Urban Big Data Analytics

Lecture 10
Advanced Modeling

July 31, 2019

Instructor: Andy Hong, PhD
Lead Urban Health Scientist
The George Institute for Global Health
University of Oxford

Final group project

  • Five elements: 1. Problem; 2. Hypotheses; 3. Data and methods; 4. Results and Interpretation; 5. Conclusions
  • Minimum 6 page, single space, Times New Roman 12 font size
  • August 8 (Weds), 12:00 Midnight

Final group presentation

  • Presentation (12 mins), Q&A (2 mins)
  • Each group member needs to present
  • Share some preliminary results

Special Guest Speakers

A 14-week program to work on collaborative projects

2019 DSSG Fellows

Advanced modeling

Beyond linear regressions

  • Linear models are good for numbers
  • But, what about categorical data?
  • What about survey data with yes or no questions?
  • Can you convert categories into numbers?

BC Generations Survey

Survey questionaires

Logistic Regression

  • "Logit" regression
  • "Logit" model
  • Developed by David Cox in 1958
  • Regression model for categorical outcome Y

Sir David Cox (age 95)

Why Logistic Regression?

  • Linear model, not appropriate for a qualitative response
  • Ex) Question - How would you rate this course?
  • Aweful - Okay - Good - Very Good - Excellent
  • Can we turn this into 1-2-3-4-5?
  • No, because the distance between each item is not the same

Types of Logistic Regression

  • Simple logistic model
    • Binary outcome: "0" and "1"
    • Pass/Fail, Win/Lose, Dead/Alive, Sick/Healthy
  • Multinomial logistic model
    • Multiple categorical outcomes
    • A range of values: Unsatisfied - Satisfied - Very Satisfied

Logistic Regression

Linear vs. Logistic Regression

Linear function Logistic function
$$ f(x) = \beta_{0} + \beta_{1}x $$
$$ f(x) = \frac{e^{\beta_{0} + \beta_{1}x}}{1 + e^{\beta_{0} + \beta_{1}x}} $$

$$ \log_e (\frac{p}{1-p}) = \beta_{0} + \beta_{1}x $$

Log Odds

Odds

Odds and Odds Ratio

Odds Ratio Example

Simple Logistic Regression

$$ corruption \approx f(income) $$


					# Simple Logit Model
					m1 = glm(data = gapminder, 
							 corruption ~ income, 
							 family = "binomial")
		
					exp(coef(m1))	
					confint(m1)

Multiple Logistic Regression

$$ corruption \approx f(income, population, democracy) $$


					# Multiple Logit Model
					m2 = glm(data = gapminder, 
							 corruption ~ income + population + democracy, 
							 family = "binomial")
					
					exp(coef(m2))	
					confint(m2)

2019 DSSG Fellows

Lecture 10 Group Session

Go to the group session

Final Group Project

Instruction

Any questions?

For all the course materials, go to urbanbigdata.github.io