I hope I got the right subforum! I would really appreciate if someone takes the time to help me and guide me into th right direction.

Generally, I am trying to calculate correlation coefficients (best case even Pearson r) of several independent variables on one single dependent variable. I am looking at several studies, where some use Likert scales for the measurement of the independent variables, others use agreement statements.

Several motivational factors are the independent variables; [the likelihood of] participation is the dependent. The problem is, that for some studies, the data was collected on a basis of people who were participating anyway. i.e. the binary dependent variable is 1(=did participate) for all subjects. Those are all individual observations (i.e. a cross section of individuals) by the way.

I want to know which factor influences the likelyhood of participation the most. I am looking at many studies though and I want to transform the data into a comparable and aggregatable format. (I am just dealing with a constant dependent variable for some of those studies).

Going the normal way, the correlation equals zero, as no matter what they answered to the questions (e.g. "I participate because I want to earn money"), the subjects all participated anyway.

I was thinking that maybe I can assume, that for the certain study, all 4 independent variables are responsible for x% of the total variance of the dependent variable. From there, I could maybe allocate fractions of x to the respective independent variables by considering the agreement level of the regarded independent variable as a fraction of the total agreement.

A short example might clarify what I am looking at:

651 participants were asked why they participated in a crowd-sourcing application. They could either agree with a statement("I participated because I...") or not agree. The results (% of participants agreeing) are the following:

71,9% Fun

79,1% Improving skills

89,8% Payment

49,8% Recognition

If I would assume that those 4 variables explain x% of the variance for the dependent variable, (estimation based on other studies concerned with the same correlations, that explicitly state that R^2) is there any way I could calculate correlation coefficients?

I would really appreciate if somebody would take the time to help me or point me towards the right direction!