Abstract: The information matrix of a sequence of independent experiments is the sum of their information matrices but the value taken on that sequence by the real valued measures of the information based on that matrix is not the sum of the values they take on the individual experiments. Nevertheless, when information is measured through the determinant of the information matrix and one observes a response that can be modeled through a generalized linear model, a different type of additivity holds. Here, that property is stated in its full generality, and it is used to obtain the determinant of the information matrix for any two-level generalized linear experiment. That allows us to explore how the information in two-level factorial experiments depends on the location of their center point and on their range for linear normal, log-linear Poisson and logistic and probit binary response models. That property is also used to explore the effect of the addition of one support point on the information in the experiment.
Keywords: D-optimality, optimal design, two-level experiments, two-level factorial, generalized linear model, log-linear Poisson model, logistic model
