Title: A General Framework for Robust Estimation and Inference in Discrete Data

Author: Max Welz

Abstract:
Survey studies often face challenges due to inaccurate or untruthful responses
from participants, stemming from factors such as (but not limited to)
inattention, carelessness, item misunderstanding, or misresponding. Such
inaccuracies pose a threat to the validity of research results when fitting
psychometric models, as they can lead to biases, poor model fit, and errors in
hypothesis testing.

In this work, we propose a novel approach to estimating models for discrete
data, aiming to enhance robustness against inaccurate responses compared to
classical maximum likelihood estimation (MLE). Our method makes no assumptions
about the prevalence or type of inaccurate responding, a departure from
existing literature. The estimator generalizes MLE and maintains consistency
and asymptotic normality of estimates, facilitating hypothesis testing. It
furthermore has the same time complexity as MLE, meaning that it comes at no
additional computational cost.

Our estimation framework is very general and can be applied to any model for
discrete data. We explore relevant special cases, such as factor models and
item response models, by demonstrating the estimator's performance and
robustness in practice. We provide implementation through the free open source
R-package "robord." Developed predominantly in C++ to maximize speed and
enhance performance, the package flexibly integrates robust estimation with a
rich set of methods for plotting and printing. Pairing computational
efficiency with a high degree of user friendliness through a simple interface,
"robord" is designed to enhance accessibility and adoption by empirical
researchers.