Regression of proportions

Modeling
5

Thanks,

I am using beta regression, inspired by your message

data { 
	int P;
  int<lower=1> S; 
	int R;
  matrix<lower=0,upper=1>[P,S] y; 
  matrix[S,R] x; 
} 
parameters { 
  real<lower=0> phi; 
  matrix[P,R] alpha; 
} 
model { 

    matrix[P,S] mu; 
    mu = inv_logit( alpha * x'); 
    to_vector(y) ~ beta(to_vector(mu) * phi, (1 - to_vector(mu)) * phi); 

}

Indeed it fails to converge for components of the multiple correlation with little slope

image
image.jpg900×893 139 KB

And it converge if I force the phi (error) parameter bigger than a threshold, then all the proportion predictions are kind of squeezed around the convergence function