Besides Maximum Likelihood Estimation of the Logit and Probit Model

question 46

Essay

Besides maximum likelihood estimation of the logit and probit model, your textbook mentions that the model can also be estimated by nonlinear least squares. Construct the sum of squared prediction mistakes and suggest how computer algorithms go about finding the coefficient values that minimize the function. You may want to use an analogy where you place yourself into a mountain range at night with a flashlight shining at your feet. Your task is to find the lowest point in the valley. You have two choices to make: the direction you are walking in and the step length. Describe how you will proceed to find the bottom of the valley. Once you find the lowest point, is there any guarantee that this is the lowest point of all valleys? What should you do to assure this?

---

Definitions:

Poisson Distribution

A statistical probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event.

Negative Exponential Distribution

A probability distribution used to model time between independent events that occur at a constant average rate.

Average Arrival Rate

The average rate at which entities (such as customers or products) arrive at a specific point or system over a defined period.

M/D/1

A notation in queue theory representing a system with a single server, where arrivals are Markovian (Poisson process), service times are deterministically fixed, and there is one server.