Appendix 15a

15A.1 MAXIMUM LIKELIHOOD ESTIMATION OF THE LOGIT AND PROBIT MODELS FOR INDIVIDUAL (UNGROUPED) DATA*

As in the text, assume that we are interested in estimating the probability that an individual owns a house, given the individual's income X. We assume that this probability can be expressed by the logistic function (15.5.2), which is reproduced below for convenience.

We do not actually observe Pi, but only observe the outcome Y = 1, if an individual owns a house, and Y = 0, if the individual does not own a house. Since each Y, is a Bernoulli random variable, we can write

The following discussion leans heavily on John Neter, Michael H. Kutner, Christopher J. Nachsteim, and William Wasserman, Applied Linear Statistical Models, 4th ed., Irwin, 1996, pp. 573-574.

634 PART THREE: TOPICS IN ECONOMETRICS

Suppose we have a random sample of n observations. Letting fi(Y) denote the probability that Yi = 1 or 0, the joint probability of observing the n Y values, i.e., f (Y1, Y2,..., Yn) is given as:

n f (Yi, Y2,..., Yn) = n fi(Yi) = n PY(1 - Pi)1-Yi (4)

Was this article helpful?

0 0
Rules Of The Rich And Wealthy

Rules Of The Rich And Wealthy

Learning About The Rules Of The Rich And Wealthy Can Have Amazing Benefits For Your Life And Success. Discover the hidden rules and beat the rich at their own game. The general population has a love / hate kinship with riches. They resent those who have it, but spend their total lives attempting to get it for themselves. The reason an immense majority of individuals never accumulate a substantial savings is because they don't comprehend the nature of money or how it works.

Get My Free Ebook


Post a comment