# System with two Dependent Variables: One binary and one categorical with 4 categories

My data has around 5,000 clients who are admitted to treatment/recovery services. I have two Dependent Variables.

The first Dependent Variable is treatment outcome ("was the treatment successful?"), which is dichotomous categorical value of Yes or No. Here, I coded Yes as 1 and No as 0.

The Second Dependent Variable is treatment satisfaction, which are grouped in four category:

• Completed with satisfaction,
• Incomplete with satisfaction,
• Incomplete with no satisfaction,
• Others

I may re-group them in to 2 groups as Positive (completed with satisfaction, incomplete with satisfaction) and Negative (Incomplete with not satisfaction) and just discard Others.

I have multiple Independent Variables, which vary in their variable types.

To mention couple of them,

• Duration (days spent in the service) - continuous
• Locations of the medical service - categorical
• Types of the medical service - categorical
• Types of medicine they use - categorical
• First age of using the medicine - Is this categorical or continuous?

The purpose is to see whether taking the medicine at early age yields differences from those who took in later ages. Categorical or Continuous?

Applying a $\chi^2$ analysis I've found that the gender and treatment outcome/ gender and treatment response were dependent to each other. The same applies to race/ethnicity. So I want to control for gender, race, and other possible covariates.

I'd like to know whether any of those Independent Variables have effect/relationship to my two Dependent Variables. Do you recommend two different analysis for the two dependent variables?

For instance,

1. Do clients with longer duration in service tend to show unsuccessful treatment outcome and/or treatment response?
2. Do clients who started taking medicine in early age show successful treatment outcome and/or treatment response?
3. Do clients who received service from Location A shows better treatment outcome and/or and/or treatment response than those who received from Location B?

What tests do you think will be the most appropriate and effective?

Your research questions are a shoe in for regression models:

Do clients with longer duration in service tend to show unsuccessful treatment outcome and/or treatment response?

For your first binary dependent variable (treatment) you can do a logistic regression, in which you see how covariate said effect the probability of successful treatment. see this UCLA logistic tutorial. Depending on your statistical package you can also see which covariate is most important by standardizing them.

The second dependent variable is slightly trickier. You can perform an ordinal logistic regression, which works with ordered categories (which I don't think yours is), or a multinomial logistic regression which works with unordered dependent variables. See this UCLA multinomial tutorial with R (other statistical packages also available - just google it).

The question here is what exactly is this variable? I would advise caution before offhandedly merging or removing categories. If the feedback on satisfaction is the key, and complete or incomplete matters not on a theoretical level - than you can perhaps even merge (or based on he completeness, which I did not understand the meaning of in truth). But, the other category warrants extra attention. If other = unknown, than you must not merge it with other categories. Either leave it as a separate category or delete it - but it can skew your results. Try to find out more about this group doing some descriptives. Maybe you can find a pattern.

Regarding:

The purpose is to see whether taking the medicine at early age yields differences from those who took in later ages. Categorical or Continuous?

A regular continuous variable will show a linear relation where each added year adds a certain percentage to the probability of the event. Adding a polynomial (x + x^2...) can show a non linear relationship, so can any number of transformations. Like turning it to a categorical variable, it is best relying on evidence. When you plot age for different groups how does it look? Is there a big difference in the mean age for successful and unsuccessful treatment? Without one, or a strong theoretical reason I wouldn't categorize it.