By Scott Menard
Emphasizing the parallels among linear and logistic regression, Scott Menard explores logistic regression research and demonstrates its usefulness in examining dichotomous, polytomous nominal, and polytomous ordinal established variables. The ebook is geared toward readers with a historical past in bivariate and a number of linear regression.
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Extra info for Applied Logistic Regression Analysis (Quantitative Applications in the Social Sciences)
All of this is done by means of computer-implemented numerical algorithms designed to search for and identify the best set of parameters to maximize the log-likelihood function. 7 When the assumptions of OLS Page 14 regression are met, however, the OLS estimates for the linear regression coefficients are identical to the estimates one would obtain using maximum likelihood estimation (Eliason, 1993, pp. 13-18). OLS estimation is in this sense a special case of maximum likelihood estimation, one in which it is possible to calculate a solution directly, without iteration.
It appears that the relationship between frequency of marijuana use and both of the predictors considered so far is substantively nonlinear, but we are still able to use a formally linear model to describe those relationships, and we are still able to use OLS to estimate the parameters of the model. Page 12 Probabilities, Odds, Odds Ratios, and the Logit Transformation for Dichotomous Dependent Variables As noted earlier, for a dichotomous dependent variable, the numerical value of the variable is arbitrary, a matter of convenience, and is not intrinsically interesting.
It is necessary in interpreting the results to consider the actual values of the dependent and independent variables. The intercept indicates that for an individual with zero as the value of exposure to delinquent friends, the frequency of marijuana use would be negative. This seemingly impossible result occurs because exposure, as noted above, is measured on a scale that ranges from a minimum of 8 (no exposure at all; none of one's friends involved in any of 8 delinquent activities) to 40 (extensive exposure; all of one's friends involved in all of 8 delinquent activities).