From Structural Equation Modelling to Double Machine Learning: Robustness Analysis for Survey-Based Research
Authors: Ka Ching Chan, Qiana Liu, Sanjib Tiwari, Ranga Chimhundu
Abstract
Structural equation modelling (SEM) is widely used in survey-based business and information systems research to assess latent constructs and theory-driven structural relationships. However, SEM path significance is obtained within a particular model specification and may not show whether findings remain stable under alternative estimation frameworks. This study develops and demonstrates a staged robustness analysis framework that connects SEM, ordinary least squares (OLS) regression, and Double Machine Learning (DML). SEM is first used to refine the measurement structure and estimate the robustness-baseline SEM model, in which the full theory-specified structural path system is retained for downstream robustness analysis before final structural path evaluation. OLS regression is then applied to SEM-derived construct scores as a transparent regression benchmark. Finally, DML-style residualisation is used to examine whether each tested focal relationship remains stable after flexible machine-learning-based adjustment for observed controls. Learner-sensitivity checks compare Random Forest, Gradient Boosting, and Support Vector Machine learners, and selected reverse-direction diagnostics are used to examine directional sensitivity. The framework is demonstrated using a FinTech Digital Customer Intimacy survey model. The findings identify which relationships are stable across SEM, OLS, and DML-style checks, and which require more cautious interpretation. A reproducible Google Colab workbook and generated result files are publicly available, providing a reusable template that researchers and students can adapt to other survey-based latent-construct studies. The paper contributes a practical robustness workflow and interpretation guide for survey-based researchers seeking to complement SEM with conventional and machine-learning-based robustness checks.
Double Machine Learning (DML) is a popular approach for treatment effect estimation in various settings, which allows a wide range of flexible machine learning methods to be used for nuisance parameter estimation while preserving valid inference. In practice, however, applied researchers must choose among many machine learning algorithms for nuisance models, and the impact of this choice on the variance estimation of DML is not well characterized. We conduct a comprehensive simulation study to compare the coverage probability of DML confidence intervals across different machine learning algorithms. In this study, we compare (1) analytical confidence intervals derived by DML theory versus (2) bootstrap confidence interval. We use a set of learners including ordinary least squares, LASSO, Random Forest, LightGBM, and Neural Networks under different data generation settings. We evaluate the performance across difference settings by bias, confidence interval width, and most importantly, coverage probability. Our results show substantial variability in coverage performance across analytical and bootstrap confidence intervals, highlighting that learner choice plays a critical role in reliable DML inference. Surprisingly, we find that in many settings, when sample size increases, the coverage probability of both DML analytical and bootstrap confidence interval decreases. We further investigate coverage probabilities using a real dataset on rural urban differences among U.S. counties. The real data analysis discovers that (1) the model performance still varies by the learner choices and (2) greater rurality has a statistically significant increasing effect on county level obesity prevalence.
Factor-based Structural Equation Modeling (SEM) relies on likelihood-based estimation assuming a nonsingular sample covariance matrix, which breaks down in small-sample settings with p>n. To address this, we propose a novel estimation principle that reformulates the covariance structure into self-covariance and cross-covariance components. The resulting framework defines a likelihood-based feasible set combined with a relative error constraint, enabling stable estimation in small-sample settings where p>n for sign and direction. Experiments on synthetic and real-world data show improved stability, particularly in recovering the sign and direction of structural parameters. These results extend covariance-based SEM to small-sample settings and provide practically useful directional information for decision-making.
Survey research faces mounting structural challenges: declining response rates, sample bias, block-wise missingness among at-risk respondents, and AI-assisted fraudulent completions in online panels. Large language models (LLMs) have been proposed as a remedy, yet rigorous evaluations across the full survey workflow remain scarce, particularly in disaster contexts where data quality matters most. We present and evaluate a five-stage framework for LLM integration covering questionnaire design, sample selection, pilot testing, missing-data imputation, and post-collection analysis, using the 2024 Hurricane Milton preparedness survey of Florida residents (n=946) as a shared empirical testbed. We introduce a Protection Motivation Theory (PMT)-constrained co-occurrence knowledge graph and develop seven LLM configurations spanning zero-shot inference, retrieval-augmented baselines, and novel theory-informed variants. Our proposed Anchored Marginal Theory-Informed LLM (A-TLM) outperforms all three classical imputation baselines (IPW/MI, MICE+PMM, missForest) on RMSE under disaster-relevant block-wise MNAR conditions (S4 RMSE 1.439 vs. 1.496 for the next-best), while achieving near-zero signed bias (-0.121) where the random-forest imputer produces the largest absolute bias (-0.631). Organizing retrieval around PMT causal structure and integrating all evidence in a single model call outperforms unstructured retrieval and staged sequential inference (MAE 0.993 vs. 1.097 for standard RAG). We document that near-zero aggregate bias can mask opposing subgroup errors and propose subgroup-stratified bias auditing as a reporting standard. A retrieval-constrained knowledge-graph chatbot demonstrates that hallucination is architecturally manageable through grounded refusal.