Logistic Regression

Logistic regression is a statistical method to test for associations, or relationships, between variables. Like all regression analyses, logistic regression is a predictive analysis where a model is tested to find out whether the value of one variable, or the combination of values of multiple variables, can predict the value of another variable. The distinguishing feature of logistic regression is that the dependent (also called outcome or response) variable is categorical. This entry first describes the method and the concepts of causal inference and biological plausibility. It then discusses positive and negative associations and the odds ratio and provides an example of the use of logistic regression analysis to determine whether depression increases the risk of older people needing home help. The entry concludes by reviewing some assumptions and sources of error in logistic regression.

In binary logistic regression, which is the most common type of logistic regression, the dependent variable is binary or dichotomous. That means that there can only be two options for its value. For example, yes/no, pass/fail, alive/dead, satisfied/unsatisfied, and so on. In logistic regressions where there are more than two categories for the dependent variable, a less common multinomial logistic regression test is needed.

The dependent variable is the thing you are trying to explain or predict. There can be one or multiple independent (also called predictor or explanatory) variables tested in your model, and these can be either discrete variables (including dichotomous or ordinal), or they can be continuous (interval) variables. The term dependent suggests that this variable is dependent upon the status of the independent or predictor variable(s). As with all regression analyses, when there are multiple independent variables in a model, you are testing the predictive ability of each independent variable while controlling for the effects of other predictors. [Page 995]In logistic regression, the results lead to an estimation of the change in probability or odds of the outcome event occurring with a change in the value of the independent variable(s) relative to the probability or odds of the outcome event occurring given no change in the predictor variables. The results are not as easily interpreted as the results of a linear regression analysis, where the level of the outcome can be predicted from the predictor variables.

In logistic regression, the odds of the outcome of interest occurring for one unit change in the predictor variables is given in relation to the null hypothesis or equal odds. Equal odds is represented by an odds ratio value of 1.0. An increase in odds of the outcome occurring is indicated by an odds ratio value of greater than 1.0, and a decrease in the odds of the outcome occurring is indicated by an odds ratio value of less than 1.0. Statistically significant odds ratios are an indication of an association existing between the variables. The further the odds ratio number is from 1.0, the greater or stronger the association.

An example of a logistic regression inquiry can be: Does the value of x (independent variable) change the likelihood of y (dependent variable) being “yes” (rather than “no”)? For example, does eating bread crusts increase the likelihood of having curly hair (rather than straight hair)? In this case, a statistically significant odds value of greater than 1.0 would indicate that eating bread crusts does increase the chance of hair being curly.

...