Hi,
I have some confusion as to which one is better for outcomes as a model using binomial regression or logistic regression. currently i am working on judicial decisions, outcomes in tax courts where the cases go either in favour of assessee or the taxman. The factors influencing the judges as reflected in the cases are duly represented by presence(1) or absence (0) of the same. If a factor is not considered in final judgment it takes '0' else '1'. if outcome is favourable to assessee - it is '1' else'0' - now which would be the best approach to put this into a regression model showing relationhip between outcome (dependant) and independent ( factors - may be 5-6 variables). I need some guidance on this . can i use any other better model for forecast after i can perform a bootstrap run for say 1000 simulations and then arrive average outcomes and related statistics.
It depends: if the Judges (dependent) are counts you need Poisson or Binomial, if the dep. var is 0-1 the logistic
In the case of presence(1) or absence (0), the dependent variable is dichotomous. You can use logistic regression.
In your case, the appropriate choice would be logistic regression rather than binomial regression. Logistic regression is specifically designed for binary outcomes, which seems to align with your scenario where the judicial decisions can go either in favor of the assessee (1) or the taxman (0).
Logistic regression models the probability of a binary outcome, and it's well-suited for situations where the dependent variable is categorical and has two possible outcomes. Binomial regression, on the other hand, is a more general term that can encompass logistic regression as a special case, but it's not the same thing. Logistic regression is a type of binomial regression.
Given that you have a binary outcome and you want to model the relationship between this outcome and several independent variables (factors), logistic regression would be the more appropriate choice.
As for incorporating bootstrapping for more robust estimates, that's a good approach. By running simulations and generating multiple bootstrap samples, you can assess the stability of your model and obtain more reliable estimates of model parameters. This can be especially helpful when dealing with a limited number of observations.
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