Subjective perceptions and attitudes are usually measured by administering questionnaires with ordered response scales. Among them, a particular case are semantic differential scales, where the respondent has to declare his/her position between two bipolar adjectives. To model ordinal variables measured on semantic differential scales, a novel model is introduced as an extension in the framework of the CUB (Combination of discrete Uniform and shifted Binomial random variables) class of models. The proposed model addresses the analysis of ordinal variables measured on semantic differential scales. However, it is definitely well suited to all the rating scales that have a middle option that means indifference between two extremes. This is a circumstance that occurs in the main part of the most commonly used Likert scales. The proposal is based on a mixture of a discrete Uniform and a - linearly transformed - Multinomial random variable, so it is called CUM. Parameter estimation is carried out using the expectation-maximization algorithm, and the parameters can be represented in a triangular space with a ternary plot. A simulation study is carried out and, finally, applications on real data are examined in order to show limits and potentialities of the proposal.

主观感知和态度通常通过使用有序响应量表进行问卷调查来衡量。其中，一个特殊情况是语义差异量表，其中被访者必须声明他/她在两个双极形容词之间的位置。为了对在语义差异尺度上测量的序数变量进行建模，引入了一种新模型作为 CUB（离散均匀和移位二项式随机变量的组合）类模型的框架中的扩展。所提出的模型解决了在语义差异量表上测量的序数变量的分析。但是，它绝对适合所有具有中间选项的评级量表，这意味着两个极端之间的差异。这是最常用的李克特量表的主要部分出现的情况。该提议基于离散 Uniform 和 - 线性变换 - 多项式随机变量的混合，因此称为 CUM。使用期望最大化算法进行参数估计，并且可以在具有三元图的三角形空间中表示参数。进行了模拟研究，最后对真实数据的应用进行了检查，以显示该提案的局限性和潜力。