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A Flexible Model for Count Data: The COM-Poisson Distribution

Published on Sep 26, 20126632 Views

Galit Shmuéli

Count data arise in many contexts, from word lengths to traffic volume to number of bids in online auctions, and generally in many event-counting applications. Yet, there is a scarcity of statistical

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Statistical LearningStatistics

Chapter list

A Flexible Model for Count Data: The COM Poisson00:00
Deaths from horse-kicks in Prussian army (Bortkewicz, 1898)04:23
Non-Poisson data used to be exotic05:20
Today non-Poisson counts are common05:56
Quantitative Linguistics06:48
Conway-Maxwell-Poisson07:44
Generalizes well-known distributions10:32
Over- and Under-dispersion12:15
Properties: Exponential Family12:49
Properties: Moments15:17
Estimation: Three Methods17:01
Conjugate Analysis of the Conway-Maxwell-Poisson Distribution17:23
Quarterly sales of socks - Word length in Hungarian dictionary20:52
Better fit21:56
Data Disclosure23:30
Modeling Bi-Modal Data via Mixtures26:18
Modeling Bi-Modal Count Data Using COM-Poisson Mixture Models28:47
From CMP Distribution to CMP Regression30:22
Bayesian Implementation: Marketing (1)31:07
Bayesian Implementation: Marketing (2)32:25
Bayesian Implementation: Transportation (1)33:30
Bayesian Implementation: Transportation (2)33:52
Our Approach: Classic GLM34:05
Link Function34:42
Maximum Likelihood Estimation37:03
Option 2: Solve normal equations iteratively37:07
Iteratively reweighted least squares: 2-parameter generalization37:22
Standard Errors: Fisher Information38:02
Dispersion Test38:14
Fitted Values39:19
Model Inference40:22
Diagnostics41:09
Alternative Regression Models41:35
Example 1: Airfreight Breakage42:52
Example 1: Airfreight Breakage43:10
Effect of Under-Dispersion44:56
Inference: Small Sample45:57
Example 1: Diagnostics46:08
Example 2: Book Purchases (1)46:32
Example 2: Book Purchases (2)46:40
Example 3: Motor Vehicle Crashes (1)47:48
Example 3: Motor Vehicle Crashes (2)48:20
Example 3: Motor Vehicle Crashes Lord et al. (2008)48:44
Example 3: Diagnostics49:27
Detecting Dispersion Mixtures49:32
Elephant Matings (1)50:41
Elephant Matings (2)53:43
Model Selection54:26
Summary & Conclusion54:47
CMP Regression has several advantages54:49
Weaknesses57:21
The COM-Poisson Model for Count Data: A Survey of Methods and Applications59:11
Wikipedia: Conway-Maxwell-Poisson distribution59:56