tslumley

---
title: "Zero-inflated Poisson from complex samples"
author: "Thomas Lumley"
date: "18 May 2015"
output: html_document
---

The Zero-Inflated Poisson model is a model for count data with excess zeros. The response distribution is a mixture of a point mass at zero and a Poisson distribution: if $Z$ is Bernoulli with probability $1-p_0$ and $P$ is Poisson with mean $\lambda$ then
$$Y=Z+(1-Z)P$$
is zero-inflated Poisson. The ZIP is a latent-class model; we can have $Y=0$ either because $Z=0$ or because $P=0$. That's natural in some ecological examples: if you didn't see any moose it could be because the area is moose-free (it's downtown Montréal) or because you just randomly didn't see any. 

tslumley

Data from two replicates of a 2^{5-1} fractional factorial experiment on paper helicopters

We used the helicopter template from the R SixSigma package. Our experimental factors were body height, wing length, paper type, paper size (A4 vs A5), and paperclip or not. The paperclip and size are interesting because they have a big effect on how the flight looks, but not a big effect on the flight time.

The experiments were performed at the Science Street Fair hosted by the Auckland Museum of Transportation and Technology (MOTAT), March 29, 2015. Replicate 1 was done in the morning; replicate 2 in the afternoon. The drop height was approximately 2.2m. Times are in seconds.

tslumley

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tslumley

Election donations, New Zealand, 2014.

tslumley

moe = function(pct, N=1000, deff=c(1,2)){
	p.L = function(x, n) {
        ifelse (x == 0,0,qbeta(0.025, x, n - x + 1))
    }
    p.U = function(x, n) {
        ifelse(x == n,1,qbeta(0.975, x + 1, n - x))
    }
    N = rep(N,length(pct))
		
	lower = function(pct,deff){