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
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