Correlations among responses to a forced-choice scale

I have data from participants who rate emotional content of pictures. Specifically, people see 20 pictures of abstract paintings (one at a time) and are asked, "what emotions is expressed in the picture?" There are 5 response options: anger, fear, sadness, happiness, and none. The key info here is that for each picture people choose only one of the emotion choices. I then add number of pictures rated as expressing anger, fear, sadness etc. and have 5 continuous variables. The 5 continuous variable are obviously not independent because if someone rated X pictures as expressing anger and Y as expressing happiness, then they could not choose more than 20-(X+Y) pictures as expressing fear or sadness; hence the variables have negative correlations. My question is, how can I examine correlations among these responses (emotions) if they are not independent of one another? Secondary question: how can I examine internal consistency of such forced-choice scale?
I really appreciate your time and any help in this regard,


Less is more. Stay pure. Stay poor.
Unsure what you are describing by saying that you add number of pictures rated and now have 5 continuous variables. You may what to add more information how you are rating/scoring these.
If a person rates 3 pictures as expressing anger, than he/she would receive a score of 3 on the 'anger' variable; similarly, if he/she rates 5 pictures as expressing fear, the person would get a score of 5 on the 'fear' variable; same for the other responses (sadness, happiness, and none). So in the end, I would have 5 variables (anger, fear, sadness, happiness, and none), each representing the number of pictures rated by participants as expressing the corresponding emotion. However, while the raw data are comprised of categorical responses, the 5 new variables are continuous.


TS Contributor
Tha fact that the variable are not independent does not affect the correlations. In fact, you usually calculate correlations as part of a procedure to verify whether they are independent or not.

Regarding internal consistency I think you could use Cronbach's Alpha for the continous variables. The wy I see it you have 5 categorical variables (not continous), where each variable can have a value between 0 and 20 (If they only see 20 pictures, the maximum number of "anger" pictures would be 20, the same for the other categories). BEcause of this, your continuous variables all use the same scale. So, I don't think that there should be any problems by using Cronbach's Alpha. In fact, this number could tell you if some of the variables are too highly correlated, meaning that your probably are measuring the same thing twice.