lec6 - VI. Logistic Regression An event occurs or doesnt. A...

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Unformatted text preview: VI. Logistic Regression An event occurs or doesnt. A category applies to an observation or doesnt. A student passes or fails. A patient survives or dies. A candidate wins or loses. A person is poor or not poor. A person is a citizen or not. These are examples of categorical data. They are also examples of binary discrete phenomena. Binary discrete phenomena usually take the form of a dichotomous indicator, or dummy, variable. Its best to code binary discrete phenomena 0/1 so that the mean of the dummy variable equals the proportion of cases with a value of 1, & can be interpreted as a probability: e.g., mean of female=.545 (=samples probability of being female). Heres what were going to figure out how to interpret: . logit hsci read math female, or nolog Logit estimates Number of obs = 200 LR chi2(3) = 60.07 Prob > chi2 = 0.0000 Log likelihood = -79.013272 Pseudo R2 = 0.2754------------------------------------------------------------------------------ hsci | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- read | 1.073376 .0274368 2.77 0.006 1.020926 1.128521 math | 1.10315 .0316097 3.43 0.001 1.042904 1.166877 female | .3380283 .1389325 -2.64 0.008 .1510434 .7564918------------------------------------------------------------------------------ OLS regression encounters serious problems in dealing with a binary dependent variable: OLSs explanatory variable coefficients can extend to positive or negative infinity, but binary probabilities & proportions cant exceed 1 or fall below 0. OLS is premised on linearity, but with a binary dependent variable the effects of an explanatory variable are non-linear at the binary variables lower & upper levels. (3) OLS is also premised on additivity, but with a binary outcome variable an explanatory variables effect depends on the relative effects of the other variables: if, say, one explanatory variable pushes the probability of the binary outcome variable near 0 or near 1, then the...
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This note was uploaded on 07/11/2011 for the course SYA 6306 taught by Professor Tardanico during the Spring '09 term at FIU.

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lec6 - VI. Logistic Regression An event occurs or doesnt. A...

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