In binomial data modeling, we often encounter situations where the value range of p is [0, 1], while the value range of the general linear model response π¦ is (ββ, +β); there is nonlinearity between p and factor x; and the variance of p for different factor x values ββis unequal. When there are many explanatory variables, a small sample size, and uneven data distribution, fitting is prone to separation problems. Applying Firth penalized maximum likelihood estimation is a good way to solve the data separation problem. The basic idea of ββFirth penalized maximum likelihood estimation (PMLE=Penalized Maximum Likelihood Estimation) is to add a penalty term to the log-likelihood function to reduce the deviation of the maximum likelihood estimate of the parameter. The maximum likelihood estimation MLE is based on asymptotic theory and depends on the layout of each data point in the sample space; when the sample size is large and the data distribution is balanced, a more ideal result can be obtained. This video will introduce in detail how to use Firth penalized maximum likelihood estimation to solve the data separation problem in GLM through actual cases.
