a Faculty of Psychology , University of Barcelona.
b Department of Mathematical Sciences , University of Exeter.
Multivariate Behav Res. 2007 Apr-Jun;42(2):323-47. doi: 10.1080/00273170701360555.
The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification constraints can recover any true utilities' covariance matrix, but it is not unique. Indeed, we show how to transform the estimated correlation matrix into alternative correlation matrices that are equally consistent with the data but may be more consistent with substantive theory. Also, we show how researchers can investigate the sample size needed to estimate a particular model by exploiting the simulation capabilities of a popular structural equation modeling statistical package.
由于数据的比较性质，证明了对无约束效用协方差矩阵的 Thurstonian 模型进行解释是困难的。我们表明，在适当的约束下，可以估计效用相关矩阵，从而得到一个易于解释的解。这组识别约束可以恢复任何真实的效用协方差矩阵，但它不是唯一的。事实上，我们展示了如何将估计的相关矩阵转换为其他相关矩阵，这些矩阵与数据同样一致，但可能更符合实质性理论。此外，我们还展示了研究人员如何利用流行的结构方程建模统计软件包的模拟功能来研究估计特定模型所需的样本量。
