Response Item Network (ResIN): A network-based approach to explore attitude systems

Researching attitudes is crucial in the social sciences, as attitudes reflect internal representations of the world and influence social interactions. They act as cues for evaluating and categorizing social environments, particularly in less explicit contexts like social media. Network-based methods, such as Belief Network Analysis (BNA), offer novel opportunities to study the structural basis of complex attitude systems, enhancing understanding of social influence and attitude change. BNA treats beliefs as nodes, linking them using linear correlation, providing a structure of belief systems. While computationally efficient and applicable to various data types, existing BNA methods have limitations. Linear correlation methods fail to capture non-monotonic relationships, and summarizing relationships with a single number obscures complexities in attitude systems, especially asymmetries between groups. For instance, individuals at both political extremes might share high scores on a particular item, while moderates score lower, yielding a zero correlation despite a clear, non-linear relationship. Similarly, identical correlation coefficients can mask different underlying relationships, hindering precise interpretations. This paper addresses these limitations by introducing ResIN.

Belief Network Analysis (BNA) is a relatively new approach to exploring the interplay of attitudes, goals, or values. Typically, items are treated as nodes, and edges are derived from inter-item correlations, often using linear correlation coefficients. While offering quick visual inspection of belief systems and quantitative analysis of attitudinal architecture, BNA faces limitations when dealing with non-linear relationships. Standard correlation methods like Pearson's correlation can fail to detect non-monotonic relationships, such as U-shaped curves, where the correlation coefficient might be zero even if the relationship is highly predictable. Furthermore, identical correlation values can represent very different underlying relationships, limiting the interpretation of latent constructs and potentially leading to misinterpretations of group identities and asymmetries in attitude systems. While alternatives like Kullback-Leibler distance have been suggested, they do not entirely resolve these issues, as different response patterns can produce similar coefficient values. Existing methods often assume symmetry in attitudes between groups, but this is often not the case in reality.

ResIN, unlike traditional BNA, models item-responses as nodes. For instance, if an item has five response options, ResIN creates five nodes. This is achieved through dummy coding, creating binary variables representing each response option. This allows for a more detailed description of the relationship between items, moving away from the assumption of interval measurement properties at the individual level. Link weights in ResIN are calculated as correlations between the corresponding node variables; for binary variables, the result is consistent across different correlation coefficients (Pearson, Spearman, Phi). The method then uses a force-directed algorithm to assign spatial coordinates to each node in a latent space. This algorithm models nodes as charged particles, with repulsion between them and attraction based on link weights. Strongly correlated nodes are positioned closer together, while weakly correlated ones are further apart. The algorithm primarily uses positive correlations for spatial positioning, although the information from negative correlations is retained for other analyses. The x-coordinate of each node obtained through ResIN is connected to the mean of the item characteristic curve (IC curve) in IRT. The mathematical relationship between ResIN's correlation measure (Phi coefficient) and the overlap of IC curves is established. It's shown that for positive correlations, the Phi coefficient is a good measurement of the curves' distance, while it loses sensitivity for negative correlations. The force-directed method aims to position nodes at the equilibrium of attractive and repulsive forces, with the attractive force proportional to the link weight (correlation) and the distance between nodes. A simplified model, assuming only attractive forces and fixing all but one node at the mean of their IC curves, demonstrates a strong linear relationship between the node's position and the mean of its IC curve. Further simulations, using the graded response model from IRT, validate the relationship between ResIN and IRT across various conditions. ResIN is compared against Multidimensional Scaling (MDS).

Simulations using the graded response model from IRT show that the position of nodes in ResIN strongly correlates (r ≈ 0.95) with the mean of corresponding IC curves in IRT, even when relaxing assumptions about curve shapes and amplitudes. Analysis of empirical data from a survey of 402 Americans on political issues reveals a correlation of r = 0.97 (p < 10⁻²⁷) between ResIN node positions and IRT IC curve means. ResIN's visualization clearly reveals a division within the responses, splitting into two main clusters, one predominantly Democratic and the other predominantly Republican, which aligns with participants' self-reported political affiliations. This split is not evident in BNA. Interestingly, some responses considered moderate or even slightly leaning Democrat are more strongly associated with the Republican cluster, suggesting the importance of extreme stances for defining Democrat identity compared to the more diverse range of beliefs within Republican views. Further comparisons against Multidimensional Scaling (MDS) reveal that ResIN consistently outperforms MDS in aligning node positions with IRT means across multiple simulations, indicating that the force-directed algorithm in ResIN is both robust and efficient. The analysis of the force-directed method itself shows minimal variation in the output despite its stochastic nature, and a chaotic algorithm yields vastly different results, reinforcing the reliability of ResIN.

ResIN successfully integrates strengths from BNA and IRT, providing a user-friendly tool for exploring complex attitude systems and identifying group-specific patterns within latent opinion spaces. The method's ability to capture both network-based relationships and latent space information proves valuable for uncovering hidden structures and asymmetries not readily apparent in other methods. ResIN offers a more intuitive way to analyze and interpret non-linear and asymmetric relationships between identities and attitudes. The study highlights the utility of ResIN in revealing unexpected nuances in opinion structure, such as the observed asymmetry in attitudes between Democrats and Republicans. This asymmetry suggests that certain positions are more central to self-identification within one group than another.

ResIN offers a robust and valuable tool for social scientists studying attitudes and identities. It combines the simplicity of BNA with the depth of IRT, allowing for the exploration of complex phenomena while providing relatively straightforward outputs. Future research could explore its application to multiple-choice items with non-mutually exclusive responses and adapt the force-directed algorithm to incorporate negative correlations. ResIN, BNA, and IRT offer complementary perspectives on attitude systems, providing a multi-faceted approach to understanding these complex phenomena.

While ResIN shows strong correlations with IRT, its reliance on the force-directed algorithm introduces stochasticity, although the impact is minimal and does not affect the overall conclusions. The study focuses on political attitudes; further research is needed to assess its applicability to diverse domains. The interpretation of the identified clusters relies on the assumption that spatial proximity reflects attitudinal similarity, which needs further validation in future studies.