EPSE 682: Multivariate Analysis
2021/22, Winter Term 2
Course overview:
This course is essentially two combined mini-courses. The first half of the course is devoted to GLMs and nonparametric regression (i.e., conditional modelling techniques: one response variable as a function of many predictors), while the second half of the course focuses on common statistical techniques for studying dependencies between many response variables simultaneously (i.e., joint modelling). The basics of ANOVA (EPSE 592) and regression (EPSE 596) will be reviewed in-class as needed.
Recommended textbooks:
- Generalized Linear Models, P. McCullagh and J.A. Nelder. The definitive resource on GLMs (Part I of the course). The text is heavily mathematical, however. Available online through UBC Library.
This course is essentially two combined mini-courses. The first half of the course is devoted to GLMs and nonparametric regression (i.e., conditional modelling techniques: one response variable as a function of many predictors), while the second half of the course focuses on common statistical techniques for studying dependencies between many response variables simultaneously (i.e., joint modelling). The basics of ANOVA (EPSE 592) and regression (EPSE 596) will be reviewed in-class as needed.
Recommended textbooks:
- Generalized Linear Models, P. McCullagh and J.A. Nelder. The definitive resource on GLMs (Part I of the course). The text is heavily mathematical, however. Available online through UBC Library.
Class Notes:
-Week 1: Introduction; review of linear regression
-Week 2: Logistic regression for binomial response data
-Week 3: More binomial regression; intro to GLMs
-Week 4: Power, separation, over/underdispersion, and quasilikelihood
-Week 5: Multinomial regression, Poisson regression, zero-inflation
-Week 6: Gamma and Beta/ZOIB regression; numerical and estimation issues
-Week 7: Bootstrapping; techniques in nonparametric regression (splines, LOESS, kernel smoothing)
-Week 8: More nonparametrics; joint vs. conditional vs. marginal probability
-Week 9: Copulas; multivariate normality
-Week 10: Hotelling's T^2, MANOVA, discriminant analysis
-Week 11: Principal component analysis
-Week 12: Factor analysis; canonical correlation; clustering
-Week 1: Introduction; review of linear regression
-Week 2: Logistic regression for binomial response data
-Week 3: More binomial regression; intro to GLMs
-Week 4: Power, separation, over/underdispersion, and quasilikelihood
-Week 5: Multinomial regression, Poisson regression, zero-inflation
- Ver Hoef & Boveng: How to choose between a Poisson and Negative Binomial model for count response data
-Week 6: Gamma and Beta/ZOIB regression; numerical and estimation issues
-Week 7: Bootstrapping; techniques in nonparametric regression (splines, LOESS, kernel smoothing)
-Week 8: More nonparametrics; joint vs. conditional vs. marginal probability
- Ver Hoef & Boveng (2007): Quasi-Poisson vs. Negative Binomial regression
-Week 9: Copulas; multivariate normality
- Kroc & Astivia (2021)
- Dorey & Jourbert: Intro to copula modelling
- Vuolo (2017): Intro to copula modelling
-Week 10: Hotelling's T^2, MANOVA, discriminant analysis
-Week 11: Principal component analysis
-Week 12: Factor analysis; canonical correlation; clustering