Influence on smoothness in penalized likelihood regression for binary data

Penalized likelihood is a nonparametric regression technique that can be used to estimate a mean function for binary data. This fitting procedure incorporates a penalty for roughness in the fitting function; the weight given to the penalty is controlled by a 'smoothing parameter'. As part of the fitting procedure, the optimal value of the smoothing parameter and the optimal function estimate are determined from the data. We wish to measure the sensitivity of the smoothing parameter to gross changes in the data. 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 that 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 analytical and numerical approximations for measuring sensitivity in penalized likelihood regression with binary data. These techniques have been applied to selected data sets to compute changes in the smoothing parameter resulting from changes in individual data values.