Linear Models with R
By Julian J. Faraway. 2014
304 citations recorded by the source corpus.
Introduction Before You Start Initial Data Analysis When to Use Linear Modeling History Estimation Linear Model Matrix Representation Estimating b Least Squares Estimation Examples of Calculating b Example QR Decomposition Gauss-Markov Theorem Goodness of Fit Identifiability Orthogonality Inference Hypothesis Tests to Compare Models Testing Examples Permutation Tests Sampling Confidence Intervals for b Bootstrap Confidence Intervals Prediction Confidence Intervals for Predictions Predicting Body Fat Autoregression What Can Go Wrong with Predictions? Explanation Simple Meaning Causality Designed Experiments Observational Data Matching Covariate Adjustment Qualitative Support for Causation Diagnostics Checking Error Assumptions Finding Unusual Observations Checking the Structure of the Model Discussion Problems with the Predictors Errors in the Predictors Changes of Scale Collinearity Problems with the Error Generalized Least Squares Weighted Least Squares Testing for Lack of Fit Robust Regression Transformation Transforming the Response Transforming the Predictors Broken Stick Regression Polynomials Splines Additive Models More Complex Models Model Selection Hierarchical Models Testing-Based Procedures Criterion-Based Procedures Summary Shrinkage Methods Principal Components Partial Least Squares Ridge Regression Lasso Insurance Redlining-A Complete Example Ecological Correlation Initial Data Analysis Full Model and Diagnostics Sensitivity Analysis Discussion Missing Data Types of Missing Data Deletion Single Imputation Multiple Imputation Categorical Predictors A Two-Level Factor Factors and Quantitative Predictors Interpretation with Interaction Terms Factors with More than Two Levels Alternative Codings of Qualitative Predictors One Factor Models The Model An Example Diagnostics Pairwise Comparisons False Discovery Rate Models with Several Factors Two Factors with No Replication Two Factors with Replication Two Factors with an Interaction Larger Factorial Experiments Experiments with Blocks Randomized Block Design Latin Squares Balanced Incomplete Block Design Appendix: About R Bibliography Index
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Citations in the corpus
- Extensive gaps and biases in our knowledge of a well‐known fauna: implications for integrating biological traits into macroecology (2012, unknown): “Our predictors are inter-related, meaning that models may suffer from problems associated with collinearity (Faraway, 2005).”
- Worldwide trends in gastric cancer mortality (1980-2011), with predictions to 2015, and incidence by subtype. (2014, background): “The PI is a measure of uncertainty that accounts for the random nature of future predicted values, by adding an extra term in the standard error calculation [19].”
- Factors influencing epiphytic bryophyte and lichen species richness at different spatial scales in managed temperate forests (2012, methodology): “168 169 Data analyses 170 171 At stand level, general linear regression models were built to explore relationships between 172 epiphyte richness and potential explanatory variables (Faraway 2005).”