Abstract

Item Response Theory (IRT) is a robust framework used for measuring latent traits across various fields, particularly in psychometrics and educational assessments. However, its application within complex survey data often overlooks the critical aspect of sampling design, leading to potential biases and limitations in result reliability.
This study aims to enhance the application of the Rasch model—a fundamental dichotomous IRT model—by integrating it with complex survey schemes, including stratified and clustered sampling designs. Using data from Brazilian household and budget survey (Pesquisa de Orçamento Familiar – POF) conducted by the Brazilian National Statistical Office (IBGE), we adapt the Rasch model to accommodate the intricate sampling characteristics inherent in these surveys. Our goal is to provide more accurate and unbiased estimates of food insecurity levels, thereby improving the reliability of the measurement scales used in these assessments.
We employ the Rasch model to analyse responses to food insecurity-related items from the national survey. These items, which reflect a range of food insecurity experiences such as meal skipping and portion reduction, are evaluated to determine their difficulty and discrimination parameters. We adjust the model to account for the complex sampling design of POF, ensuring that stratification and clustering effects are appropriately integrated into the parameter estimation process.
Our findings reveal that ignoring the complex survey design can lead to significant biases in the estimation of item parameters. By incorporating the survey design into the Rasch model, we achieve more reliable estimates of food insecurity levels. Specifically, we observe that households experiencing severe food insecurity are more accurately identified, with less misclassification compared to traditional methods that do not consider sampling design. The adjusted Rasch model provides a clearer continuum of food insecurity severity, distinguishing more precisely between different levels of deprivation. This refined measurement allows for better targeting of interventions and resources to those most in need.
In conclusion, this study underscores the importance of considering complex survey designs in the application of IRT models like the Rasch model. By doing so, we enhance the accuracy and reliability of food insecurity measurements, contributing to more effective policymaking and resource allocation. Future research should continue to explore the integration of IRT with complex survey data across various domains to improve the measurement of latent traits and ensure the robustness of statistical inferences.