We look into high school students’ college preferences. In order to achieve this, we use the empirical data, students’ decision behavior throughout the application process for schools, and estimate the parameters of the utility model by maximum likelihood estimation. Due to the fact that every student considers a variety of options when making a decision, the empirical data is nonidentical, which complicates the likelihood function. In our research, we need to estimate more than 2300 parameters from the large and nonidentical samples (240000 students). I find that by assessing the scoring function and hessian function of the utility model in analytical form, one can greatly reduce the computation time of the Fisher scoring algorithm from two months to two minutes.