A SAS/IML Companion for Linear Models

• Jamis J. Perrett
Book

Part of the Statistics and Computing book series (SCO)

1. Front Matter
Pages i-xiv
2. Jamis J. Perrett
Pages 1-32
3. Jamis J. Perrett
Pages 33-53
4. Jamis J. Perrett
Pages 55-74
5. Jamis J. Perrett
Pages 75-90
6. Jamis J. Perrett
Pages 91-105
7. Jamis J. Perrett
Pages 107-117
8. Jamis J. Perrett
Pages 119-128
9. Jamis J. Perrett
Pages 129-177
10. Jamis J. Perrett
Pages 179-202
11. Jamis J. Perrett
Pages 203-220
12. Back Matter
Pages 221-228

Introduction

Linear models courses are often presented as either theoretical or applied. Consequently, students may find themselves either proving theorems or using high-level procedures like PROC GLM to analyze data. There exists a gap between the derivation of formulas and analyses that hide these formulas behind attractive user interfaces. This book bridges that gap, demonstrating theory put into practice.

Concepts presented in a theoretical linear models course are often trivialized in applied linear models courses by the facility of high-level SAS procedures like PROC MIXED and PROC REG that require the user to provide a few options and statements and in return produce vast amounts of output. This book uses PROC IML to show how analytic linear models formulas can be typed directly into PROC IML, as they were presented in the linear models course, and solved using data. This helps students see the link between theory and application. This also assists researchers in developing new methodologies in the area of linear models.

The book contains complete examples of SAS code for many of the computations relevant to a linear models course. However, the SAS code in these examples automates the analytic formulas. The code for high-level procedures like PROC MIXED is also included for side-by-side comparison. The book computes basic descriptive statistics, matrix algebra, matrix decomposition, likelihood maximization, non-linear optimization, etc. in a format conducive to a linear models or a special topics course.

Also included in the book is an example of a basic analysis of a linear mixed model using restricted maximum likelihood estimation (REML). The example demonstrates tests for fixed effects, estimates of linear functions, and contrasts. The example starts by showing the steps for analyzing the data using PROC IML and then provides the analysis using PROC MIXED. This allows students to follow the process that lead to the output.

Keywords

Descriptive statistics IML Interactive matrix language Linear mixed models Mathematica Matrix book Nonlinear optimization SAS SAS matrices SAS/IML STATISTICA Statistical modeling

Authors and affiliations

• Jamis J. Perrett
• 1
1. 1.Dept. StatisticsTexas A & M UniversityCollege StationU.S.A.

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4419-5557-9
• Copyright Information Springer-Verlag New York 2010
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics
• Print ISBN 978-1-4419-5556-2
• Online ISBN 978-1-4419-5557-9
• Series Print ISSN 1431-8784