PhD defence M.F.O. (Max) Welz

Below is a brief summary of the dissertation:

Many quantities of scientific, political, or public interest are measured through categorical variables. A categorical variable is characterized by only taking values in a known countable range. Examples include survey items where a respondent chooses from prespecified response options such as “strongly disagree”, “disagree”, “neutral”, “agree”, “strongly agree” , income groups such as “low”, “middle”, “high”, or  counting variables like one’s number of children (0, 1, 2,...).  However, low-quality data points might be present in a sample of a categorical variables due to (but not limited to) inattentive responses, data entry errors, or improper use of measurement tools. This thesis studies the effects of low-quality categorical data on statistical analyses and proposes novel methods for robustly analyzing such data. It turns out that having already 5% or less data points being low-quality in a categorical sample suffices to invalidate the results of popular analysis methods. In contrast, the proposed novel methods remain robust to the adverse effects of low-quality data points and help identify them. For instance, the proposed methods can be used to answer questions such as “Which survey respondents have been inattentive?”, “When has a respondent started responding carelessly due to fatigue in lengthy surveys?”, or “For which categorical data points is a statistical model misspecified?” The thesis furthermore shows that its proposed methods have unusual but attractive theoretical properties. In the spirit of open science, all methods are implemented in free, publicly available open-source software packages.