Expanding on the Poisson regression
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α
βM
βG
β
Potential problem:
Our model under-predicts the number of large and small values in the outcome (not enough variation)
AKA negative binomial AKA over-dispersed Poisson
Extra “dispersion” from gamma
Two students who look identical based on covariates can have different Poisson rates λi.
One more prior
“Negative binomial regression” is the typical terminology
θ
Our model under-predicts the number of zero-valued outcomes
Outcome variable is the result of one of two processes:
Either the student is structurally constrained to play zero hours per week–e.g. they do not own a game console ()
Or the student is able to play games and does so at a rate ()
Each student’s probability of not owning a console is modeled with
The probability is modeled with a linear function of family income
The rate is modeled with a linear function of gender
Figures by Peter McMahan (source code)
Still from National Treasure (2004)
Still from Brazil (1985)
Merchandise from The Nightmare Before Christmas (1993)
