Measuring Agreement

CHAPTER 6 HETEROSCEDASTIC DATA

6.1 PREVIEW

The methodologies of Chapters 4 and 5 allow the measurement methods to have different variances, but they are assumed to remain constant over the range of values being measured. In other words, the measurements are assumed to be homoscedastic. In practice, however, a method’s variability often depends on the magnitude of measurement. This chapter is concerned with paired and unlinked repeated measurements data that exhibit such magnitude-dependent heteroscedasticity. We assume that the measurement methods have the same scale and extend the homoscedastic models of Chapters 4 and 5 to incorporate heteroscedasticity by letting the variances be functions of a suitably defined variance covariate. Two case studies illustrate this methodology.

6.2 INTRODUCTION

For homoscedastic data, the method comparison measures involve variances that are constant in that they do not depend on the values being measured. This assumption fails in many circumstances. In these cases, it is important to incorporate heteroscedasticity into the model. Otherwise, subsequent model-based inference on the measures may become unreliable. It may be possible to remove the heteroscedasticity altogether by a variance stabilizing transformation of data, such as the log transformation. Indeed, this transformation has been successful in removing the heteroscedasticity in vitamin D data (see Sections 1.13.3 and 4.4.3). But a transformation will not always be successful. Besides, ...