A Framework to Interpret Nonstandard Log-Linear Models
The formulation of log-linear models within the framework of Generalized Linear Models offers new possibilities in modeling categorical data. The resulting models are not restricted to the analysis of contingency tables in terms of ordinary hierarchical interactions. Such models are considered as th...
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2016-04-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | http://www.ajs.or.at/index.php/ajs/article/view/323 |
| _version_ | 1818328668785606656 |
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| author | Patrick Mair |
| author_facet | Patrick Mair |
| author_sort | Patrick Mair |
| collection | DOAJ |
| description | The formulation of log-linear models within the framework of Generalized Linear Models offers new possibilities in modeling categorical data. The resulting models are not restricted to the analysis of contingency tables in terms of ordinary hierarchical interactions. Such models are considered as the family of nonstandard log-linear models. The problem that can arise is an ambiguous interpretation of parameters. In the current paper
this problem is solved by looking at the effects coded in the design matrix and determining the numerical contribution of single effects. Based on these results, stepwise approaches are proposed in order to achieve parsimonious models. In addition, some testing strategies are presented to test such (eventually non-nested) models against each other. As a result, a whole interpretation framework is elaborated to examine nonstandard log-linear models in depth. |
| first_indexed | 2024-12-13T12:35:50Z |
| format | Article |
| id | doaj.art-9245182de8be4e75b7e50cad286ae733 |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-12-13T12:35:50Z |
| publishDate | 2016-04-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-9245182de8be4e75b7e50cad286ae7332022-12-21T23:45:52ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2016-04-0136210.17713/ajs.v36i2.323A Framework to Interpret Nonstandard Log-Linear ModelsPatrick Mair0Vienna University of Economics and Business AdministrationThe formulation of log-linear models within the framework of Generalized Linear Models offers new possibilities in modeling categorical data. The resulting models are not restricted to the analysis of contingency tables in terms of ordinary hierarchical interactions. Such models are considered as the family of nonstandard log-linear models. The problem that can arise is an ambiguous interpretation of parameters. In the current paper this problem is solved by looking at the effects coded in the design matrix and determining the numerical contribution of single effects. Based on these results, stepwise approaches are proposed in order to achieve parsimonious models. In addition, some testing strategies are presented to test such (eventually non-nested) models against each other. As a result, a whole interpretation framework is elaborated to examine nonstandard log-linear models in depth.http://www.ajs.or.at/index.php/ajs/article/view/323 |
| spellingShingle | Patrick Mair A Framework to Interpret Nonstandard Log-Linear Models Austrian Journal of Statistics |
| title | A Framework to Interpret Nonstandard Log-Linear Models |
| title_full | A Framework to Interpret Nonstandard Log-Linear Models |
| title_fullStr | A Framework to Interpret Nonstandard Log-Linear Models |
| title_full_unstemmed | A Framework to Interpret Nonstandard Log-Linear Models |
| title_short | A Framework to Interpret Nonstandard Log-Linear Models |
| title_sort | framework to interpret nonstandard log linear models |
| url | http://www.ajs.or.at/index.php/ajs/article/view/323 |
| work_keys_str_mv | AT patrickmair aframeworktointerpretnonstandardloglinearmodels AT patrickmair frameworktointerpretnonstandardloglinearmodels |