From what I understand, maximum likelihood is used to estimate a parameter alpha in a way that maximizes the probability P(Y=|x,alpha) for example. It is used for logistic regression in order to get better estimation. I'm using weka and I read that, without the user making an explicit choice, the maximum likelihood algorithm is used.
Further reading led me to the subject of goodness-of-fit and more precisely Hosmer–Lemeshow test, and it was defined as a method to estimate "the best fit value of unknown parameters".
So here are my questions: are both maximum likelihood and goodness-of-fir tests meant for the same thing? if not what is the difference between the two? if they are meant for the same reason can maximum likelihood be considered a subfamily of the goodness-of-fit tests?