Logistic Analysis

Odds Ratio and Logistic Regression

One consideration in logistic analysis involves the issue of the nature of prediction and how to examine the improvement in estimation. For example, in a random world where the outcomes are equally likely, the odds of male or female as a writer of any text or passage would be 50%. One way to measure the effect of any improvement in prediction is to consider whether the accuracy rate is greater than 50% when using some variable or set of variables to improve predictability. So, the baseline probability of correct classification due to random change starts at 50% (assuming that 50% of the writing is generated by each gender). Predictors only become useful when the percentage of accuracy increases beyond 50%. The value of the equation that incorporates predictors must be evaluated against that random benchmark to determine whether the application of the equation provides a measured improvement.

When the outcome is not equally likely, then the outcome is measured against a random probability involving the baseline outcome. For example, suppose in the sample of writing, the number of female writers was 75% and the number of male writers accounted for 25% of the authors. The baseline for this outcome then becomes not 50/50 but instead 75/25 in terms of gender. What the logistic regression or odds ratio measures is the departure from accuracy using those values. The reason that this becomes important is that if one guessed in the 75/25 baseline that the writer was female in all examples, the accuracy rate would be 75%. The 75% represents the base accuracy for predicting female outcomes and the accuracy is only 25% if predicting a male author. For this example, we assume that the text is equally probable (in terms of a random chance prediction) at 50%.

...