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I am going to model a response variable with multiple outcomes, e.g. clear, cloudy, rainy, snowy, and windy, on a set of explanatory variables. However I cannot simply use multinomial regression (or similar models) because the response variable is actually not one variable, since it can be, for example clear and windy at the same time. There are many other possible combinations of two outcomes. I do not want to make a response variable with a lot of levels (clear and windy, cloudy and windy, rainy and windy, snowy and windy, cloudy and rainy, cloudy and snowy, etc.) since it will not be useful. One option is to estimate binary response models for each outcome, which I am also not convenient with as I feel it will not capture the fact the these outcomes are occurring at the same time. I ran into a topic in categorical data analysis book by Bilder, called "Choose all that apply" data. But the model he introduces does not exactly cover my case, I guess. What kind of model do you recommend that captures this characteristic in my response variable?

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I would recode the data to accomodate for the fact that one observation can belong into multiple groups. If for example one day is classified as cloudy and windy I would double the entry (predictive variables) but would label one entry as cloudy and the other as windy. If one day has three different classifications I would triple the entry etc. In this case you will have some points that occupy the same place in variable space (multiplied entries) but will belong to different groups. This is not a problem but a feature of your data but it will result in less clear discrimination.

You can then use discriminant analysis or multinomial logistic regression as usual.

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  • $\begingroup$ I actually am familiar with Discriminant Analysis and have worked with lda() function in R. However, I don't understand why you think DA will work here and multinomial regression do not. As far as I understand, they both have the same issue of presence of multiple response variables. Don't you mean I use DA separately for each response variable and then look at the results together? I also am not sure how the results of DA (the b's in the linear discriminant rule) are as interpretable as the coefficients of multinomial regression. Can you explain more how I can implement what you said? $\endgroup$
    – Fred
    Apr 14 '17 at 4:01
  • $\begingroup$ I think both will work. The main suggestion is to recode the variables as I proposed. With this you keep the number of categories small and account for the fact that they often appear together. I wrote about DA because you might like it. $\endgroup$
    – Vivaldi
    Apr 14 '17 at 8:17
  • $\begingroup$ I edited the questio . Kind regards! $\endgroup$
    – Vivaldi
    Apr 14 '17 at 8:22
  • $\begingroup$ So @Fred, how did the suggestion work out? $\endgroup$
    – Vivaldi
    Apr 21 '17 at 14:00
  • $\begingroup$ It actually worked very well. I recoded the data and made a number of response variables and estimated a number of models (multinoimal regression and mixed logit) and the results are logical and satisfying. Thank you again and thank you for following up. $\endgroup$
    – Fred
    Apr 21 '17 at 19:12

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