Multidimensional connection preferences in high school friendship networks from the AddHealth dataset

Caption for the figure:Latent preference structures. Schematic preference matrices illustrating the possible ways in which preferences may depend on multidimensional or one-dimensional group membership in a two-dimensional system where the relevant dimensions are sex (female ♀ or male ♂) and nationality ((A)rmenian, (B)razilian, (C)hinese). Each element of the matrices represent the preference of the group in the row to connect to the group in the column. As a running example, in each matrix we mark the preferences relevant to the connection ♀C → ♂B and build the corresponding preference vector h in the bottom.Coding scheme for the CSV file:Results obtained from the computations performed in https://doi.org/10.48550/arXiv.2406.17043 in a CSV file. In this file, each row corresponds to a school from the AddHealth dataset (https://networks.skewed.de/net/add_health). The table columns’ name structure is as follows:– School identifier: school– Population size columns:• One-dimensional populations: N_[attribute] where [attribute] is the name of the one-dimensional group(e.g. N Asian).• Multidimensional populations: N_[attr1]|[attr2]|[attr3] where ([attr1], [attr2], [attr3]) is the multidimensional attribute vector (e.g. N_9th|Asian|Male).– Multidimensional preference columns: They all have the structureH_[aggregation function] [preference structure] [source multidim. group]-[target multidim. group]• [aggregation function] can be {and,or,mean}.• [preference structure] can be any of the ones shown in figure "preference_structure_v4":∗ multi-full: fully multidimensional. This structure has no preceding [aggregation function] label, as it is unnecessary.∗ multi-1d: (multi×1D).∗ 1d-full: (1D×1D).∗ 1d-simple: (1D).• [source multidim. group] and [target multidim. group] are labeled as for the multidimensional populations [attr1]|[attr2]|[attr3] (e.g. 9th|Asian|Male).– One-dimensional preference columns:• The column can start with h_ or with h_norm_:∗ h_ is for the raw inferred preference values.∗ h_norm_ is for the in-group-normalized values, as explained in the paper.• For all preference structures but 1D, they have the structureh_[aggregation function]_[preference structure]_[source group]-[target group]• For preference structure 1D, they have the structureh_[aggregation function]_[preference structure]_[dimension]_[source group]-[target group], where [dimension] can be {grade,race,sex}.– MRQAP columns. These columns have the structureMRQAP_[quantity] [h / h_norm]_[aggregation function]_[preference structure]_[dimension]_[source group]-[target group]. Here, [quantity] can be:• pval1s: numerically computed p-value from 100 MRQAP simulations. Proportion of MRQAP randomizations where preference is less than the empirical.• pval2s: numerically computed p-value from 100 MRQAP simulations. Proportion of MRQAP randomizations where preference is either less or more than the empirical, whichever is lower. This is not the two-sided, which would be 2 times that value if the distribution is symmetric.• av: average value of one-dimensional preference h from 100 simulations.• std: standard deviation of one-dimensional preference h from 100 simulations.– Model performance metrics columns. The structure is [metric]_[aggregation function]_[preference structure], where [metric] can be {L,AIC,BIC}.