Question

What statistical assumptions must be met to use logistic regression?

Answer 1

solution:

Some Logistic regression assumptions that will reviewed include: dependent variable structure, observation independence, absence of multicollinearity, linearity of independent variables and log odds, and large sample size.

Logistic regression is quite different than linear regression in that it does not make several of the key assumptions that linear and general linear models (as well as other ordinary least squares algorithm based models) hold so close: (1) logistic regression does not require a linear relationship between the dependent and independent variables, (2) the error terms (residuals) do not need to be normally distributed, (3) homoscedasticity is not required, and (4) the dependent variable in logistic regression is not measured on an interval or ratio scale. However, logistic regression still shares some assumptions with linear regression, with some additions of its own. ASSUMPTION OF APPROPRIATE OUTCOME STRUCTURE To begin, one of the main assumptions of logistic regression is the appropriate structure of the outcome variable. Binary logistic regression requires the dependent variable to be binary and ordinal logistic regression requires the dependent variable to be ordinal. ASSUMPTION OF OBSERVATION INDEPENDENCE Logistic regression requires the observations to be independent of each other. In other words, the observations should not come from repeated measurements or matched data. ASSUMPTION OF THE ABSENCE OF MULTICOLLINEARITY Logistic regression requires there to be little or no multicollinearity among the independent variables. This means that the independent variables should not be too highly correlated with each other. ASSUMPTION OF LINEARITY OF INDEPENDENT VARIABLES AND LOG ODDS Logistic regression assumes linearity of independent variables and log odds. Although this analysis does not require the dependent and independent variables to be related linearly, it requires that the independent variables are linearly related to the log odds. ASSUMPTION OF A LARGE SAMPLE SIZE Finally, logistic regression typically requires a large sample size. A general guideline is that you need at minimum of 10 cases with the least frequent outcome for each independent variable in your model. For example, if you have 5 independent variables and the expected probability of your least frequent outcome is .10, then you would need a minimum sample size of 500 (10*5 / .10)