I am performing probit regressions using the glmfit code in conjunction with the probit link.
- Newey-West (1984) adjustment
In linear regressions it is common to adjust the standard errors following the procedure suggested by Newey and West. I have seen several papers on probit regressions that use the Newey-West adjustment and I would like to adjust my model as well.
Do you know how I could do this adjustment in Matlab for my probit model?
- Pseudo R-squared
One of the measures of goodness of fit is a pseudo R-squared as proposed by Estrella (1998).
Estrella R-squared = 1 - [ log L(u) / log L(c) ] ^ [ - (2 / n) * log L(c) ]
where L(u) is the maximized unconstrained log-likelihood value and L(c) the maximized constrained one (the null hypothesis says all coefficients except for the constant are equal to zero).
Theory suggests that the Estrella R-squared should not be negative in in-sample regressions (degrees of freedom etc.). However, I receive negative R-squareds which is why I assume that there might be something wrong with my distribution link and the parameters of this distribution.
I am using the following formula in Matlab (assumption: standard normal distribution):
LLU0 = sum(log(pdf('Normal',yhatU0,0,1)));
LLR0 = sum(log(pdf('Normal',yhatR0,0,1)));
Estrella0 = 1-(LLU0/LLR0)^(-(2/obsx)*LLR0);
Do you have any suggestions how I could fix this problem? How would the code look like in Matlab?