Causal Inference in Survey Data and Divergence Measures in Ordinal Patterns

Weiwei Xie

Modern statistical methods provide powerful tools for studying complex data, but theirsuccessful application often depends on how well uncertainty, structure, and data limitations are addressed. In many real-world problems, meaningful inference requires both methodological development and careful attention to the process by which the data are observed. This dissertation presents two studies motivated by these challenges. The first study focuses on gender-related differences in pay rates using survey data andan attention to the methodological challenges created by missing responses to wage-related questions. Because pay rate is a sensitive topic, survey participants may be unwilling to disclose this information, and such nonresponse can introduce substantial bias into the analysis if it is not properly addressed. The goal of this study is therefore twofold: first, to examine pay rate differences between female and male participants for statistical consultants while accounting for important background characteristics, and second, to better understand the missingness mechanism associated with pay-related survey question. To accomplish these objectives, we designed and administered a survey, obtained Institutional Review Board (IRB) approval, and collected responses from participants across relevant demographic and employment-related characteristics. Exploratory data analysis was conducted to study the structure of the observed data and the pattern of missing responses. Multiple imputation techniques were then applied to address the missing-data problem before proceeding to the main analysis. To estimate the effect of gender on pay rate while reducing the impact of confounding variables, several causal inference methods based on matching were implemented and compared. In addition, the study examines the likelihood that participants decline to answer pay-related questions, providing further insight into response behavior in sensitive survey settings. The results of this study contribute to both substantive and methodological understanding. Substantively, they provide evidence regarding pay rate disparities in this specific labor market. Methodologically, they illustrate how combining missing-data methods with causal inference techniques can improve the validity of conclusions drawn from survey data when sensitive questions are subject to nonresponse. The second study analyzes distributions of ordinal patterns using null models for timeseries data. Permutation entropy has emerged as a widely used statistical measure for assessing the complexity of time series, with applications spanning diverse fields such as biology, economics, and physics. Recent work has applied divergence measures, including Kullback- Leibler divergence and Jensen-Shannon divergence, to quantify the similarity between time series based on ordinal patterns, and to measure the deviation from generative models. This approach also allows for creating meaningful embeddings of the data. While early approaches implicitly assumed a uniform null model for the underlying distribution of patterns, many real-world applications involve more complex distributions and are better modeled with random walks. In this study, we present an analysis of several null models for generating time series data, from both theoretical and empirical perspectives. We successfully derive theorems describing the behavior of random walks with uniformly and normally distributed steps, as well as introducing a novel random walk null model based on transition matrices inferred from real-world data. We show that this data-driven approach allows for a more accurate representation of empirical distributions. We also demonstrate the practical utility of these methods by applying them to real-world datasets from economics and other domains, highlighting the effectiveness of divergence measures in capturing the complexity of empirical time series data. We conclude by exploring a threshold-based method to capture structure of subsets of the data with a strong suggestion of a 20% threshold, for aligning the distribution of patterns below the threshold with those from the complete data. This approach allows us to learn the ordinal pattern distributions, even in the presence of noise, with a smaller data set and less computation cost when analyzing high-dimensional, large, or more complex series.

Causal Inference in Survey Data and Divergence Measures in Ordinal Patterns

Files and links (1)

Abstract

Metrics

Details