by Peter H. Westfall, Andrea L. Arias
Understanding Regression
Analysis unifies diverse regression applications including the classical
model, ANOVA models, generalized models including Poisson, Negative
binomial, logistic, and survival, neural networks, and decision trees
under a common umbrella -- namely, the conditional distribution model.
It explains why the conditional distribution model is the correct
model, and it also explains (proves) why the assumptions of the
classical regression model are wrong. Unlike other regression books,
this one from the outset takes a realistic approach that all models are
just approximations. Hence, the emphasis is to model Nature’s
processes realistically, rather than to assume (incorrectly) that
Nature works in particular, constrained ways.
Key features of the book include:
- Numerous worked examples using the R software
- Key points and self-study questions displayed "just-in-time" within chapters
- Simple mathematical explanations ("baby proofs") of key concepts
- Clear
explanations and applications of statistical significance (p-values),
incorporating the American Statistical Association guidelines
- Use of "data-generating process" terminology rather than "population"
- Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case)
- Clear explanations of probabilistic modelling, including likelihood-based methods
- Use of simulations throughout to explain concepts and to perform data analyses
This
book has a strong orientation towards science in general, as well as
chapter-review and self-study questions, so it can be used as a
textbook for research-oriented students in the social, biological and
medical, and physical and engineering sciences. As well, its
mathematical emphasis makes it ideal for a text in mathematics and
statistics courses. With its numerous worked examples, it is also
ideally suited to be a reference book for all scientists.
