Approximations of the information matrix for a panel mixed logit model

Information matrices play a key role in identifying optimal designs. Panel mixed logit models are more flexible than multinomial logit models for discrete choice experiments. For panel mixed logit models, the information matrix does not have a closed-form expression and is difficult to evaluate. We propose three methods to approximate the information matrix, namely, importance sampling, Laplace approximation, and joint sampling. The three methods are compared through simulations. Since our ultimate goal is to find optimal designs, the three methods are compared on whether they rank designs similarly, not on how accurate the approximations are. Although the Laplace approximation is not as accurate as the other two methods, it can still be used to rank designs accurately and it is much faster than the other two methods. When an optimal design search using an exchange algorithm takes days to run, the Laplace approximation may be the only viable choice to use in practice.