Relaxing linearity assumption for continuous predictors (14)
nonparametric smoothing
simple nonlinear terms
splines for estimating shape of regression function and determining predictor transformations
cubic spline functions
restricted cubic splines
advantages of splines over other methods such as nonparametric regression
recursive partitioning and tree models in a nutshell
Tests of association (18)
Assessment of model fit (_K_5, _K_10)
regression assumptions
modeling and testing interactions (_K_8.3)
Missing data (_H_3, _K_8.7-8.8)
Types of missing data (19)
Prelude to modeling
Problems with alternatives to imputation
Strategies for developing imputations
Single imputation
Multiple imputation
Multivariable modeling strategy (_H_4, _K_6) (21)
Pre-specification of predictor complexity
Variable selection (_K_8.9-8.12) (22)
Overfitting and number of predictors
Shrinkage
Data reduction (_H_4.7, first page and summary chart, _H_14 up to _H_14.4, _K_7.2 (23)
Overall modeling strategy (_K_9,_K_13) (24)
Bootstrap, Validating and Describing the Model (_H_5)
Bootstrap (25)
Model validation (26)
Describing the model (27)
R Multivariable Modeling/Validation/Presentation Software (_H_6, Alzola & Harrell 9.3-4) (28)
Case study in OLS regression (_H_7) (29)
Case study in data reduction and missing value imputation (_H_8 up until discussion of principal components) (H14.2,14.3)
Project: Understanding interrelationships of predictor variables, dealing with missing data, developing and validating a multiple regression model using least squares Assigned 23 Due 28
Maximum Likelihood Estimation (_H_9 up until 9.3, _K_8.13-8.15) (30)
Binary Logistic Model (_H_10, Background reading: Rosner Section 13.1-13.2, 13.3.3, 13.4.1, 13.7) (30) 1 Model 1 Odds ratios 1 Special residual plots (33) 1 Applications of general methods 1 Graphically presenting model (34) 1 Case studies
Project: Develop and validate a binary logistic regression model Assigned 32 Due 35
Proportional Odds Ordinal Logistic Models (_H_13.1-13.3) (36) 1 Model 1 Odds ratios 1 Applications of general methods
Case study (_H_14-14.3) Assignment: Interpret an analysis that used a proportional odds ordinal logistic model Assigned 38 Due 41
Brief Introduction to Survival Analysis (Rosner 14.8-14.11, _H_16, _K_3.3, 7, 8.4-8.6,10.6) (37) 1 Survival data and right-censoring 1 log-rank test for comparing two groups
Cox regression model (_H_19.1) (38)
Other Case Studies and Labs (40-41)
Maximum Likelihood Estimation (_H_9) (6)
Three test statistics (_H_6.3.3)
Robust covariance matrix estimator (_H_9.5)
Correcting variances for clustered or serial data using sandwich and bootstrap estimators (_H_9.5)
Bootstrap simultaneous confidence regions using Tibshirani's bootstrap bumping (_H_9.7) (7)
R bootcov and rm.boot functions
Simulations to study coverage of simultaneous bootstrap confidence regions
Further use of the log likelihood (_H_9.8) (8)
Weighted MLE (_H_9.9)
Penalized MLE (_H_9.10, _HTF_3.4.3)
Effective d.f. (_H_9.10,_HTF_7.6)
Tibshirani's lasso (_HTF_3.4.3,3.4.5,10.12.3)
Ordinal Logistic Models (_H_13, 14) (9)
Models
Using ordinal models and the Cox model for robust rank-based analysis of continuous response data
Special residual plots
Special use of penalized MLE
Case study Project: Develop and validate a proportional odds ordinal logistic model
Projection-pursuit regression (_VR_9.2) and MARS (_HTF_9.4) (10)