Measuring Agreement

CHAPTER 3 A GENERAL APPROACH FOR MODELING AND INFERENCE

3.1 PREVIEW

This chapter is concerned with a general discussion that is relevant for much of the book. First, we provide an introduction to linear mixed-effects models. This includes a discussion of prediction, model fitting, and model diagnostics. Next, we present the large-sample methodology for statistical inference based on ML estimators. Special attention is paid to construction of confidence intervals and bounds using both the standard large-sample theory and bootstrap. Finally, we present a general framework for modeling method comparison data using mixed-effects models and doing inference on measures of similarity and agreement. This framework is followed in subsequent chapters in the analysis of various types of data. Readers familiar with mixed-effects modeling and large-sample inference may just skim through this chapter. Those not interested in technical details may skip it entirely.

3.2 MIXED-EFFECTS MODELS

Suppose there are n subjects in the study. Let Y_i be an M_i × 1 vector of observations on the ith subject, i = 1,...,n. The M_i need not be equal for all i. The total number of observations in the data is . The observations from different subjects are independent, whereas those from the same subject are assumed to be dependent.

3.2.1 The Model

A general mixed-effects model for the data Y₁,..., Y_n can be written ...