Influence on Smoothness in Penalized Likelihood Regression for Binary Data

Penalized likelihood is a nonparametric regression technique which can be used to estimate a mean function for binary data. We wish to measure the sensitivity of the smoothing parameter to gross changes in the data when the optimal value of the smoothing parameter is selected using generalized cross-validation. Since penalized likelihood curve fitting requires both a grid search to determine the optimal value of the smoothing parameter and iterative solution for each grid point, naive calculations to determine the change in the optimal value of the smoothing parameter when each data value is modified are computationally intensive and time-consuming. We have developed techniques based on mathematical and numerical approximations for measuring sensitivity in penalized likelihood regression with binary data. These techniques have been applied to selected data sets to compute change in the smoothing parameter resulting from changes in individual data values.