In this dissertation, I present my work on model selection diagnostics and model combining in thecontext of longitudinal data analysis and semiparametric regression.

Of course, model selection delivers both simple interpretability and accuracte information if it is reliable.  However, if there is large amount of uncertainty involved in model selection, insisting on simple interpretability is not appropriate because it usually leads to overly optimistic or misleading results. In such a situation, a more complicated approach such as model averaging/combining should be considered.  Although model selection uncertainty has been well recognized, proper diagnostics of model selection, a key for choosing between model selection and model combining, has not been seriously studied. In this work we propose measures that characterize uncertainty in model selection from different perspectives.  BIS (bootstrap instability in selection) is a measure about selection instability using bootstrap resampling method, and PIS (perturbation instability in selection) measures the same quantity but using a data perturbation technique. We also notice that some quantities of interest are sensitive to the model selection process, others are not. BIE and PIE (bootstrap/perturbation instability in estimation) are sensible measures for the estimation instability due to selection. And SDV S and SDES (variable selection standard deviation and estimation standard deviation) are the corresponding measures for uncertainty in variable selection and in estimation with respect to a certain weighting distribution on the candidate models. In general, a high value is an indication of severe uncertainty and in such a situation model combining can be helpful to obtain more reliable results.