Originally Posted by

**mirrormirror** Hi! I have a problem to solve:

**|y/x** **0** **1_****|**

|**0__** 5 15**|**

**|1** _10 20**_|**

Above are the observations of which a dataset consists (N=50). I hope that you can read the table: (there are 5 observations with x=0 and y=0, 15 with y=0 and x=1, etc) Both x and y are binary and I need to plug these into a logit model and find the MLE. I start out by defining the likelihood function:

L = $\displaystyle \prod_{i=1}^{50} (\frac{exp(\beta_0 +\beta _1X_i )}{1 + exp(\beta_0 +\beta _1X_i) })^{Y_i}(\frac{1}{1 + exp(\beta_0 +\beta _1X_i })^{1-Y_i}

$

After this I go on with the usual MLE-process. I take the log of the expression above, I then calculate the first derivative with respect of beta_0 and thereafter beta_1. I then maximize these expressions with respect to the actual parameter. My problem is that I don't know how to use these observations above to receive a numerical MLE. Can someone please help me with this? Thank you.