Local likelihood estimation has proven to be an effective method for
obtaining estimates of parameters that vary with a
covariate. To obtain useful estimates of such parameters, approximating
models are used. In such cases it is useful to 
consider window based estimates. We may need to choose
between competing approximating models. In this paper we propose a
modification to the methods used to motivate many information and
posterior probability criteria for the weighted likelihood case.
We derive weighted versions for two of the most widely known
criteria, namely the AIC and BIC. Via a simple modification, the 
criteria are also made useful for window span selection. The
usefulness of the weighted version of these criteria are
demonstrated through a simulation study and an 
application to three data sets.