Categorical data analysis (Stat-411) Self Support

Time Table:

Day Time
Monday 12;30 to 1;30
Tuesday 2:00 to 3:00
Thursday 4:00 to 5:00

Objective

The prescribed course is concerned with the applicable knowledge about statistics in the field of categorical nature of variables. The course aimed at providing students with a formal treatment of categorical data specifically in the social sciences and decision-making theories based on behavioural 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 a 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.

Contents include Introduction, describing two-way contingency tables. Models for binary response variables, log-linear models, fitting log-linear and logit models. Building and applying log-linear models, log-linear logit models for ordinal variables. Multinomial response models for matched pairs. Analyzing repeated categorical response data. Logistic regression models and their analysis.

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.

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

Course Plan:

Week Topics and Readings Books
1 Categorical Data and its Types, Probability Distributions for Categorical Data. Categorical Data Analysis (Page no. 1 to 5)
2 Two-Way Contingency Tables, Probability Structure for Contingency Tables. Categorical Data Analysis  (Page no. 21,22)
3 Comparing proportions in Two-by-Two Tables. Categorical Data Analysis  (Page no. 25 to 27)
4 Independence: Chi-square Test and Fisher’s Exact Test. Categorical Data Analysis   (Page no. 34 to 40)
5 Generalized Linear Models (GLMs) and its Components. Categorical Data Analysis   (Page no. 66,67)
6 GLMs for Binary Data: Linear Probability Model, Logit Model and Probit Model. Categorical Data Analysis   (Page no. 68 to 72)
7 GLMs for Count Data: Log-linear Model. Model Comparison Using the Deviance. Categorical Data Analysis   (Page no. 74 to 82)
8 The Newton-Raphson Algorithm Fits GLMs. Wald and Likelihood Ratio Inference Use the Likelihood Function. Categorical Data Analysis    (Page no. 88,89)
9 Logistic Regression: Binary Logistic Regression. Categorical Data Analysis     (Page no. 99 to 104)
10 Building, Applying and Interpreting Binary Logistic Regression model. Categorical Data Analysis     (page no.  137 to 144)
11 Multinomial Logistic Regression. Categorical Data Analysis     (Page no.  173 to 179)
12 Ordinal Logistic Regression. Categorical Data Analysis      (Page no.  180 to 189)
13 Poisson Regression Categorical Data Analysis      (Page no.  173 to 179)
14 Log-linear Models for Contingency Tables. Categorical Data Analysis      (Page no.  204 to 209)
15 Models for Matched Pairs Categorical Data Analysis      (Page no.  245,246)
16 Analyzing Repeated Categorical Response Data. Categorical Data Analysis      (Page no.  260)

Distribution of Marks:

Assignment:         05

Presentation:        05

Project:                 05

Participation:        02

Attendance:          03

Mid Exam:            30

Final exam:          50

 

 

Course Material

Other Courses by Syed Muhammad Shoaib hassan