Class Notes for 20^th March

Reminder: Homework 4 on Design due on Wednesday.

Wednesday 15^th Class - leftover

· All our models so far are homoskedastic normal NLINs, but data in Ex. 2.7 show non-constant variance. Letting “rhs” denote the (mean) model function, we propose that VAR = s²*rhs^r, where r is an additional parameter to be estimated. The case where r = 0 is then constant variances across X. To test H₀: r = 0, we use Wald or LR. Wald gives t₅₅ = 1.4707/0.4699 = 3.13 and p = 0.0028. More reliable is the LR test c² = 254.0 – 245.3 = 8.7 and p = 0.0032. That Wald gives a similar p-value means quadratic approx. is good here. Regardless, we reject the null, and accept heteroskedasticity. One of the ramifications is that the SE for the LD50 drops from 0.3805 to 0.3297 (drops 13.4%).

Monday 20^th Class

· Laetisaric acid – Wald and Likelihood intervals really do differ, so use PLCI’s when available

· Huet ELISA illustrates a new way to consider dummy variables

· Curvature example – SE1 – new handout pp.4-6

· Seefeldt modeling variance example (see above)

· Return to Menarche example (generalized nonlinear e.g.)

· Return to Budworms example