{"action":"created","issue":{"url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2898","repository_url":"https://api.github.com/repos/statsmodels/statsmodels","labels_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2898/labels{/name}","comments_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2898/comments","events_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2898/events","html_url":"https://github.com/statsmodels/statsmodels/issues/2898","id":150234784,"number":2898,"title":"ENH: GMM-GLM dispersion Poisson/NegativeBinomial - optimal instruments","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-discrete","name":"comp-discrete","color":"ededed"},{"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-regression","name":"comp-regression","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":3,"created_at":"2016-04-22T01:09:06Z","updated_at":"2016-04-23T23:09:36Z","closed_at":null,"body":"just parking a reference:\r\n\r\nissue is replicating GLM with GMM, specifically with dispersion modelling, related to Quadratic Estimating Equations.\r\n\r\nIn Tweedie PR #2872, issue #2858 the question was how to find the moment condition for the dispersion parameters, specifically the \"instrument\" in front of the conditional moment restriction for dispersion/variance.\r\nThe approach we finally took is directly from a reference for Pearson function estimator.\r\nThe more general question is what are the optimal, or at least better than ad-hoc, instruments.\r\n\r\nI just saw that Cameron and Trivedi count data 2nd ed. have sections (11.7) on QEE and GMM for moment estimators for Poisson/NegativeBinomial type count models.\r\nexpression for optimal instruments look too complicated, but it's a more specific example than Chamberlain and Newey.\r\n\r\n---\r\ntopic: models that include functions for 2nd moment (variance and correlation functions)\r\nGLSHet, Garch, QIF, GEE, GMM, double exponential, ...\r\nMixed Models are also in this category but they are just MLE where all the work is computational"},"comment":{"url":"https://api.github.com/repos/statsmodels/statsmodels/issues/comments/213851999","html_url":"https://github.com/statsmodels/statsmodels/issues/2898#issuecomment-213851999","issue_url":"https://api.github.com/repos/statsmodels/statsmodels/issues/2898","id":213851999,"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},"created_at":"2016-04-23T23:09:36Z","updated_at":"2016-04-23T23:09:36Z","body":"I thought about GMM in the Tweedie context, if we want to get the corrected covariance matrix for the variance/dispersion parameter, which according to Jorgensen depends on the estimation and covariance of the mean parameters.\r\nGMM provides a generic setup to combine different equations to get consistent inference. But it would also be possible to do it explicitly case by case as in Jorgensen, or to use a specific generic function.\r\nI kind of have this in some unfinished PRs, but I'm always looking out for more applications because some details and API issues are not yet clear to me."}}