Goodness of fit of generalized linear models to sparse data
We derive approximations to the first three moments of the conditional distribution of the deviance statistic, for testing the goodness of fit of generalized linear models with non-canonical links, by using an estimating equations approach, for data that are extensive but sparse. A supplementary est...
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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2000, Vol.62 (2), p.323-333 |
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| container_issue | 2 |
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| container_title | Journal of the Royal Statistical Society. Series B, Statistical methodology |
| container_volume | 62 |
| creator | Paul, S. R. Deng, D. |
| description | We derive approximations to the first three moments of the conditional distribution of the deviance statistic, for testing the goodness of fit of generalized linear models with non-canonical links, by using an estimating equations approach, for data that are extensive but sparse. A supplementary estimating equation is proposed from which the modified deviance statistic is obtained. An application of a modified deviance statistic is shown to binomial and Poisson data. We also conduct a performance study of the modified Pearson statistic derived by Farrington and the modified deviance statistic derived in this paper, in terms of size and power, through a small scale simulation experiment. Both statistics are shown to perform well in terms of size. The deviance statistic, however, shows an advantage of power. Two examples are given. |
| doi_str_mv | 10.1111/1467-9868.00234 |
| format | Article |
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R.</creatorcontrib><creatorcontrib>Deng, D.</creatorcontrib><title>Goodness of fit of generalized linear models to sparse data</title><title>Journal of the Royal Statistical Society. Series B, Statistical methodology</title><description>We derive approximations to the first three moments of the conditional distribution of the deviance statistic, for testing the goodness of fit of generalized linear models with non-canonical links, by using an estimating equations approach, for data that are extensive but sparse. A supplementary estimating equation is proposed from which the modified deviance statistic is obtained. An application of a modified deviance statistic is shown to binomial and Poisson data. We also conduct a performance study of the modified Pearson statistic derived by Farrington and the modified deviance statistic derived in this paper, in terms of size and power, through a small scale simulation experiment. Both statistics are shown to perform well in terms of size. The deviance statistic, however, shows an advantage of power. Two examples are given.</description><subject>Approximation</subject><subject>Binomial and Poisson linear model</subject><subject>Binomials</subject><subject>Data analysis</subject><subject>Degrees of freedom</subject><subject>Deviance</subject><subject>Deviance statistic</subject><subject>Distribution</subject><subject>Exact sciences and technology</subject><subject>Generalized linear model</subject><subject>Goodness of fit</subject><subject>Linear inference, regression</subject><subject>Linear models</subject><subject>Linear regression</subject><subject>Mathematical moments</subject><subject>Mathematics</subject><subject>P values</subject><subject>Power</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Regression analysis</subject><subject>Sciences and techniques of general use</subject><subject>Size</subject><subject>Sparse data</subject><subject>Statistical models</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Stochastic analysis</subject><issn>1369-7412</issn><issn>1467-9868</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2000</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFUU1v1DAQjRBIlJYzFw45IG5p_ZH1hzhBBQvVCgQt4mhNkgl48cbBk0KXX4_TVMuxI41n5Hlv9PSmKJ5xdspznPFa6coaZU4ZE7J-UBwdfh7mXipb6ZqLx8UToi3LobQ8Kl6tY-wGJCpjX_Z-mst3HDBB8H-xK4MfEFK5ix0GKqdY0giJsOxggpPiUQ-B8OldPS6-vnt7df6-2nxafzh_vanaWrO64toYbBqjmLBgVq01HbeaNwi2q7VtmG3R9lJrXGGWrEzTdFwoYNBZqxHlcfFy2Tum-OsaaXI7Ty2GAAPGa3LSWDYTM_BsAbYpEiXs3Zj8DtLeceZmk9xsiZstcbcmZcbFwkg4YnuANwG2MRE17reToER-9jlFdi0XP7c5x5xSSCeldD-mXV724k4nUAuhTzC0nv5rkEzXlmVYvcD--ID7-yS6L5eXbxapzxfalqaYDjTJjDFK5HG1jD1NeHMYQ_rp8qH1yn37uHYX9kroz4a5jfwHyUal9A</recordid><startdate>2000</startdate><enddate>2000</enddate><creator>Paul, S. R.</creator><creator>Deng, D.</creator><general>Blackwell Publishers Ltd</general><general>Blackwell Publishers</general><general>Blackwell</general><general>Royal Statistical Society</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope></search><sort><creationdate>2000</creationdate><title>Goodness of fit of generalized linear models to sparse data</title><author>Paul, S. R. ; Deng, D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4704-1788ebb86029a85c98d1971bea9d479b09ce9f377e5e14668bbd126a0ad997ee3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2000</creationdate><topic>Approximation</topic><topic>Binomial and Poisson linear model</topic><topic>Binomials</topic><topic>Data analysis</topic><topic>Degrees of freedom</topic><topic>Deviance</topic><topic>Deviance statistic</topic><topic>Distribution</topic><topic>Exact sciences and technology</topic><topic>Generalized linear model</topic><topic>Goodness of fit</topic><topic>Linear inference, regression</topic><topic>Linear models</topic><topic>Linear regression</topic><topic>Mathematical moments</topic><topic>Mathematics</topic><topic>P values</topic><topic>Power</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Regression analysis</topic><topic>Sciences and techniques of general use</topic><topic>Size</topic><topic>Sparse data</topic><topic>Statistical models</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Stochastic analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Paul, S. R.</creatorcontrib><creatorcontrib>Deng, D.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><jtitle>Journal of the Royal Statistical Society. Series B, Statistical methodology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Paul, S. R.</au><au>Deng, D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Goodness of fit of generalized linear models to sparse data</atitle><jtitle>Journal of the Royal Statistical Society. Series B, Statistical methodology</jtitle><date>2000</date><risdate>2000</risdate><volume>62</volume><issue>2</issue><spage>323</spage><epage>333</epage><pages>323-333</pages><issn>1369-7412</issn><eissn>1467-9868</eissn><abstract>We derive approximations to the first three moments of the conditional distribution of the deviance statistic, for testing the goodness of fit of generalized linear models with non-canonical links, by using an estimating equations approach, for data that are extensive but sparse. A supplementary estimating equation is proposed from which the modified deviance statistic is obtained. An application of a modified deviance statistic is shown to binomial and Poisson data. We also conduct a performance study of the modified Pearson statistic derived by Farrington and the modified deviance statistic derived in this paper, in terms of size and power, through a small scale simulation experiment. Both statistics are shown to perform well in terms of size. The deviance statistic, however, shows an advantage of power. Two examples are given.</abstract><cop>Oxford, UK and Boston, USA</cop><pub>Blackwell Publishers Ltd</pub><doi>10.1111/1467-9868.00234</doi><tpages>11</tpages></addata></record> |
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| ispartof | Journal of the Royal Statistical Society. Series B, Statistical methodology, 2000, Vol.62 (2), p.323-333 |
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| source | Wiley Online Library; JSTOR Mathematics and Statistics; RePEc; JSTOR; Oxford Journals; EBSCOhost Business Source Complete |
| subjects | Approximation Binomial and Poisson linear model Binomials Data analysis Degrees of freedom Deviance Deviance statistic Distribution Exact sciences and technology Generalized linear model Goodness of fit Linear inference, regression Linear models Linear regression Mathematical moments Mathematics P values Power Probability and statistics Probability theory and stochastic processes Regression analysis Sciences and techniques of general use Size Sparse data Statistical models Statistical variance Statistics Stochastic analysis |
| title | Goodness of fit of generalized linear models to sparse data |
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