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Linear Models in Matrix Form: A Hands-On Approach for the Behavioral Sciences

Autor Jonathon D. Brown
en Limba Engleză Paperback – 5 oct 2016
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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Specificații

ISBN-13: 9783319345697
ISBN-10: 3319345699
Pagini: 555
Ilustrații: XIX, 536 p. 77 illus., 28 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:Softcover reprint of the original 1st ed. 2014
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

Matrix Properties and Operations.- Simple Linear Regression.- Maximum Likelihood Estimation.- Multiple Regression.- Matrix Decompositions.- Problematic Observations.- Errors and Residuals.- Linearizing Transformations and Nonparametric Smoothers.- Cross-Product Terms and Interactions.- Polynomial Regression.- Categorical Predictors.- Factorial Designs.- Analysis of Covariance.- Moderation.- Mediation.

Recenzii

“This book appears to be a very solid work that contains a lot of useful material in one place in a manner. It is written in a manner inviting to intermediate readers who want to deepen their understanding of a key statistical technique. … I recommend it to the intermediate student or colleague who feel a need to boost up their understanding of the linear model.” (Jay Verkuilen, Psychometrika, Vol. 83, 2018)

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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