Mixed Effects Kernel Bernoulli Regression

For the mixed effects nonlinear Bernoulli regression, an estimating procedure of the success probability is introduced, which is based on the penalized negative log-likelihood including random effects term. The proposed procedure provides the estimates of the success probability of the response variables, where the canonical parameter is es expressed as the sum of the nonlinear function of input vectors and the random effects. The generalized cross validation function is introduced to choose optimal hyper-parameters in the procedure. Numerical studies are performed through the simulated data set and the real data set to indicate the performance of the proposed estimating procedure.