The Model
The model assumes that, for a binary outcome (Bernoulli trial), Y, and its associated vector of explanatory variables, X,
For this model,
and hence the vector of parameters β can be estimated using least squares. This method of fitting would be inefficient This method of fitting can be improved by adopting an iterative scheme based on weighted least squares, in which the model from the previous iteration is used to supply estimates of the conditional variances, var(Y|X=x), which would vary between observations. This approach can be related to fitting the model by maximum likelihood.
A drawback of this model for the parameter of the Bernoulli distribution is that, unless restrictions are placed on, the estimated coefficients can imply probabilities outside the unit interval . For this reason, models such as the logit model or the probit model are more commonly used.
Read more about this topic: Linear Probability Model
Famous quotes containing the word model:
“AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
—Susan Sontag (b. 1933)
“She represents the unavowed aspiration of the male human being, his potential infidelity—and infidelity of a very special kind, which would lead him to the opposite of his wife, to the “woman of wax” whom he could model at will, make and unmake in any way he wished, even unto death.”
—Marguerite Duras (b. 1914)