Authors:
- Comprehensively covers use of linear models in matrix form
- Utilizes R and open source spreadsheets as standard tools for algebraic calculations
- Many examples and full-color screenshots data files to help readers work through the exercises
- East chapter contains useful summary and R code
- Includes supplementary material: sn.pub/extras
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses.
The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum of squares, the determinant, and the inverse. These operations are explained in everyday language, and their calculations are demonstrated using concrete examples. The remaining chapters build on these operations, progressing from simple linear regression to mediational models with bootstrapped standard errors.
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Authors and Affiliations
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Department of Psychology, University of Washington, Seattle, USA
Jonathon D. Brown
About the author
Jonathon D. Brown is a social psychologist at the University of Washington. Since receiving his Ph.D. from UCLA in 1986, he has written three books, authored numerous journal articles and chapters, received a Presidential Young Investigator Award from the National Science Foundation, and been recognized as one of social psychology's most frequently-cited authors.
Bibliographic Information
Book Title: Linear Models in Matrix Form
Book Subtitle: A Hands-On Approach for the Behavioral Sciences
Authors: Jonathon D. Brown
DOI: https://doi.org/10.1007/978-3-319-11734-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-11733-1Published: 06 February 2015
Softcover ISBN: 978-3-319-34569-7Published: 05 October 2016
eBook ISBN: 978-3-319-11734-8Published: 21 January 2015
Edition Number: 1
Number of Pages: XIX, 536
Number of Illustrations: 49 b/w illustrations, 28 illustrations in colour
Topics: Statistics for Social Sciences, Humanities, Law, Psychometrics, Statistical Theory and Methods