Detecting Differential Item Functioning in Partial Credit Models by Penalization Techniques

本研究的重点是项目反应数据中差异项目功能（DIF）的检测。DIF现象在应用心理测量学或其他社会科学中是一个非常重要的问题，其中项目反应数据被用来测量某种潜在的兴趣特质。需要特别认真地编制各个调查表。每一个项目都必须以一种只测量潜在的兴趣特征的方式来构建。在二分项目的情况下，如果两个具有相同水平的相应潜在特质的人对某个项目的正面回答的概率不同，则发生DIF。在大多数情况下，人们在参与者中的两个群体之间寻找DIF，例如男性和女性参与者。例如，在智力测试中，具有相同智力水平的男性和女性参与者正确回答一个问题的概率可能不同。这些项目必须被检测出来，并可能从问卷中删除，因为它们可能导致对潜在特征的有偏见的估计。已经开发了许多统计方法来检测两个预先指定的组之间的DIF，主要使用统计检验。毕竟，参与者可能有许多不同的特征可能导致DIF，例如种族等多类别变量或年龄等连续变量。不同的变量不应单独测试DIF，因为自动出现多重测试的问题，并且变量之间可能的相关性将不被考虑。为此，Tutz和Schauberger（2015）提出了DIFlasso方法，该方法能够处理分类和连续变量，并同时处理多个变量。它是一种基于模型的方法，使用惩罚技术来识别DIF项目。该方法的最大优点是，从业者可以指定一些可能的DIF诱导变量（连续和分类），该方法自动检测相关项目。然而，Tutz和Schauberger（2015）的方法仅限于在二分项目中检测DIF。 该项目的目标是，将该方法扩展到部分信用模型的一般框架内的多分支项目。为此目的，DIF效应的适当参数化是必要的，并且是自动检测DIF的惩罚估计程序。

The proposed research project focuses on the detection of Differential Item Functioning (DIF) in item response data. The phenomenon of DIF is a very important issue in applied psychometrics or other social sciences, where item response data are used to measure a certain latent trait of interest. The construction of the respective questionnaires needs to be done with special diligence. Every item has to be constructed in a way that it only measures the latent trait of interest. In the case of dichotomous items, DIF occurs if the probability to answer a certain item positively differs between two persons with the same level of the respective latent trait. In most cases, one looks for DIF between two groups within the participants, e.g. male and female participants. For example in intelligence tests, the probability to answer an item correctly might differ between male and female participants with the same level of intelligence. Such items have to be detected and possibly be removed from the questionnaire because they might lead to biased estimates of the latent traits. Many statistical methods have been developed to detect DIF between two pre-specified groups, mostly using statistical tests. After all, there might be many different characteristics of the participants that potentially cause DIF, for example multi-categorical variables like ethnicity or continuous variables like age. Different variables should not be tested separately for DIF because automatically the issue of multiple testing will arise and possible correlations between the variables will not be regarded. For that purpose, Tutz and Schauberger (2015) proposed the method DIFlasso which is able to handle both categorical and continuous variables and to handle several variables simultaneously. It is a model-based approach which uses penalization techniques to identify DIF-items. The big advantage of the approach is that the practitioner can specify a number of possibly DIF-inducing variables (both continuous and categorical) and the method automatically detects the relevant items. However, the approach of Tutz and Schauberger (2015) is restricted to the detection of DIF in dichotomous items. The goal of the proposed project is, to extend the method to polytomous items within the general framework of partial credit models. For that purpose, a suitable parameterization of DIF-effects is necessary and a penalized estimation procedure that automatically detects DIF.