Generalized Linear Models with Varying Dispersion
Generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean. It is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separate...
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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1989, Vol.51 (1), p.47-60 |
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| container_title | Journal of the Royal Statistical Society. Series B, Methodological |
| container_volume | 51 |
| creator | Smyth, Gordon K. |
| description | Generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean. It is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately. Mean and dispersion submodels are formulated for this, the dependent variable for the dispersion submodel being the deviance components of the mean submodel. The fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests. Estimation algorithms are proposed which have good convergence properties. The results apply mainly to the normal, inverse Gaussian and gamma distributions but can be extended to discrete distributions by using quasi-likelihoods. The methods developed are applied to a well-known data set. |
| doi_str_mv | 10.1111/j.2517-6161.1989.tb01747.x |
| format | Article |
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The methods developed are applied to a well-known data set.</description><subject>deviance components</subject><subject>Exact sciences and technology</subject><subject>Gaussian distributions</subject><subject>Generalized linear model</subject><subject>Induced substructures</subject><subject>inverse gaussian and gamma distributions</subject><subject>iterative algorithms</subject><subject>Linear inference, regression</subject><subject>Linear models</subject><subject>Linear regression</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>normal</subject><subject>Parametric models</subject><subject>Probability and statistics</subject><subject>quasi‐likelihood</subject><subject>Sciences and techniques of general use</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Variance</subject><issn>0035-9246</issn><issn>1369-7412</issn><issn>2517-6161</issn><issn>1467-9868</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><recordid>eNqVkF9LwzAUxYMoOKffwIei-Niav23j25w6hYng1NeQpqmm1LYmHdv89KZ2zGfzcgP33N85HADOEIyQf5dlhBlKwhjFKEI85VGXQZTQJFrvgdFutQ9GEBIWckzjQ3DkXAkhRISSEUAzXWsrK_Ot82Buai1t8NjkunLBynQfwZu0G1O_BzfGtdo609TH4KCQldMn2zkGr3e3L9P7cP40e5hO5qEisfeleQIJzTlDEGUpx1ixNIdYyYyxwodSMccKQ50UKc9RkkmY8yLGfplmVLOYjMH5wG1t87XUrhNls7S1txSIQMw5Igx71dWgUrZxzupCtNZ8-tACQdFXJErR9yD6HkRfkdhWJNb--GJrIZ2SVWFlrYz7I3DMEx_d6yaDbmUqvfmHg3heLK5__55xOjBK1zV2x8CEspRC8gPe8oNF</recordid><startdate>1989</startdate><enddate>1989</enddate><creator>Smyth, Gordon K.</creator><general>Royal Statistical Society</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>HGTKA</scope><scope>JILTI</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope></search><sort><creationdate>1989</creationdate><title>Generalized Linear Models with Varying Dispersion</title><author>Smyth, Gordon K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3617-4d7034d95101b8922c58d02cab55f616c692c20e7f89d17ba0d9f6255f8b4e563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>deviance components</topic><topic>Exact sciences and technology</topic><topic>Gaussian distributions</topic><topic>Generalized linear model</topic><topic>Induced substructures</topic><topic>inverse gaussian and gamma distributions</topic><topic>iterative algorithms</topic><topic>Linear inference, regression</topic><topic>Linear models</topic><topic>Linear regression</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>normal</topic><topic>Parametric models</topic><topic>Probability and statistics</topic><topic>quasi‐likelihood</topic><topic>Sciences and techniques of general use</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Variance</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Smyth, Gordon K.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Periodicals Index Online Segment 18</collection><collection>Periodicals Index Online Segment 32</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - 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Series B, Methodological</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Smyth, Gordon K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Linear Models with Varying Dispersion</atitle><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle><date>1989</date><risdate>1989</risdate><volume>51</volume><issue>1</issue><spage>47</spage><epage>60</epage><pages>47-60</pages><issn>0035-9246</issn><issn>1369-7412</issn><eissn>2517-6161</eissn><eissn>1467-9868</eissn><coden>JSTBAJ</coden><abstract>Generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean. It is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately. Mean and dispersion submodels are formulated for this, the dependent variable for the dispersion submodel being the deviance components of the mean submodel. The fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests. Estimation algorithms are proposed which have good convergence properties. The results apply mainly to the normal, inverse Gaussian and gamma distributions but can be extended to discrete distributions by using quasi-likelihoods. The methods developed are applied to a well-known data set.</abstract><cop>London</cop><pub>Royal Statistical Society</pub><doi>10.1111/j.2517-6161.1989.tb01747.x</doi><tpages>14</tpages></addata></record> |
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| identifier | ISSN: 0035-9246 |
| ispartof | Journal of the Royal Statistical Society. Series B, Methodological, 1989, Vol.51 (1), p.47-60 |
| issn | 0035-9246 1369-7412 2517-6161 1467-9868 |
| language | eng |
| recordid | cdi_proquest_journals_1302991352 |
| source | Periodicals Index Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | deviance components Exact sciences and technology Gaussian distributions Generalized linear model Induced substructures inverse gaussian and gamma distributions iterative algorithms Linear inference, regression Linear models Linear regression Mathematical functions Mathematics Maximum likelihood estimation normal Parametric models Probability and statistics quasi‐likelihood Sciences and techniques of general use Statistical variance Statistics Variance |
| title | Generalized Linear Models with Varying Dispersion |
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