The co-varying ties between networks and item responses via latent variables

Relationships among teachers are known to influence their teaching-related perceptions. We study whether and how teachers’ advising relationships (networks) are related to their perceptions of satisfaction, students, and influence over educational policies, recorded as their responses to a questionnaire (item responses). We propose a novel joint model of network and item responses (JNIRM) with correlated latent variables to understand these co-varying ties. This methodology allows the analyst to test and interpret the dependence between a network and item responses. Using JNIRM, we discover that teachers’ advising relationships contribute to their perceptions of satisfaction and students more often than their perceptions of influence over educational policies. In addition, we observe that the complementarity principle applies in certain schools, where teachers tend to seek advice from those who are different from them. JNIRM shows superior parameter estimation and model fit over separately modeling the network and item responses with latent variable models.

💡 Research Summary

The paper introduces a novel joint statistical framework, the Joint Network and Item Response Model (JNIRM), designed to simultaneously analyze relational network data and multivariate questionnaire responses. The authors motivate the need for such a model by highlighting the limitations of existing approaches that either treat networks and item responses separately or incorporate item responses as simple covariates in a network model, thereby discarding rich structural information and the latent dimensionality of questionnaire data.

In JNIRM, each individual (teacher) is associated with two sets of latent variables: one governing the formation of the directed advice‑seeking network (latent network dimensions) and another governing the responses to a set of Likert‑type items (latent item dimensions). These two latent vectors are assumed to follow a multivariate normal distribution with a shared covariance matrix Σ. The off‑diagonal blocks of Σ capture the correlation between the network and item latent spaces, providing a direct measure of their dependence without imposing a priori causal direction.

The network component is modeled as a logistic regression on the latent network scores, yielding the probability of an edge from teacher a to teacher b. The item component adopts a linear factor‑analytic (IRT‑like) model for the continuous treatment of Likert scores, with factor loadings informed by an initial principal component analysis. Estimation proceeds via a Bayesian Markov chain Monte Carlo algorithm that iteratively samples latent scores, factor loadings, and the covariance matrix, allowing uncertainty to propagate across both data domains.

The methodology is applied to a real‑world dataset collected in 2015 from 378 teachers across 14 schools in Nebraska. Teachers reported up to 12 advisors, producing a binary, asymmetric adjacency matrix of advice‑seeking ties. They also completed a 16‑item School Staff Social Network Questionnaire covering three constructs: overall satisfaction (4 items), perceived influence on school policies (7 items), and perceptions of students (5 items). PCA of the item correlation matrix suggested three dominant components aligning with the three constructs, which were used to initialize the item latent factors.

Key empirical findings include: (1) The estimated covariance between the latent network scores and the satisfaction and student perception factors is substantially larger than that with the policy influence factor, indicating that teachers’ advice‑seeking relationships are more closely linked to how satisfied they feel and how they view their students than to how much influence they perceive over policy. (2) In several schools, the “complementarity principle” emerges: teachers tend to seek advice from peers who differ from them on key attributes, suggesting a strategic diversification of information sources. (3) Model fit indices (AIC, BIC, DIC) for JNIRM are markedly better than those obtained from separate analyses using Exponential Random Graph Models (or latent space models) for the network and standard IRT or factor models for the items, confirming the efficiency gains from joint estimation.

Beyond the primary analysis, the authors discuss several practical advantages of JNIRM. Because the Bayesian framework naturally handles missing data, the model can impute absent ties and item responses simultaneously, a common scenario in educational surveys. The paper also outlines potential extensions: incorporating graded‑response or partial‑credit models for ordinal items, adding hierarchical layers to capture school‑level effects, and modeling dynamic networks where ties evolve over time.

In summary, the study provides a robust, flexible statistical tool for researchers interested in the co‑variation of social structures and latent psychological constructs. By jointly modeling networks and item responses through correlated latent variables, JNIRM yields richer inference, improved parameter precision, and novel substantive insights into how teachers’ advisory relationships shape—and are shaped by—their perceptions of school climate.