Inductive item tree analysis is an established method of Boolean analysis of questionnaires. By exploratory data analysis, from a binary data matrix, the method extracts logical implications between dichotomous test items. For example, assume that we have the problems $i$ and $j$ of a test that can be solved or failed by subjects. With inductive item tree analysis, an implication $i\to j$ between the items $i$ and $j$ can be uncovered, which has the interpretation ”If a subject is able to solve item $i$, then this subject is also able to solve item $j$”. Hence, in the current form of the method, solely dichotomous items are considered. In this paper, we extend this approach to the general case of polytomous items, when more than two answer categories are possible. Thus, we introduce extensions of inductive item tree analysis that can deal with nominal polytomous (including dichotomous) and ordinal polytomous, each with item-specific, answer scales. To show their usefulness, the extensions proposed in this paper are illustrated with empirical data examples.

归纳项目树分析是一种既定的问卷布尔分析方法。通过探索性数据分析，该方法从二进制数据矩阵中提取二分测试项目之间的逻辑含义。例如，假设我们有问题$\mathrm{一世}$ 和 $j$可以由受试者解决或失败的测试。通过归纳项目树分析，一个含义$\mathrm{一世}\to j$ 物品之间 $\mathrm{一世}$ 和 $j$ 可以被发现，其解释为“如果一个主题能够解决项目 $\mathrm{一世}$，那么这个题目也能解题 $j$”。因此，在该方法的当前形式中，仅考虑二分项。在本文中，当可能有两个以上的答案类别时，我们将这种方法扩展到多分项的一般情况。因此，我们引入了归纳项目树分析的扩展，它可以处理名义多分（包括二分）和序数多分，每个都有特定于项目的答案量表。为了显示它们的有用性，本文中提出的扩展用经验数据示例进行了说明。