class: center, middle, inverse, title-slide # IDS 702: Module 2.5 ## Logistic regression with multiple predictors I ### Dr. Olanrewaju Michael Akande --- ## Logistic regression with multiple predictors: motivating example - In many developing countries, people get their drinking water from wells. -- - Sometimes these wells are contaminated with the chemical arsenic, which when consumed in high concentrations causes skin and bladder cancer, as well as cardiovascular disease. -- - Fortunately, in many cases people living near contaminated wells have the opportunity to get water from nearby uncontaminated wells. --- ## The contaminated wells analysis - In one study, several researchers measured the concentrations of arsenic in wells in a particular region of Bangladesh. -- - They labeled wells as safe or unsafe based on the measurements. -- - The researchers encouraged people drinking from unsafe wells to switch to safe wells. -- - Several years later, the researchers returned to the area with the goal of seeing who had switched from unsafe to safe wells. -- - They recorded information on a sample of 3020 individuals who had wells at their homes that were unsafe. -- - Let's address the question: what predicts why people switch wells? -- - The data is in the file `arsenic.csv` on Sakai. --- ## The contaminated wells analysis Data description Variable | Description :------------- | :------------ Switch | 1 = if respondent switched to a safe well <br /> 0 = if still using own unsafe well Arsenic | amount of arsenic in well at respondent's home (100s of micro-grams per liter) Dist | distance in meters to the nearest known safe well Assoc | 1 = if any members of household are active in community organizations <br /> 0 = otherwise Educ | years of schooling of the head of household Treat `switch` as the response variable and others as potential predictors. --- ## Logistic regression with multiple predictors - We can then formally extend the .hlight[logistic regression model] we had before to allow for multiple predictors. -- - We still have .block[ .small[ `$$\Pr[y_i = 1 | x_i] = \pi_i \ \ \textrm{and} \ \ \Pr[y_i = 0 | x_i] = 1-\pi_i,$$` ] ] -- or .block[ .small[ `$$y_i | x_i \sim \textrm{Bernoulli}(\pi_i)$$` ] ] -- as before, but with .block[ .small[ `$$\textrm{log}\left(\dfrac{\pi_i}{1-\pi_i}\right) = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \ldots + \beta_p x_{ip}$$` ] ] now in both cases. -- - Let's fit the model to our motivating example. --- ## The contaminated wells analysis: EDA ```r arsenic <- read.csv("data/arsenic.csv",header=T, colClasses=c("numeric","numeric","numeric","factor","numeric")) head(arsenic) ``` ``` ## switch arsenic dist assoc educ ## 1 1 2.36 16.826 0 0 ## 2 1 0.71 47.322 0 0 ## 3 0 2.07 20.967 0 10 ## 4 1 1.15 21.486 0 12 ## 5 1 1.10 40.874 1 14 ## 6 1 3.90 69.518 1 9 ``` ```r summary(arsenic[,-1]) ``` ``` ## arsenic dist assoc educ ## Min. :0.510 Min. : 0.387 0:1743 Min. : 0.000 ## 1st Qu.:0.820 1st Qu.: 21.117 1:1277 1st Qu.: 0.000 ## Median :1.300 Median : 36.761 Median : 5.000 ## Mean :1.657 Mean : 48.332 Mean : 4.828 ## 3rd Qu.:2.200 3rd Qu.: 64.041 3rd Qu.: 8.000 ## Max. :9.650 Max. :339.531 Max. :17.000 ``` ```r table(arsenic$switch) ``` ``` ## ## 0 1 ## 1283 1737 ``` --- class: center, middle # Move to the R script [here](https://ids-702-f20.github.io/Course-Website/slides/Arsenic-I.R). --- class: center, middle # What's next? ### Move on to the readings for the next module!