Omnibus Test - Omnibus Tests in Logistic Regression

Omnibus Tests in Logistic Regression

In statistics, logistic regression is a type of regression analysis used for predicting the outcome of a categorical dependant variable (with a limited number of categories) or dichotomic dependant variable based on one or more predictor variables. The probabilities describing the possible outcome of a single trial are modeled, as a function of explanatory ( independent ) variables, using a logistic function or multinomial distribution. Logistic regression measures the relationship between a categorical or dichotomic dependent variable and usually a continuous independent variable (or several), by converting the dependent variable to probability scores. The probabilities can be retrieved using the logistic function or the multinomial distribution, while those probabilities, like in probability theory, takes on values between zero and one:

So the model tested can be defined by:

<

,whereas y_i is the category of the dependant variable for the i-th observation and x_ij is the j independent variable (j=1,2,...k) fot that observation, β_j is the j-th coefficient of x_ij and indicates its influence on and expected from the fitted model .

Note: independent variables in logistic regression can also be continuous.