Coming back to degrees of freedom for chi squared, I have found a wonderful answer here: How to understand degrees of freedom?
However it is hard for me to apply it to my particular case. Let's say we observed counts of objects of 3 types:
A B C 35 121 344
The model, which has only one parameter, p, says that we should observe these objects with frequencies 0.01, 0.3, 0.69, which are some non-linear functions of p, let's say f(p), h(p), t(p). Given these frequencies, calculated using our model parameter p, we calculate expected counts and chi square statistic.
Question: how many degrees of freedom for chi square distribution should we use in this case?