Instead of maximising the log-likelihood via the Newton-Raphson algorithm in order to perform the hypothesis testing that "beta_i=0" we use the score test. This is dramatcially faster as no model need to be fitted. The first derivative of the log-likelihood is known in closed form and under the null hypothesis the fitted values are all equal to the mean of the response variable y. The test is not the same as the likelihood ratio test. It is size correct nonetheless but it is a bit less efficient and less powerful. For big sample sizes though (5000 or more) the results are the same. It is also much faster then the classical likelihood ratio test.
Authors: Michail Tsagris and Manos Papadakis