Diagnostics for Assessing the Accuracy of Normal Approximations in Exponential Family Nonlinear Models

Abstract

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is illustrated with several examples.

Key Words:

• Exponential family nonlinear models
• Logistic regression
• Nonlinear regression
• Parameter-effects curvature