{"action":"opened","issue":{"url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2890","repository_url":"https://api.github.com/repos/statsmodels/statsmodels","labels_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2890/labels{/name}","comments_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2890/comments","events_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2890/events","html_url":"https://github.com/statsmodels/statsmodels/issues/2890","id":147491665,"number":2890,"title":"ENH: dispersed contingency tables, counts, rates and proportions","user":{"login":"josef-pkt","id":440735,"avatar_url":"https://avatars.githubusercontent.com/u/440735?v=3","gravatar_id":"","url":"https://api.github.com/users/josef-pkt","html_url":"https://github.com/josef-pkt","followers_url":"https://api.github.com/users/josef-pkt/followers","following_url":"https://api.github.com/users/josef-pkt/following{/other_user}","gists_url":"https://api.github.com/users/josef-pkt/gists{/gist_id}","starred_url":"https://api.github.com/users/josef-pkt/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/josef-pkt/subscriptions","organizations_url":"https://api.github.com/users/josef-pkt/orgs","repos_url":"https://api.github.com/users/josef-pkt/repos","events_url":"https://api.github.com/users/josef-pkt/events{/privacy}","received_events_url":"https://api.github.com/users/josef-pkt/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/statsmodels/statsmodels/labels/comp-genmod","name":"comp-genmod","color":"ededed"},{"url":"https://api.github.com/repos/statsmodels/statsmodels/labels/comp-stats","name":"comp-stats","color":"ededed"},{"url":"https://api.github.com/repos/statsmodels/statsmodels/labels/type-enh","name":"type-enh","color":"99ffff"}],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":0,"created_at":"2016-04-11T17:04:44Z","updated_at":"2016-04-11T17:04:44Z","closed_at":null,"body":"When I was reviewing contingency tables, loglinear models and one or two sample tests for rates and proportions, I saw that all inference relies on the correctly specified model in terms of absence of unobserved heterogeneity, correlation or similar sources of over or under dispersion.\r\n\r\nrelated:\r\n#2718 #2723 two sample hypothesis test and confidence intervals for Poisson rates\r\n#2743 #2605 #2608 two sample hypothesis test and confidence intervals for proportions\r\nand others\r\n#2418 (merged) and others for contingency tables\r\n\r\none possibility is to use negative binomial as the relevant distribution.\r\npossible problem with having only aggregate data\r\n\r\nEfron, Bradley. 1986. “Double Exponential Families and Their Use in Generalized Linear Regression.” Journal of the American Statistical Association 81 (395): 709–21. doi:10.2307/2289002.\r\nhas a contingency table example\r\n\r\nMütze, Tobias, Axel Munk, and Tim Friede. 2016. “Design and Analysis of Three-Arm Trials with Negative Binomially Distributed Endpoints.” Statistics in Medicine 35 (4): 505–21. doi:10.1002/sim.6738.\r\n(I have not yet looked at it)\r\n\r\nSudhir Paul & Khurshid Alam (2014): Testing equality of two negative binomial\r\nmeans in presence of unequal over-dispersion parameters: a Behrens–Fisher problem analog,\r\nJournal of Statistical Computation and Simulation, DOI: 10.1080/00949655.2014.955025\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n"}}