Valid Randomization for Models with Neighbour Effects From Treatments

Valid methods of randomization have been proposed for several classes of neighbour-balanced designs, but the assumed models did not include the neighbour effects from treatments. We present sufficient conditions for such randomizations to be also valid for direct and neighbour effects simultaneously. It is shown through several examples that these sufficient conditions can be satisfied for uni- or bi-directional neighbour effects, provided a particular block structure is used. The covariance between estimators of direct and neighbour effects over the randomization is also studied.