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A first-order modification to Pearson's statistic is proposed which induces local orthogonality with the regression parameters, resulting in substantial simplifications and increased power. Accurate and easily computed approximations to the moments of the modified Pearson statistic conditional on the estimated regression parameters are obtained for testing goodness of fit to sparse data. Both the Pearson statistic and its modification are shown to be asymptotically independent of the regression parameters. Simulation studies and examples are given.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1996.tb02086.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:42:30Z","timestamp":1544164950000},"page":"349-360","source":"Crossref","is-referenced-by-count":33,"title":["On Assessing Goodness of Fit of Generalized Linear Models to Sparse Data"],"prefix":"10.1093","volume":"58","author":[{"given":"C. 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Epidem."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1996.tb02086.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/58\/2\/349\/49098601\/jrsssb_58_2_349.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/58\/2\/349\/49098601\/jrsssb_58_2_349.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T21:56:45Z","timestamp":1725919005000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/58\/2\/349\/7027916"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7,1]]},"references-count":13,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1996,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1996.tb02086.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1996,7]]},"published":{"date-parts":[[1996,7,1]]}}}