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I have a dataset of 393 people and I am running binary logit regression. The goal of this regression is to examine which predictors are significant in predicting the dependent variable.

The dependent variable is 1 = not taking a ride with public transport after the price increase 0 = taking public transport even if the price increases. In the data 82 people said 1, 311 people said 0

The reason I am doing this regression is to answer whether different groups of people based on independent variables like (age, gender, income, etc..) and on different types of trips (based on distance, train vs bus, etc.) have different elasticities.

The model is not meant to predict.

However, when I test the predictive power of the model it gives me this table

enter image description here

meaning, a very high specificity of over 81 %, but a very low sensitivity of 15,85 %. Overall correctly predicted is almost 80 %.

If my goal is to explore whether the groups are different from each other, is this test even relevant? If so, how would you interpret those results?

If not, are there any other tests I should run, or just examining where each individual explanatory variable is significant is enough?

Thank you in advance!

vojta9
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  • If, as you said, the aim is to determine which covariates can help predict the outcome, the coefficient estimates and their standard errors are all you need.

    If you also want to test the predictive power of the model, it is better not to dichotomise the prediction. The output of your model is a probability; you presumably turned it into a binary variable (0 or 1) by looking at whether the value is >0.5 or <0.5. It is more sensible to use a scoring rule instead.

     – Doctor Milt Mar 22 '23 at 16:07
  • For a formal significance test, you can compare the null deviance to the residual deviance of your model. There's an explanation here: https://stats.stackexchange.com/questions/108995/interpreting-residual-and-null-deviance-in-glm-r – Doctor Milt Mar 22 '23 at 16:14

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