Predict best action sequence for dataset of debt observations

Question

I need some suggestions of general predicting practice in the following case: I have a dataset of debt observations; there are ~8 variables defining each debtor situation (debt details and person details), quantitative and qualitative. The Debt Management applied for each person a sequence of actions (there are a few types of actions, each of different cost and different average effectiveness). The results I have in use consist of 2-elem vector:

[agreement, success_in_court]

• agreement is of 1/0 value, stands for reaching an agreement with debtor or not
• success_in_court is of 1/0 value, stands for reaching success in court in case this action (to sue a debtor) was applied by the Debt Management

Logically, no more than one element of a "response vector" may be of value 1. The point is to predict the most profitable sequence of action for future debtors. What methods should I use? It sould be implemented in R.

Answer 1

To answer the question, I am assuming that the variables you have in the data are like this. Each observation is one debt. The dependent variables are the two you mention. The independent variables are of two types. One type are characteristics of the debt and/or the debtor. Another type are descriptions of what sequence of actions was taken.

Then the research question is "How do the sequence of actions and the debt/debtor characteristics determine the outcomes?" Let me know if this characterization is wrong, and I will modify my answer.

The first thing you do is to define a new variable $Y$. This new variable is going to equal 1 if (agreement==0 & success_in_court==0). It will equal 2 if (agreement==1 & success_in_court==0). It will equal 3 if (agreement==0 & success_in_court==1). I assume it never happens that both variables are equal to 1, but if that happens sometimes, then make a fourth level of $Y$.

Now, collect together the characteristics of the debt/debtor, actions taken, and interactions among these in a vector of independent variables $X_i$. To model the probability of the three outcomes, I would use multinomial logit: \begin{align} P\{Y_i=k|X_i\} &= \frac{exp(X_i\beta_k)}{\sum_{k'=1}^K exp(X_i\beta_{k'})} \end{align}

This model can be estimated in R using the mlogit package, here.

A great deal more could be said about this, of course. All the usual concerns about endogeneity arise in these models as in other models. There are additional concerns about the assumptions multinomial logit puts on the correlations among the different possible outcomes. You have to be careful in calculating the marginal effects of each $X$ on the probabilities of the various outcomes.