Formulas in R
Generalized Linear Models in R
Richard Erickson
Instructor
Why care about formulas for multiple logistic regression?
- Formulas backbone of regression
- Tricky to figure out
- Understanding
model.matrix()key
Slopes
- Estimates coefficient for continuous variable
- e.g.,
height = c(72.3, 21.1, 3.7, 1.0)
- e.g.,
- Formula also requires a global intercept
- Multiple slopes: Slope for each predictor
Intercepts
- Discrete groups used to predict
- factor or character in R:
fish = c("red", "blue") - Single intercept has two options:
- Reference intercept + contrast:
y ~ x - Intercept for each group:
y ~ x -1
- Reference intercept + contrast:
Multiple intercepts
- Estimates effect of each group compared to reference group
- The first group, alphabetically, in the factor
- Default has one reference group per variable
y ~ x1 + x2
- Can specify one group to estimate an intercept for all groups
y ~ x1+ x2 - 1
- First variable has intercept estimated for each group
Dummy variables
- Codes group membership
- Used under the hood (i.e.,
model.matrix()) - 0s and 1s for each group
- Example input:
color = c("red", "blue") - Dummy variables for
y ~ colors:intercept = c(1, 1)blue = c(0, 1)
- Dummy variables for
y ~ colors - 1:red = c(1, 0)blue = c(0, 1)
model.matrix()
model.matrix()does legwork for us- Foundation for formulas in R
model.matrix( ~ colors)
(Intercept) colorsred
1 1 1
2 1 0
attr(,"assign")
[1] 0 1
attr(,"contrasts")
attr(,"contrasts")$colors
"contr.treatment"
- Order determined by factor order
- Change order change with Tidyverse or
factor()
Factor vs numeric caveat
- R thinks variable is numeric
- e.g.,
month = c(1, 2, 3)
- e.g.,
month <- c( 1, 2, 3)
model.matrix( ~ month)
(Intercept) month
1 1 1
2 1 2
3 1 3
attr(,"assign")
0 1
- Need to specify factor or character
- e.g.,
month = factor(c( 1, 2, 3))
- e.g.,
model.matrix( ~ month)
(Intercept) month2 month3
1 1 0 0
2 1 1 0
3 1 0 1
attr(,"assign")
0 1 1
attr(,"contrasts")$month
"contr.treatment"
Let's practice!
Generalized Linear Models in R
