21-25) 3 Comparing proportions in Two-by-Two Tables. An Introduction to Categorical Data Analysis (25-34) 4 Independence: Chi-square Test and Fisher’s Exact Test. An Introduction to Categorical Data Analysis (34-48) 5 Generalized Linear Models (GLMs) and its Components. An Introduction to Categorical Data Analysis (65-68) 6 GLMs for Binary Data: Linear Probability Model, Logit Model and Probit Model. An Introduction to Categorical Data Analysis (68-73) 7 GLMs for Count Data: Log-linear Model. Model Comparison Using the Deviance. An Introduction to Categorical Data Analysis (74-87) 8 The Newton-Raphson Algorithm Fits GLMs. Wald and Likelihood Ratio Inference Use the Likelihood Function. An Introduction to Categorical Data Analysis (88-90) 9 Logistic Regression: Binary Logistic Regression. An Introduction to Categorical Data Analysis (99-121) 10 Building, Applying and Interpreting Binary Logistic Regression model. An Introduction to Categorical Data Analysis (137-162) 11 Multinomial Logistic Regression. An Introduction to Categorical Data Analysis (173-179) 12 Ordinal Logistic Regression. An Introduction to Categorical Data Analysis (180-196) 13 Poisson Regression An Introduction to Categorical Data Analysis (Ch#7) 14 Log-linear Models for Contingency Tables. An Introduction to Categorical Data Analysis (Ch#7) 15 Models for Matched Pairs An Introduction to Categorical Data Analysis (244-266) 16 Analyzing Repeated Categorical Response Data. An Introduction to Categorical Data Analysis (276-290)

Assessment criteria:

Mid Exam:            30

Final exam:          50

Sessional (Assignment, Presentation, Participation, Attendance, Quizes):       20

Time Table:

BS 8th(R):           Tuesday(11:00-12:00)     Wednesday(08:00-09:00)      Thrusday(09:00-10:00)