Hi,
I am estimating a random effects logit model with panel data and I want to calculate McKelvey-Zavoina Pseudo R2. Genereally, I would calculate the R2 in this manner: After the xtlogit command, i would estimate:

predict Xb_ori, xb
sum Xb_ori
return list
gen R2MZ = r(Var)/(r(Var) + _pi^2/3)
sum R2MZ

I have learned that this calculation only estimates the within variance, and thus shows how much of the within variance can be explained by the regression of y on x. Thus, when adding time constant variables, the residual variance will not decrease.

However, I have also looked at the two stata ados meresc and r2_mz and they both calculate the McKelvey-Zavoina R2differently for xtmelogit,xtlogit,xtprobit. Instead of setting the variance of the level 1 random effect zero, as the calculation above does, they calcualte a value for e(Var_u1) - the variance of the level 1 - random effect and add that to the denominator:

// Random effects variance (for McKelvey-Zavoina R2)
// -------------------------------------------------

if inlist("`e(cmd)'","xtmelogit","xtlogit","xtprobit" ) {
mata: r2_mz_var_u()
}
else {
sca `Var_ut' = 0
}
predict double `Xb_ori', xb
sum `Xb_ori'
drop `Xb_ori'
scalar `R2_MZ' = r(Var)/(`Var_ut' + `Var_R' + r(Var))

}

With Var_R defined in the ado as _pi^2/3

Do I understand it correctly, that this way of calculating the Pseudo R2 shows how much of the within and between variance can be explained by the regression of y on x? Because know, when adding time constant variables, the residual variance will decrease?

Would it be generally recommended to report the calculation of the ados, and if yes, why?