**Re: Binomial regression with x as the dependent variable and n as an independent vari**
I don't quite understand this constraint you want to impose. Are your data going to be like (1 for success; 0 not):

Code:

```
1st 2nd
0 0
1 0
1 1
0 0
1 0
1 1
```

Or might you have

Code:

```
1st 2nd
0 1
1 0
1 1
0 0
1 0
1 1
```

The second has successes in the 2nd stage while not successes in the 1st. The first example has 2nd stage 0's where there are 1st stage 0's. If it is like the first stage, then the constraint you want is implicit in the data, and no constraint on the model is necessary. If your data is like the second, I have to wonder why you would want to constrain your model. That would impose a constraint that doesn't reflect the data (phenomena) you observe. The easy solution would be to simply remove those observations where you have a (0, 1) pair between your 1st and 2nd stages. Then your data is prepared for the model you want to use without having to impose the constraint on the model. However, it has to be stated clearly that you've imposed that constraint on your data.

Edit: The above comment follows my thoughts on how to model this. Just do a logistic regression using the data as-is, checking if one is a successful predictor of the other. Sometimes sometimes you'll have success/failure pairs of (0, 0), (0, 1), (1, 0), or (1, 1), but the number of 1's in either the first or second stage shouldn't matter. If it is something unattainable from the process that generated it, then it's even more queer that you would have impossible data. Hence, why I wonder why you need this constraint at all.