Monte Carlo Methods & Simulation

Although measurement error (ME) in functional covariates has been addressed in generalized functional linear regression models, attempts to simultaneously account for measurement error in both functional and scalar covariates are limited. We propose a Monte Carlo corrected score (MCCS) method that uses complex variable simulation-extrapolation for functional logistic regression to fill this gap. The MCCS method effectively handles serially correlated ME without relying on distributional assumptions about the true or observed measures, in contrast to approaches that assume discrete MEs. MCCS is used when the exact forms of the corrected score do not exist. We conducted simulation studies under Gaussian and non-Gaussian ME distributions to evaluate its performance. Our simulations showed that the biases of MCCS estimations were consistently smaller than those of average and naive estimations. Furthermore, the MCCS estimation is robust to increased ME scales and non-Gaussian ME distributions. The method is applied to examine how device-based physical activity and self-reported fiber intake relate to type 2 diabetes risk among U.S. adults. 

Permutation entropy has emerged as a widely used statistical measure for assessing the complexity of time
series. 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
assumed a uniform null model for the underlying data generation process, many real-world applications involve
more complex distributions and random walk models. In this study, we present an analysis of several
null models for generating time series data, from both theoretical perspectives. We successfully
derive theorems describing the behavior of random walks with uniformly and normally distributed steps respectively,
as well as introducing a novel random walk null model based on transition matrices inferred from
real-world data using Markov chains. We apply these methods to real-world datasets from economics and other fields, showcasing how divergence measures effectively capture the complexity of empirical time series data. 

Panel models are extensively utilized in social and psychological sciences to examine dynamic relationships between constructs measured repeatedly over time. Despite their widespread use, these models carry inherent limitations, particularly regarding assumptions of omitted confounders, challenges in precise model specification, and uncertainty in choosing appropriate measurement intervals. Of specific concern in panel models is the synchronous effect—the contemporaneous relationship between variables measured simultaneously—which is frequently ignored or presumed negligible due to methodological difficulties in verifying its directionality and potential confounding influences.

Recognizing this limitation, our study introduces Panel Data Direction Dependence Analysis (Panel DDA). Standard DDA, originally developed for cross-sectional data, does not take into account either prior measures or cross-lagged effects and does not take the advantage of panel data structure. We propose a two-stage procedure for Panel Data DDA, controlling for potential confounding from previous measurements and subsequently applying standard DDA procedures to determine the causal direction of synchronous effects.

To evaluate the effectiveness of Panel Data DDA, we conducted two extensive Monte Carlo simulation studies, each comprising 500 iterations. Our simulations compared the panel-based approach with traditional cross-sectional DDA under varying conditions of synchronous and cross-lagged effects. Results demonstrated superior performance of Panel DDA.

To promote broader adoption and practical application, we developed an accessible Shiny application. This tool allows users to intuitively conduct both panel and cross-sectional DDA analyses, visualize data distributions, manage outliers. We illustrate the practical utility of our method using real-world longitudinal data from the Network for Educator Effectiveness (NEE), focusing on teacher-student relationships (TSR), teacher cognitive engagement (CE), and teacher problem-solving and critical thinking (PCT). Empirical findings confirmed that TSR significantly predicts CE synchronously, reinforcing the importance of positive teacher-student interactions. Moreover, TSR emerged as a critical confounder when evaluating the relationship between CE and PCT, underscoring the necessity of controlling confounders in synchronous effect analyses.

Overall, this study advances methodological rigor in analyzing synchronous effects within panel data, significantly enhancing causal inference capabilities. The integration of a user-friendly analytical tool further ensures that this methodological advancement is widely accessible, offering substantial practical benefits to researchers across social sciences, education, and psychology who engage with longitudinal data.

 

Reference ranges are essential tools in interpreting laboratory test results. In many situations, measurements on several analytes are needed by medical practitioners to diagnose complex conditions such as kidney function or liver function. In such situations, multivariate reference regions (MRRs), which account for the cross-correlations among the analytes, are preferred over univariate reference ranges. Traditionally, these MRRs have been constructed as ellipsoidal regions, with the disadvantage of not being able to detect component-wise outlying measurements. To address this problem, rectangular reference regions have recently been put forward in literature. This study develops methodologies to compute rectangular MRRs that incorporate covariate information, which are often vital in evaluating laboratory test results. We construct reference regions using tolerance-based criteria so that resulting regions possess the multiple use property. Results show that the proposed regions yield coverage probabilities that are accurate and robust to the sample size. These procedures are then applied to a real-life example for three components of the insulin-like growth factor system. 

We consider the problem of exact simulation from the joint distribution of the maximum and its location for several Brownian processes: the Brownian meander, restricted Brownian meander and the Brownian excursion. Such distributions have complicated probability density functions (pdfs), expressed in terms of infinite series. Thus, a direct sampling approach is not feasible. In this work we derive the joint pdf of the maximum and its location for the restricted Brownian meander process as an infinite series and devise exact sampling algorithms for all three processes above. We present a simulation study to assess the efficiency of our algorithms. 

We consider the problem of pooling means from multiple random samples from lognormal
populations. Under the homogeneity assumption of means that all mean values
are equal, we propose improved large sample asymptotic methods for estimating
p log-normal population means when multiple samples are combined. Accordingly,
we suggest estimators based on linear shrinkage, pretest, and Stein-type methodology,
and consider the asymptotic properties using asymptotic distributional bias and
risk expressions. We also present a simulation study to validate the performance of
the suggested estimators based on the simulated relative efficiency. Historical data
from finance and weather are used to in the application of the proposed estimators.