Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 15
15
ST 762, M. DAVIDIAN
Nonlinear mixed eects models
15.1
Introduction
In this chapter, we focus on methods for estimation of the parameters in subjectspecic nonlinear mixed
eects models, which were introduced in Section 13.3. As noted in our m
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 13
13
ST 762, M. DAVIDIAN
Approaches to modeling multivariate response
13.1
Introduction
In the previous chapters, we have focused on the situation in which the responses may be viewed as
independent. We thought about this in dierent ways.
In som
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 14
14
14.1
ST 762, M. DAVIDIAN
Estimating equation methods for populationaveragemodels
Introduction
In this chapter, we focus on methods for estimation of the parameters in a populationaveraged marginal
model of the general form discussed in Ch
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 7
7
ST 762, M. DAVIDIAN
Detection and modeling of nonconstant variance
7.1
Introduction
So far, we have focused on approaches to inference in meanvariance models of the form
E(Yj xj ) = f (xj , ),
var(Yj xj ) = 2 g2 (, , xj )
(7.1)
under the as
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 8
8
ST 762, M. DAVIDIAN
Large sample theory: A casual approach
So far, we have discussed a number of approaches to inference in the general meanvariance model
E(Yj xj ) = f (xj , ),
var(Yj xj ) = 2 g2 (, , xj ).
(8.1)
In particular, we have pro
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 11
11
ST 762, M. DAVIDIAN
The role of estimating weights in GLS second order theory
11.1
Introduction
The folklore theorem for GLS discussed in Chapter 9 is used routinely as the basis for assessing
uncertainty of GLS estimation (e.g. standard err
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 6
6
ST 762, M. DAVIDIAN
Unknown parameters in the variance function
6.1
Introduction
So far, we have considered the general meanvariance model
E(Yj xj ) = f (xj , ),
var(Yj xj ) = 2 g2 (, , xj )
(6.1)
in the case where is known; that is, the fo
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 3
3
ST 762, M. DAVIDIAN
Implementation of generalized least squares
We have indicated that, for the general model
E(Yj xj ) = f (xj , ),
var(Yj xj ) = 2 g2 (, , xj ),
(3.1)
a popular method for estimating in the mean specication is generalized l
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 2
2
ST 762, M. DAVIDIAN
Introduction to nonlinear models
2.1
Introduction
In this chapter, we will discuss the model that will be our central focus in Chapters 312. Through
the course of our discussion, we will identify dierent approaches to infer
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 1
1
ST 762, M. DAVIDIAN
Introduction and Motivation
1.1
Scope and objectives
OBJECTIVE: The goal of this course is to provide a comprehensive treatment of modern regression
models and associated inferential methods for univariate and multivariate
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 4
4
ST 762, M. DAVIDIAN
Generalized (non) linear models
4.1
Introduction
We have seen that a natural way to motivate regression models for data that do not obey the classical
regression assumptions, whether the postulated relationship is linear or
Nonlinear Models for Univariate and Multivariate Response
STATISTICS 762

Fall 2009
CHAPTER 5
5
ST 762, M. DAVIDIAN
Normal theory maximum likelihood and quadratic estimating equations
5.1
Introduction
We recall the general meanvariance model:
E(Yj xj ) = f (xj , ), var(Yj xj ) = 2 g2 (, , xj ).
(5.1)
In Chapter 2, we discussed (Approa