My response variable is made up by Pearson correlation coefficients, therefore it is a continuous variable between -1 and 1.
What other distribution could I use?
Or how can I transform this data to achieve normality of the model residuals? I tried log(x+1) but it did not solve the problem.
Your hypothesis is not clear: how many correlation values do you have. I do not agree with Jos in principal, but a problem is that correlation coefficients are not homoscedastic across all possible values. If you really have many coefficients and you want to use them as dependent variable, maybe a Fisher's z-transformation is useful.
But without knowing your model, useful advices are hard to give. Things you might consider: 1) In linear models, it is not about the normality of the data, but the errors (residuals) in the model, 2) a linear model might not be appropriate if the correlation coefficients should be the dependent variable, since they are bounded (1 -1), which might violate assumptions of the lm (a model could make predictions < -1 and > 1, which does not make any sense).
the SHASH and Johnson distributions are fairly flexible and worth looking into
Rafaela Vendrametto Granzotti , brute-force practical solution: why not a simple PERT distribution with a = -1, b = 0, and c = 1?
https://en.wikipedia.org/wiki/PERT_distribution
More elegant solution: assuming the variables you used to calculate your Pearson correlation coefficients are i.i.d., and each couple approximate quite well a bivariate gaussian distribution, then your correlation coefficients will follow individually a Student's t-distribution with degrees of freedom equal to n − 2; hence the overall distribution of your dependent variable will be a multivariate mixture of Student's t-distributions.
(It is quite fascinating to use a vector of Pearson correlations as a response variable, I have never heard about that before, what is the phenomenon you are analyzing?)
Diogo Borges Provete I wanted the transformation to try to achieve normality in the model residuals, which was required by the analysis I was using before. But now iIve changed the analyses and found another solution, thanks :D
I would suggest that you consider beta regression. Redo the search attached to get full details including a simple transformation that's quite like Fisher z but I think a bit easier to explain to a reviewer. Read the entire post section prior to making a decision. Best wishes David Booth