5.10 Abbott’s formula for quantal dose-response data gives the probability of response at dose d as, P

(d) = λ + (1 − λ)F(d), where λ is the probability of natural mortality, and F

(d) is a customary cdf, as used when there is no natural mortality. For this question, set F

(d) =

1/[1 + exp{a + b log(d)}].

The data below describe the mortality of aphids exposed to nicotine. Write down the likelihood based on Abbott’s formula. Evaluate the probability of natural mortality,

(a) directly, using fminsearch, and

(b) using the EM algorithm.