Climate change belief systems across political groups in the United States

Ideally, when two variables are conditionally independent, edges should equal zero. However, partial correlation coefficients seldom reach an exact zero value. To address this limitation, the Lasso regularization technique is employed to reduce extremely weak edges to zero [18]. By discarding weak edges that potentially indicate spurious relationships, Lasso regularization prevents over-interpretation and failures to replicate estimated networks [19], as well as facili- tates the estimation of a sparse belief system, which is more readily interpretable than a fully connected belief system. The comprehensive belief system derived from all datasets was estimated in order to exam- ine centrality of elements. Moreover, we estimated 60 belief systems, each representing a politi- cal group’s belief system at each wave (4 political affiliations x 15 waves), to examine the temporal changes in density and structural heterogeneity within and between political groups. Centrality. We assessed three distinct types of centralities, including betweenness, close- ness, and strength centrality. Betweenness centrality represents the degree to which a belief system component is crucial in integrating and connecting other parts of the system [7]. Close- ness centrality aims to measure how quickly a particular element’s influence spreads to all other parts of the belief system [7]. Strength centrality indicates an element’s potential to have a greater impact on its neighboring nodes [7]. Given that the belief system in the current study

is a weighted network, which is a network where the edges have assigned weights (i.e., partial correlations), we utilized methods designed to calculate centrality for weighted networks [19]. Density. Density was measured by dividing the sum of absolute partial correlations by the total possible connections of a belief system. Theoretically, density ranges from 0, indicating no edges, to 1, indicating a fully connected network where every edge has a weight of 1 (M = .06, SD = .01). Structural difference. We employed the Graph Diffusion Distance (GDD) metric to mea- sure the structural difference between two belief systems, using the R package NetworkDistance [20]. This measurement operates under the assumption that if two networks sharing the same set of nodes possess distinct structures, their diffusion patterns of information or something that flows through these networks will vary [21]. By simulating and comparing these diffusion patterns, the algorithm quantifies the dissimilarity between two compared networks. Theoreti- cally, GDD can range from 0, denoting identical networks, to infinity. To constrain the values within a range of 0 to 1, we normalized GDD using the min-max method. GDD values were calculated for each pair within the sixty belief systems, resulting in a total of 1,770 GDD values. These comprised 420 GDD values for intra-group comparisons (M = .36, SD = .12) and 1,350 GDD values for inter-group comparisons (M = .41, SD = .12). Data analysis All statistical analyses were conducted using R, version 4.3.1 [22]. In a belief system, there is

only a single centrality score per element, which prevents us from evaluating the score statisti- cally. To address this limitation, we employed a bootstrap method. As a non-parametric sam- pling technique, it allows for estimating the distribution of statistical parameters such as confidence intervals without making assumptions about the form of the underlying population distribution. The implemented bootstrap repeatedly sampled 1,000 respondents with replace- ment from the observed data and estimated the 95% confidence interval of the centrality score for each element. To assess density change over time and across different political groups, we conducted a regression analysis in which density is regressed on an indicator for survey wave, political affiliations, and their interaction terms. A simple slope analysis is conducted to further clarify the strength and direction of the density trends within the political affiliation. To assess PLOS ONE Climate change belief system PLOS ONE | https://doi.org/10.1371/journal.pone.0300048 March 20, 2024 7 / 16