Model with Interval and Categorical Independant and Dependant Variables

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I need help with creating a model in R/choosing the right analysis.

I work for a program that trains unemployed people and eventually finds them jobs. However, we have found that many participants quit their jobs or are fired (both referred to as a negative termination) soon after beginning. I have been assigned to create a model that helps predict what factors cause these outcomes.

The model will have to be fairly complex due to the number and variety of variables. Ideally, it will take into account:

DVs - termination type (categorical) - time employed (interval)

IVs - barriers (probably 3 binary categorical variables) - number of trainings completed (interval) - percent assigned trainings completed (interval) - age (interval) - gender (binary categorical) - race/ethnicity (categorical)

I have researched various methods of analysis (particularly regression), but have yet to find one that can handle all the bases I need to cover in terms of variable diversity. I am working in R, so I would appreciate any responses to mention relevant packages or code.

Thanks so much!

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