D-optimal designs for multiresponse linear models with a qualitative factor

•Determinant of information matrix of a product design is separated into two parts.•The optimal marginal design is uniform on the index set of the qualitative levels.•D-optimal design for a hierarchically ordered system of multiresponses is given.

Consider a linear regression model with both quantitative and qualitative factors and an kk-dimensional response variable y whose components are equicorrelated for each observation. The D-optimal design problem is investigated when the levels of the qualitative factor interact with the quantitative factors. It is shown that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. It is also shown that for the hierarchically ordered system of regression models, the D-optimal design does not depend on the covariance matrix of y.