Can a contingency table be used to model probabilities?

Question

Its been a while since I did any serious statistics. I have been reading about contingency tables recently and it seems like they may offer a solution to my problem. There are people on here that know more about statistics than what I can ever expect to know, so rather than trying to "discover" things by myself, (and wasting time in the process), I decided to come here first, explain what I'm trying to do and ask the gurus here first, if it makes any sense, and second, if there is a better (and probably more simple/robust) way of achieving what I'm trying to do (highly likely I suspect).

Here is an overview of what I am trying to model:

I have a process which at any time, can be in one of N states. I have identified 4 other 'factors' that I believe are predictors of the state in which the system will be. The 'factors' are a mixture of categorical and real variables.

I am thinking of creating a multidimensional contingency table like this:

Factor1, # Dimension 1
    Factor2, # Dimension 2
        ...
            Factor4, State1  | State2  | State3  |  ... | StateN  | 

where the value in a cell is the count of the number of times that the system has been in that state given the 'levels' of the four factors.

I am hoping to use this table then to build a probabilistic model (maybe using a suitable logistic function?) to be able to answer questions of the form:

What is the probability of the system changing from state i to state j, given Factor1, .. Factor4 are at a certain specified level?

Am I able to use a contingency table to do this?

Last but not the least, I don't know if contingency tables are part of non parametric statistics - but I hope there are no strong assumptions of normality of the variables etc. If there are any strong assumptions required for the use of a contingency table, I will be grateful if someone could alert me of the fact, and hopefully suggest another method that can allow me to model the probabilities in the manner I described above.

PS: If I have fudged up any of the terms in my question, please advise so I can edit my question to make it more clear. I know that the use of 'factors' and 'levels' in my question may be a tad confusing, but I could not think of any better labels.

Answer 1

Contingency tables are used to estimate cell probabilities and to determine if there are significant differences in the discrete probability distributions for the groups being compared. These procedures do not require any parametric assumptions.

If Fisher's exact test is being used, you do assume that the other possible tables that could have occurred all have the same row and column totals. The Fisher test compares the observed table to all permutations that would lead to the same row and column totals. Under the null hypothesis that the group proportions are the same (sometimes called the independence assumption) the distribution of cell frequencies is hypergeometric.