01-06-2016 07:46 AM
I recommend reading the SAS/STAT Users Guide section "Classical Estimation Principles."
Among the good information there are these statements:
The pseudo-likelihood concept is also applied when the likelihood function is intractable, but the likelihood of a related, simpler model is available.
An important difference between quasi-likelihood and pseudo-likelihood techniques is that the latter make distributional assumptions to obtain a likelihood function in the pseudo-model. Quasi-likelihood methods do not specify the distributional family.
01-06-2016 08:16 AM
To complete understanding, may I request you to give a real time examples where these likelihood estimates takes place?
01-06-2016 09:41 AM
Because the likelihood formulas involve models, distributional assumptions, and formulas, understanding an example that compares maximum likelihood to pseudo- or quasi-likelihood will involve dealing with some math.
For an example that compares fill likelihood to quasi-likleihood, see the example "Quasi-likelihood Estimation for Proportions with Unknown Distribution" Notice that the quasi-likelihood method involves assumptions about the DATA.
The pseudo-likelihood method can arises when you use a Taylor-series expansion to replace a complicated function or optimization by a simpler function, usually quadratic or linear. You then solve the simpler model. In the GLIMMIX procedure, you can use the METHOD= option to choose a pseudo-likelihood model. For the grusome details, see a reference on Generalized Mixed Models Theory.
01-07-2016 05:19 AM
In the example below, could you please tell me how to interpret Output 45.4.9?
01-07-2016 07:52 AM
By itself, Output 45.4.9 isn't very useful. It becomes useful when you compare the model to other models. This example models the variance as _mu_**2 * (1-_mu_)**2. If you run further analyses with other potential forms for the variance function, the FitStatistics tables can be compared to help you determine which quasi-likelihood model for variance describes the data best.
01-07-2016 03:16 PM
The example you picked out uses a pseudo-likelihood (PL) method (restricted subject specific pseudolikelihood to be precise) to fit a quasi-likelihood model. Think of quasi-likelihoods as the log likelihood divided by the deviance. In a PL method the deviance is partialed out of the optimization step, and then re-introduced to calculate a quasi-likelihood. Hence, it as a way of introducing overdispersion.
PL = linearization of the likelihood function, generally using a Taylor series expansion
QL = scaled likelihood, where the likelihood is divided by the deviance
I realize that this overgeneralizes what is going on, but it is how I generally think about the difference between the two.