Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1911.02131 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929213232119808 |
|---|---|
| author | Morris, Darcy Steeg Raim, Andrew M. Sellers, Kimberly F. |
| author_facet | Morris, Darcy Steeg Raim, Andrew M. Sellers, Kimberly F. |
| contents | Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for such clustered data but assumes that trials are independent and identically distributed. Extensions such as Dirichlet-multinomial and random-clumped multinomial can express positive association, where trials are more likely to result in a common category due to membership in a common cluster. This work considers a Conway-Maxwell-multinomial (CMM) distribution for modeling clustered categorical data exhibiting positively or negatively associated trials. The CMM distribution features a dispersion parameter which allows it to adapt to a range of association levels and includes several recognizable distributions as special cases. We explore properties of CMM, illustrate its flexible characteristics, identify a method to efficiently compute maximum likelihood (ML) estimates, present simulations of small sample properties under ML estimation, and demonstrate the model via several data analysis examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_02131 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Conway-Maxwell-Multinomial Distribution for Flexible Modeling of Clustered Categorical Data Morris, Darcy Steeg Raim, Andrew M. Sellers, Kimberly F. Methodology Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for such clustered data but assumes that trials are independent and identically distributed. Extensions such as Dirichlet-multinomial and random-clumped multinomial can express positive association, where trials are more likely to result in a common category due to membership in a common cluster. This work considers a Conway-Maxwell-multinomial (CMM) distribution for modeling clustered categorical data exhibiting positively or negatively associated trials. The CMM distribution features a dispersion parameter which allows it to adapt to a range of association levels and includes several recognizable distributions as special cases. We explore properties of CMM, illustrate its flexible characteristics, identify a method to efficiently compute maximum likelihood (ML) estimates, present simulations of small sample properties under ML estimation, and demonstrate the model via several data analysis examples. |
| title | A Conway-Maxwell-Multinomial Distribution for Flexible Modeling of Clustered Categorical Data |
| topic | Methodology |
| url | https://arxiv.org/abs/1911.02131 |