Construct measurement error in latent social network relationship: An item response theory based latent space model

Abstract

Research on measurement error in social network analysis has primarily focused on proxy measurement error, which refers to inadequate or inaccurate observations of proxy measurements of social relationships. However, construct measurement error, a key concern in modern psychometric studies, has received less attention in social network studies. Construct measurement error is particularly relevant for social network relationships that are difficult or impossible to observe explicitly, such as friendships, which are better conceptualized as latent constructs.

Historically, researchers have long advocated to use multi-item scales for social relationships to address construct measurement error (Marsden, 1990). However, there is a lack of methods tailored for multivariate social network analysis using multi-item measurements. Commonly, when data on social network ties is collected from multiple items, prevalent strategies involve either choosing a representative item or analyzing each item as a distinct network.

To accommodate construct measurement error in social network analysis, this study proposes a new model, termed as IRT-LSM, that integrates an item response theory (IRT) model into a latent space model (LSM). The proposed method leverages the IRT model to take advantage of a multi-item scale to enhance the measurement of latent social relationships, providing a more comprehensive understanding of social relationships compared to relying on a single item.

To evaluate the efficacy of this novel approach, the dissertation comprises three simulation studies: One assessing model feasibility and the impact of construct measurement error, a second exploring various misspecification models, and a third investigating the effects of item parameter distributions. Additionally, an empirical data analysis demonstrates the practical application of the IRT-LSM in real-world settings.

The results underscore the effectiveness of the IRT-LSM in addressing construct measurement error. The model consistently yields unbiased estimates and demonstrates robustness against various factors influencing its performance across the simulated conditions. Notably, the IRT-LSM outperforms naive approaches that neglect construct measurement error, leading to divergent conclusions in the empirical data analyses.