Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Dynamic Link Inclusion in Online PDF Journals

Two complementary de facto standards for the publication of electronic documents are HTML on theWorldWideWeb and Adobe s PDF (Portable Document Format) language for use with Acrobat viewers. Both these formats provide support for hypertext features to be embedded within documents. We present a method, which allows links and other hypertext material to be kept in an abstract form in separate link databases. The links can then be interpreted or compiled at any stage and applied, in the correct format to some specific representation such as HTML or PDF. This approach is of great value in keeping hyperlinks relevant, up-to-date and in a form which is independent of the finally delivered electronic document format. Four models are discussed for allowing publishers to insert links into documents at a late stage. The techniques discussed have been implemented using a combination of Acrobat plug-ins, Web servers and Web browsers.