Construction of experimental designs for mixed logit models allowing for correlation across choice observations

In each stated choice (SC) survey, there is an underlying experimental design from which the hypothetical choice situations are determined. These designs are constructed by the analyst, with several different ways of constructing these designs having been proposed in the past. Recently, there has been a move from so-called orthogonal designs to more efficient designs. Efficient designs optimize the design such that the data will lead to more reliable parameter estimates for the model under consideration. The main focus has been on the multinomial logit model, however this model is unable to take the dependency between choice situations into account, while in a stated choice survey usually multiple choice situations are presented to a single respondent. In this paper, we extend the literature by focusing on the panel mixed logit (ML) model with random parameters, which can take the above mentioned dependency into account. In deriving the analytical asymptotic variance-covariance matrix for the panel ML model, used to determine the efficiency of a design, we show that it is far more complex than the cross-sectional ML model (assuming independent choice observations). Case studies illustrate that it matters for which model the design is optimized, and that it seems that a panel ML model SC experiment needs less respondents than a cross-sectional ML experiment for the same level of reliability of the parameter estimates.