Multivariate Regression - Categorical and Continuous Outputs?

Question

I am performing process characterization of a welder and want to put together a model of the inputs vs outputs of the system.

Currently I am performing individual multiple regressions with 4 inputs (all continuous numerical values) and 1 output (2 pass/fail categorical and 1 continuous numerical). There are also a few interactions in between. Is there any way to combine this into one unified model? The outputs are correlated and I want to be able to approximate settings for a Pass/Pass/0.5 sec result.

The diagram below explains the inputs vs outputs (with additional less controllable but still impactful predictors). Green are controllable inputs, Red are uncontrollable, Yellow are influenced by Green and/or Red, and Purple are outputs.

Is there any software that has functionality like this built in or will I need to create something in python? Does trying to perform a multivariate regression make sense in this application or should I look into making a neural network (less experienced with this).

Answer 1

Firstly, since Burst Timing (sec) is a numerical variable and Compression Test and Gel Fill are categorical (pass/fail), then Burst Timing as the dependent variable will need to be modelled by linear regression, and the latter two by logistic regression.

If you already have data for Weld Temperature, Load Cell Temperature, and Enclose Temperature, then it makes little sense to also include the variables that are used to derive the former, i.e. Ambient Temperature, Chiller Temperature, etc.

This will simply result in multicollinearity whereby the standard errors of these variables will be inflated, which in turn will affect the accuracy of significance tests.

Modelling using multiple dependent variables (as you are proposing) is possible if all those variables can be suitably encapsulated into one. However, this would rely on sound judgement and thus it is highly recommended to firstly build three separate regressions before attempting to model in this way - particularly as one dependent variable is numerical while the other two are categorical. Please see the following resource: Multiple Dependent Variables