Binary Data

Question 1

Odds Ratio

Answer 1

Odds = not the same as a probability, they can be larger than 1
Odds of 8:2 = 8 von 10 = 80%

OR = ratio of 2 ratios
OR = 1 -> the 2 groups do not differ
OR >< 1-> they differ

log Odds Ratio:
Log(OR) = 0 -> the 2 groups do not iffer
Og(OR) >< 0 -> they differ

Question 2

Poisson vs. Binomial

Answer 2

Poisson is appropriate when:
- no theoretical upper limit to the number of times an “event” can occur, or observed values are far from such an upper limit (e.g., number of birds observed in a forest plot)
- Counts cannot be expressed as a proportion.

Binomial is appropriate when:
- Aggregated version of many binary experiments, that is, each can be 0 or 1.
- There is an upper limit to the number of times an “event” can occur (e.g., number of deaths out of a known total number of individuals).
- Events can be expressed as a proportion (number of successes/number of trials).

Question 3

Binomial Distribution

Answer 3

probability of k successes in n trials

Question 4

Binary response/ non-aggragated data -> complications:

Answer 4

• graphical description difficult -> conditional density plot better
• mode diagnostics difficult -> not meaningful
• residual deviance cannot be used to detect overdispersion -> bc no variance can be detected

Question 5

If you mistakenly use a linear model on binomial data

Answer 5

• wavy pattern in the residuals vs fitted plot
• model will make impossible predictions
• but model will NOT fail to fit, NO error message, NO warning message