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:
“Research shows clearly that parents who have modeled nurturant, reassuring responses to infants’ fears and distress by soothing words and stroking gentleness have toddlers who already can stroke a crying child’s hair. Toddlers whose special adults model kindliness will even pick up a cookie dropped from a peer’s high chair and return it to the crying peer rather than eat it themselves!”
—Alice Sterling Honig (20th century)
“...that absolutely everything beloved and cherished of the bourgeoisie, the conservative, the cowardly, and the impotent—the State, family life, secular art and science—was consciously or unconsciously hostile to the religious idea, to the Church, whose innate tendency and permanent aim was the dissolution of all existing worldly orders, and the reconstitution of society after the model of the ideal, the communistic City of God.”
—Thomas Mann (1875–1955)