I'm doing an assignment in R for my inference theory class and i'm a bit stuck here.
I have been given a summary of some model and im being asked to confirm that the z-value is equal to the wald statistic.
The wald statistic is according to our book:
$sqrt{I(theta_{NR)}} cdot (theta_{NR}-theta_0)$
where $theta_{NR}$ is a theta value of the regression variables which was retrieved from a Newton-Raphson function and $theta_0$ is a vector of equal length of $theta_{NR}$ which only contains zeros and $I()$ is the function for the fisher's information matrix.
Well i thought that i could write a function that calculates the fishers matrix and then simply use it in the formula for the wald statistic but it wont produce the right results. Maybe i have interpreted the formula wrong?
any ideas anyone?
the code for the fishers matrix is confirmed to be working btw! 🙂
Best Answer
Maybe you have got it already. Otherwise, check page 99 in the book (i guess we are in the same class haha), where you may find that $se(theta_{NR})=frac{1}{sqrt{I(theta_{NR})}}$. We have already calculated the standard deviation $se(theta_{NR})$ in laboration part I. So you may just take $frac{1}{se(theta_{NR})}$ and multiply it by $theta_{NR}$ to get the z-values 🙂