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21For a comparatively simple discussion of maximum likelihood in the context of the logit model, see John Aldrich and Forrest Nelson, op. cit., pp. 49-54. See also, Alfred Demarsi, Logit Modeling: Practical Applications, Sage Publications, Newbury Park, Calif., 1992.

22From elementary statistics recall that the probability of an event is the limit of the relative frequency as the sample size becomes infinitely large.

21For a comparatively simple discussion of maximum likelihood in the context of the logit model, see John Aldrich and Forrest Nelson, op. cit., pp. 49-54. See also, Alfred Demarsi, Logit Modeling: Practical Applications, Sage Publications, Newbury Park, Calif., 1992.

22From elementary statistics recall that the probability of an event is the limit of the relative frequency as the sample size becomes infinitely large.

Gujarati: Basic I III. Topics in Econometrics I 15. Qualitative Response I I © The McGraw-Hill

Econometrics, Fourth Regression Models Companies, 2004

Edition

CHAPTER FIFTEEN: QUALITATIVE RESPONSE REGRESSION MODELS 599

which will be a fairly good estimate of the true logit Li if the number of observations Ni at each Xi is reasonably large.

In short, given the grouped or replicated data, such as Table 15.4, one can obtain the data on the dependent variable, the logits, to estimate the model (15.6.1). Can we then apply OLS to (15.6.3) and estimate the parameters in the usual fashion? The answer is, not quite, since we have not yet said anything about the properties of the stochastic disturbance term. It can be shown that if Ni is fairly large and if each observation in a given income class Xi is distributed independently as a binomial variable, then

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