Random Location and Scale Effects: Model Building Methods for a General Class of Models

We describe an approach to building models for data with random effects. The modeling includes both random location effects and random scale effects. The approach consists of a sequence of steps. In each step, model building tools based on certain statistics are used to study the structure of the data and identify or check an aspect of the model; the results of most of the steps are used explicitly in subsequent steps. This paper presents the properties of the statistics for a general class of location and scale models, and briefly describes the sequence and the tools. The paper is a supporting document for (Cleveland, Denby, and Liu 2000), which introduces the approach and describes by example how it is used in practice for model building.