en
0.25
0.5
0.75
1.25
1.5
1.75
2
A Flexible Model for Count Data: The COM-Poisson Distribution
Published on 2012-09-266653 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
Related categories
Presentation
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
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