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

Published on 2012-09-266632 Views

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

Solomon seminar

Presentation

A Flexible Model for Count Data: The COM Poisson00:00

Deaths from horse-kicks in Prussian army (Bortkewicz, 1898)73:10:42

Non-Poisson data used to be exotic88:55:20

Today non-Poisson counts are common98:55:21

Quantitative Linguistics113:23:46

Conway-Maxwell-Poisson129:07:28

Generalizes well-known distributions175:48:07

Over- and Under-dispersion204:16:13

Properties: Exponential Family213:44:10

Properties: Moments254:43:40

Estimation: Three Methods283:49:25

Conjugate Analysis of the Conway-Maxwell-Poisson Distribution289:47:04

Quarterly sales of socks - Word length in Hungarian dictionary347:56:15

Better fit365:47:36

Data Disclosure391:50:59

Modeling Bi-Modal Data via Mixtures438:22:40

Modeling Bi-Modal Count Data Using COM-Poisson Mixture Models479:52:40

From CMP Distribution to CMP Regression506:17:17

Bayesian Implementation: Marketing (1)518:45:22

Bayesian Implementation: Marketing (2)540:28:23

Bayesian Implementation: Transportation (1)558:34:44

Bayesian Implementation: Transportation (2)564:27:22

Our Approach: Classic GLM568:05:05

Link Function578:23:59

Maximum Likelihood Estimation617:42:57

Option 2: Solve normal equations iteratively618:38:17

Iteratively reweighted least squares: 2-parameter generalization622:52:04

Standard Errors: Fisher Information634:01:57

Dispersion Test637:24:40

Fitted Values655:20:13

Model Inference673:03:10

Diagnostics686:05:25

Alternative Regression Models693:05:26

Example 1: Airfreight Breakage714:29:28

Example 1: Airfreight Breakage719:27:09

Effect of Under-Dispersion749:03:21

Inference: Small Sample766:04:06

Example 1: Diagnostics769:09:23

Example 2: Book Purchases (1)775:36:50

Example 2: Book Purchases (2)777:52:18

Example 3: Motor Vehicle Crashes (1)796:50:36

Example 3: Motor Vehicle Crashes (2)805:34:36

Example 3: Motor Vehicle Crashes Lord et al. (2008)812:16:14

Example 3: Diagnostics824:13:31

Detecting Dispersion Mixtures825:47:28

Elephant Matings (1)844:54:27

Elephant Matings (2)895:26:34

Model Selection907:29:08

Summary & Conclusion913:15:32

CMP Regression has several advantages913:48:31

Weaknesses956:04:53

The COM-Poisson Model for Count Data: A Survey of Methods and Applications986:33:45

Wikipedia: Conway-Maxwell-Poisson distribution999:00:36