Lecture 14: More on Bioassays
We may wish to estimate the dose which corresponds to a specied value of the response probability. Suppose we have t the generalized model g() = 0 + 1 x. The dosage required to achieve a 100% death rate is x= g() 0 h(), 1
wh
Lecture 6: More on the Exponential Family
(Text Section 3.3) Recall that, when is 1-dimensional and the range of Y does not depend on , a distribution that can be written in the form fY (y; ) = expcfw_a(y)b() + c() + d(y) belongs to the 1-parameter expone
Lecture 8: More on GLMs
(Text Sections 3.1, 3.4, 3.5) We have seen in Lecture 7 that there are three components to a GLM (the distribution of Yi , the linear predictor, and the link function). Formally, there are three necessary and sucient conditions for
Lecture 4: Maximum Likelihood Estimation
(Text Section 1.6) Maximum likelihood estimation (ML estimation) is another estimation method. In the case of the linear model with errors distributed as N (0, 2 ), the ML and least-squares estimators are the same.
Lecture 3: Hypothesis Testing
(Text Sections 1.4.3 and 1.4.4, and parts of Chapter 6)
Example 1: t-test Q: Does the number of days on the market significantly affect the selling price (when all the predictor variables except list price are included in the
Lecture 1: Introduction
(Text Sections 6.1 and 6.3) Prerequisite Material Concepts of estimation, sampling distributions, and hypothesis testing Experience with t-tests, ANOVA, linear regression, chi-squared tests of independence for 2-dimensional conting
Lecture 13: More on Binary Data
Link functions for Binomial models Link = g() identity logarithmic log logistic log 1 probit 1 () log-log log( log ) complementary log( log(1 ) log-log = g 1 () e
e 1+e
() exp(e ) 1 exp(e )
Comparison of Link Functions
Logi
Lecture 9: Estimation of GLMs
(Text Section 4.3) Let Y1 , . . . , Yn be n independent samples from the exponential family distribution in canonical form fYi (yi ; i ) = expcfw_yi b(i ) + c(i ) + d(yi ), and let i g(i ) =
j=1 p
xij j ,
where i = E[Yi ]. GO
Lecture 12: Binary Data
(Text Sections 7.1-7.4) Equivalence of binary and binomial data Example: In a batch of m parts, it is observed that Zi are defective. A collection of n batches are studied, and observations Z1 , . . . , Zn are recorded. Parts are i
-Fibre Data-#Make the ordering of the Bloat levels from lowest to highest degree:
fibre$Bloat_ordered(fibre$Bloat,c("none","low","med","high")
#Note that are not going to specify the order of the Cracker levels, so SPLUS will use
#the default ordering, wh