Abstract In the optimal design literature for paired comparison choice experiments it has been proposed that respondent heterogeneity can be modelled by introducing fixed block effects into the linear predictor of the multinomial logit model and D -optimal utility-neutral designs for the modified version of the model have been derived by orthogonally blocking D -optimal utility-neutral designs for the model without block effects. In this paper, we first discuss the proper interpretation of the block effects showing that they only explain a special and non-standard type of respondent heterogeneity which refers to the order in which the alternatives in each pair are presented. Secondly, for the special case of the choice model with block effects in which the main effects of K two-level attributes are to be estimated we show how by using a previously unnoticed relationship with blocked two-level main effects plans for the linear 2 K factorial model new designs for choice experiments can be constructed. These designs are usually non-orthogonally blocked and locally D -optimal in a certain subclass of designs.

中文翻译：

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配对比较选择实验中区块效应的意义及与区块2K主效应计划的关系

摘要 在配对比较选择实验的优化设计文献中，已经提出可以通过将固定块效应引入多项 logit 模型的线性预测变量和模型修改版本的 D 最优效用中性设计来模拟受访者异质性。已经通过正交分块 D -最优效用中性设计为模型推导出无分块效应。在本文中，我们首先讨论了块效应的正确解释，表明它们仅解释了一种特殊且非标准类型的受访者异质性，即每对替代方案的出现顺序。第二，对于具有块效应的选择模型的特殊情况，其中要估计 K 个两水平属性的主效应，我们展示了如何使用先前未被注意到的关系与线性 2 K 因子模型的块状两水平主效应计划可以构建用于选择实验的新设计。这些设计在设计的某个子类中通常是非正交阻塞和局部 D 最优的。