To all who have helped me on the previous thread thank you very much. I am reposting this beause the question has become more focused.
I am studying a stochastic Markov process and using a maximum likelihood technique to fit observed data to theoretical models. As a first step I am using a Monte Carlo technique to generate simulated data from a known model to see if my fitting method is acurate. In particular I want to know if I can use this techniques to dtermine the number of free parameters in the Markov Model. I have been using the Log(Likelihood) method which seems to be widely acceted. I am getting very small Log(Likelihood ratios) in cases when I know the more complex model is correct (i.e. H0 should be rejected). When I first observed this I tried increasing the N values, and found a decrease rather than an increase in the Log(Likelihood ratio). I now think I know why. I am posting in hopes of finding out if my proposed solution is 1)statistical heracy, 2)so obvious that I should have realized it 6 months ago, or 3)a plausible idea in need of validation. The likelihood fuction I have been using up to now which I will call the FULL likelihood function is: L= (1/Sqrt( | CV-Matrix |))*exp((-1/2)*(O-E).(CV-Matrix^-1).(O-E)) Where | CV-Matrix | is the determinant of the Covariance matrix, (O) is the vector of observed values in time order and (E) is the vector of the values predicted by the Markov model for the corresponding times. The Covariance matrix is generated by the Markov model. IN A NUTSHELL: It appears that the factor (1/Sqrt( | CV-Matrix |)) is the source of the problem. In many MLE discriptions this is a constant and drops out. In my case there is a big difference between the (1/Sqrt( | CV-Matrix |)) for different models (several log units). I believe this may be biasing the fit in some way. MY PROPOSAL: I have begun fitting my data to the follwing simplified likelihood formula: L= exp((-1/2)*(O-E).(CV-Matrix^-1).(O-E)). Does this seem reasonable? Thanks for any insight James Celentano ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================