In this exercise, fill in the gaps to our logistic regression derivation. (guide

Question

In this exercise, fill in the gaps to our logistic regression derivation. (guided practice We are given data (ai, bi) for i F 1, m individuals. Each ai ER" is a vector of variables describing the ith individual, and each bi E 10, 1 is binary outcome. We start by thinking of each bi as heads' or tails' from a coin flip, with proba- bility pi of getting heads. Think of all these coin flips as completely independent. The probability of getting bi is f (bi; pi) p (1 pi) exp(bi ln pi (1 bi) ln(1 pi)) ln(1 pi) exp biln

Explanation / Answer

e) In logistic regression, Deviance is used instead of sum of squares. The objective is to minimize the residual or error sum of squares. Suppose, there exists a saturated model, the by minimizing the deviance of estimated model and saturate model, we get best possible fit.

D = -2ln (likelihood of fitted model/likelihood of saturated model) Since saturated model is fixed, by minimizing likelihood of fitted model, we maximize f(x)

f) Essentially, we can minimize the sum of squares as established in part (e) which is actual - predicted

   biaiTx is predicted values after vector x is found. ln(1+ exp(aiTx)) is the actual values. The difference summed

   over m individuals gives residue and minimizing summation solves the regression parameters.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.