# Which analytic strategy is the best for discrete dependent variable?

I would like to model the number of options chosen by participants (e.g. number of tasks) to see the effects of a prime (high vs low) and several possible moderators (including an interaction).

My question is which analytic strategy would be the best for the data (e.g. ordinal, poisson regression). My problem is that the DV is non-normally distributed, not continous, not ordinal and not categorical, and bound (0 lowest value, 4 highest).

As far as I understand, multiple linear regression assumes a continuous response variable. So that would mean that my dv (whole integers in a small range 0-4) would violate this assumption. Thus, I was thinking, it would be better to use a poisson regression. However, since my data is bound by 0 and 4, I'm also not sure whether this would be a good option. As my last option, I was considering ordinal regression. But since my dv is not really ordinal, this would be also not perfect.

• DV= number of tasks (0-4)
• IV1= prime (high vs. low)
• IV2= continuous scale
• interaction= IV1*IV2
• Do you really only care about the number of tasks they choose? If these tasks differ in any way, then you would ideally model the probability of each of them being chosen separately, and only then would you try and predict how the total varies. – zipzapboing Jun 7 '18 at 18:22
• @zipzapboing yes, our main dv is how many tasks they choose. However, the models you describe also sounds like a good idea. So you would basically suggest to use logistic regression to model the probability of each task being chosen and then integrate it into a model of how the total varies? How could I perform the last step? Is there a way to do that in SPSS or R? – jonani Jun 8 '18 at 12:18
• You could do separate logistic regressions for each choice. This would, however, assume that the choice of one task is fully explained by your covariates i.e. whether I choose task 1 has no bearing on my propensity to choose any other task. This might not accurately describe the situation you're trying to model. On the other hand, if you think the amount of tasks chosen is more important than a specific one, you should use multinomial regression. This will distinguish between choosing n tasks but it won't care exactly which ones are chosen at each point. R can do both. – zipzapboing Jun 8 '18 at 17:12

Sounds like a good model for your dependent variable is a binomial distribution; the number of successes out of $k$ (in your case 4) trials. Once the number of trials is fixed, there is only one parameter left: the chance of success in a single trial. There are regression models for that, that basically model that chance of succes in a single trial as depending on explanatory variables. Whether such a model has been implemented in SPSS I don't know.