Poisson Regression Flashcards
Assumes a ___________
Poisson distribution
What is itβs outcome?
Count data. Discrete meaning that there are no half values, just units. No negative values
Is the link function used for a poisson distribution and its inverse is
Link function: log
Inverse: exponential
Explain how variance is distributed along the x axis
Bigger numbers distribute normally, smaller numbers bump against 0. So higher values get lower variance, lower values grater variance
How do you know is a poisson distribution?
Because the mean and the variance are just the same
What does a poisson regression looks like?
πΈ(π)=π^π΅_0 +π΅_1 π₯_1+π΅_2 π₯_2+β¦π΅_π π₯_π )
What are the characteristics of the outcome variable here
Cannot be negative
Has to be discrete
Cannot be below 0
Is the main issue of poisson models:
Overdisperssion
What is overdisperssion?
Where within a model there is too much variance. Values above 1 are considered overdisperse
These are the two ways to deal with overdisperssion
- Negative Binomial
- Zero Inflationg
What does overdisperssion do to your model?
1 No changes in the parameter estimates.
2 Changes in stantard errors (smaller when overdisperssed)
3 Changes the chi-square values
4 p values change (tend to be significant with overdispersion)
When should you reconsider using a poisson regression?
When your count data is bumping up at lower bound BUT is far from 0 or 1. Then you can analyze as normal.
Some examples of this non-poisson distribution
Weight, starting salary, time to complete an exam, days of work attended
These are some examples of poisson distribution
Number of students dropping off class, salary, lever choices, days missed in a year
Problems with poisson regression software wise
Canβt do Post Hocs
Canβt compute VIFs
Canβt do repeated measures
Mikeβs tip about poisson and normal residuals
Tempting as it seems but if your residuals look normal stick to a linear regression, avoid the GLM if not critical to use
When do you choose a poisson over a linear regression?
When your data is highly skewed but is not binomial. When it has lots of 0s or 1s. You also want to extrapolate
What does your Y(E)=## mean? probability? expected score?
The log score no longer the log odds actually because is count data.
How do you backtransform to predict here?
If we wanted to interpret them we do an exponential of the value of the eemean function!
What happens to variance in a Poisson distribution?
If itβs a true poisson variance will be same as the mean.
Otherwise you get greater variance with data bumping up against the floor and less variance with greater values of data
What does it look like when you backtransform?
You can see an exponential growth or an exponential decay. Bigger changes early, smaller changes later
Major problem of poisson models
Overdispersion
Why is the fact that mean and variance differ a problem?
Because it violates the assumption of a poisson distribution and increases the risk of a type I error
Overdispersion means
OVERVARIATION too much variance
This poisson allows that variance is not equal to the mean
A quassi poisson distribution
Ways to deal with overdisperssion
Use a quassi poisson
Use a negative binomial
Use the zero inflated (when overdisperssion is created because you have too many 0s)
Overdisperssion changes this__________ but doesnβt change this______________
Your standard errors can become artificially small. You have greater chi-square values
If we take that t distribution and square root it you would get a
Chi square distribution
Why do we get F distribution
Because we are testing a ratio between two variances
What do you look at when looking at the output?
We look at overdispersion first.
Overall model, is it significant or not?
Parameter estimates, try to interpret what each beta is doing to the outcome variable
Confirm with profiler
Get VIFs
In what type of space a poisson model is taking place
Since the link function is the log β¦ a log space
If your predicted output is in log terms what do you need to do to backtransform it?
A e transformation (remember e to the power of your predicted value )
