Lesson 17: Wrap-up and other regressions
Nicky Wakim
2024-06-05
Animals of the day
Today
- Let’s zoom out a little and see what types of regressions we can do
- You should have the main tools to perform these regressions
- Each has some nuances, but I’ll give you sources that help walk you through them
Types of regressions
| Dist’n of Y | Typical uses | Link name | Link function | Common name |
|---|---|---|---|---|
| Normal | Linear-response data | Identity | Linear regression | |
| Bernoulli / Binomial | outcome of single yes/no occurrence | Logit | Logistic regression | |
| Poisson | count of occurrences in fixed amount of time/space | Log | Poisson regression | |
| Bernoulli / Binomial | outcome of single yes/no occurrence | Log | Log-binomial regression | |
| Multinomial | outcome of single occurence with K > 2 options, nominal | Logit | Multinomial logistic regression | |
| Multinomial | outcome of single occurence with K > 2 options, ordinal | Logit | Ordinal logistic regression |
Linear regression
- Outcome type: continuous
- Example outcomes:
- Height
- IAT score
- Heart rate
- Population model
- Interpretations
- The change in average
- The change in average
Linear regression resources
- 512/612 class site!!
- Online textbook by Dr. Nahhas
Logistic regression
- Outcome type: binary, yes or no
- Example outcomes:
- Food insecurity
- Disease diagnosis for patient
- Fracture
- Population model
- Interpretations
- The log-odds ratio for every 1 unit increase in
- The log-odds ratio for every 1 unit increase in
Logistic regression resources
Poisson Regression
- Outcome type: Counts or rates
- Example outcomes:
- Number of children in household
- Number of hospital admissions
- Rate of incidence for COVID in US counties
- Population model
- Interpretations
- The count (or rate) ratio for every 1 unit increase in
- The count (or rate) ratio for every 1 unit increase in
Poisson Regression resources
YouTube video on R tutorial for Poisson Regression
- Dr. Fogerty is a professor in Political Science, so just beware they may not have formal statistical training
-
- Social scientist, so just beware they may not have formal statistical training
Log-binomial Regression
- Outcome type: binary, yes or no
- Example outcomes:
- Food insecurity
- Disease diagnosis for patient
- Fracture
- Population model
- Interpretations
- We have log of probability on the left
- So exponential of our coefficients will be risk ratio
Log-binomial Regression resources
Multinomial logistic regression
- Outcome type: multi-level categorical, no inherent order
- Example outcomes:
- Blood type
- US region (from WBNS)
- Primary site of lung cancer (upper lobe, lower lobe, overlapped, etc.)
- We have additional restriction that the multiple group probabilities sum to 1
Population models
Interpretations
- Basically fitting two binary logistic regressions at same time!
- First equation: how a one unit change in
- Second equation: how a one unit change in
Multinomial logistic regression resources
YouTube video on R tutorial for Poisson Regression
- Again, Dr. Fogerty is a professor in Political Science
Ordinal logistic regression
- Outcome type: multi-level categorical, with inherent order
- Example outcomes:
- Satisfaction level (likert scale)
- Pain level
- Stages of cancer
- When these variables are predictors, we are pretty lenient about treating them as continuous
- We must be VERY STRICT when they are outcomes
- They do not meet the assumptions we place on continuous outcomes in linear regression!!
- We have additional restriction that the multiple group probabilities sum to 1
- Population models , with levels
- Interpretations
- Basically fitting
- First equation: how a one unit change in
- Second equation: how a one unit change in
- Basically fitting
Ordinal logistic regression resources
Even more regressions…
| Dist’n of Y | Typical uses | Link name | Link function | Common name |
|---|---|---|---|---|
| Bernoulli / Binomial | outcome of single yes/no occurrence | Probit | Probit regression | |
| Bernoulli / Binomial | outcome of single yes/no occurrence | Complementary log-log | Complementary log-log regression | |
| Multinomial | outcome of single occurence with K > 2 options, nominal | Probit | Multinomial probit regression | |
| Multinomial | outcome of single occurence with K > 2 options, ordinal | Probit | Ordered probit regression |
More regression resources
General resources
Moment of appreciation for your growth
- Remember when we were learning simple linear regression…
- This was a slide from our second week together:
- Even if you don’t feel like you learned everything, you have learned a lot from the first time you saw the above slide
Lesson 17: Wrap-up and other regressions
Lesson 17: Wrap-up and other regressions Nicky Wakim 2024-06-05