Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Image processing basics
- 3 Preprocessing fMRI data
- 4 Spatial normalization
- 5 Statistical modeling: Single subject analysis
- 6 Statistical modeling: Group analysis
- 7 Statistical inference on images
- 8 Modeling brain connectivity
- 9 Multivoxel pattern analysis and machine learning
- 10 Visualizing, localizing, and reporting fMRI data
- Appendix A A Review of the General Linear Model
- Appendix B Data organization and management
- Appendix C Image formats
- Bibliography
- Index
Appendix A - A Review of the General Linear Model
Published online by Cambridge University Press: 01 June 2011
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Image processing basics
- 3 Preprocessing fMRI data
- 4 Spatial normalization
- 5 Statistical modeling: Single subject analysis
- 6 Statistical modeling: Group analysis
- 7 Statistical inference on images
- 8 Modeling brain connectivity
- 9 Multivoxel pattern analysis and machine learning
- 10 Visualizing, localizing, and reporting fMRI data
- Appendix A A Review of the General Linear Model
- Appendix B Data organization and management
- Appendix C Image formats
- Bibliography
- Index
Summary
The general linear model is an important tool in many fMRI data analyses. As the Name “general” suggests, this model can be used for many different types of analyses, including correlations, one-sample t-tests, two-sample t-tests, analysis of variance (ANOVA), and analysis of covariance (ANCOVA). This appendix is a review of the GLM and covers parameter estimation, hypothesis testing, and model setup for these various types of analyses.
Some knowledge of matrix algebra is assumed in this section, and for a more detailed explanation of the GLM, it is recommended to read Neter et al. (1996).
Estimating GLM parameters
The GLM relates a single continuous dependent, or response, variable to one or more continuous or categorical independent variables, or predictors. The simplest model is a simple linear regression, which contains a single independent variable. For example, finding the relationship between the dependent variable of mental processing speed and the independent variable, age (Figure A.1). The goal is to create a model that fits the data well and since this appears to be a simple linear relationship between age and processing speed, the model is Y = β0+β1X1, where Y is a vector of length T containing the processing speeds for T subjects, β0 describes where the line crosses the y axis, β1 is the slope of the line and X1 is the vector of length T containing the ages of the subjects.
- Type
- Chapter
- Information
- Handbook of Functional MRI Data Analysis , pp. 191 - 200Publisher: Cambridge University PressPrint publication year: 2011
- 2
- Cited by