Displaying and Combining Small-sample Likelihoods from Generalized Linear Models

• Activity Number: 218
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Nicholas J. Barrowman*+ and Ransom Myers and Keith O'Rourke
• Companies: Children's Hospital of Eastern Ontario Research Institute and Dalhousie University and Ottawa Health Research Institute
• Keywords: generalized linear models ; likelihood plots ; likelihood-based confidence intervals ; profile likelihood ; raindrop plot

Abstract

For large sample sizes, the asymptotic Wald approximation used in standard output from many statistical packages is usually adequate for inferences for generalized linear models. However, there are cases where these approximations are inaccurate and even inappropriate such as when zeros are present and only one-sided confidence intervals are sensible. For example, in a clinical trial if all patients experience an event, the log-likelihood is not approximately quadratic. In ecological studies, a similar situation occurs when during one time period animals of a particular kind are observed but during another none are observed. In such situations, the direct use of likelihood is both less opaque and more accurate than Wald approximations. The purpose of this paper is to provide accessible methods and guidance for directly using likelihood for plotting and construction of confidence intervals. Profile likelihood is used to summarize information about single parameters of interest and to combine information from different sources. R and S-Plus code is provided to compute profile likelihoods, display raindrop plots, and obtain confidence intervals.