Activity-Conditioned Residual Association from Aggregated Relational Data
Abstract
Aggregated relational data (ARD) record how many ties sampled respondents have to prespecified groups without revealing individual dyads. We develop a conditional test for prespecified cross-group concordance beyond an additive-activity network model. When the groups form an exhaustive partition, respondent degree is observed exactly. For arbitrary fixed activity values under an independent-Bernoulli additive-logit null, conditioning two respondents on equal degree yields a finite nonpositive sign restriction for their two disjoint group-count differences. Analyst-randomized pair thinning gives a conservative baseline. Under a stronger fixed-cell design with group-specific smooth activity profiles and positive cross-role overlap, an observable clipped full-pair statistic gives conservative one-network inference with graph-independent sampled respondents. Finite and growing matched-law constructions establish that the target contains bivariate information absent from a collapsed binary count. The full-pair procedure is uniformly consistent on a primitive relative-open neighborhood of a specified rank-one alternative. Fixed-dimensional lattice local limits make the conditioning and availability requirements explicit.
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BibTeX
@misc{tseng2026activityconditioned,
title = {{Activity-Conditioned Residual Association from Aggregated Relational Data}},
author = {Yen-hsuan Tseng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.27599},
eprint = {2608.27599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27599},
}
RIS
TY - UNPB
TI - Activity-Conditioned Residual Association from Aggregated Relational Data
AU - Yen-hsuan Tseng
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2608.27599
UR - https://arxiv.org/abs/2608.27599
AB - Aggregated relational data (ARD) record how many ties sampled respondents have to prespecified groups without revealing individual dyads. We develop a conditional test for prespecified cross-group concordance beyond an additive-activity network model. When the groups form an exhaustive partition, respondent degree is observed exactly. For arbitrary fixed activity values under an independent-Bernoulli additive-logit null, conditioning two respondents on equal degree yields a finite nonpositive sign restriction for their two disjoint group-count differences. Analyst-randomized pair thinning gives a conservative baseline. Under a stronger fixed-cell design with group-specific smooth activity profiles and positive cross-role overlap, an observable clipped full-pair statistic gives conservative one-network inference with graph-independent sampled respondents. Finite and growing matched-law constructions establish that the target contains bivariate information absent from a collapsed binary count. The full-pair procedure is uniformly consistent on a primitive relative-open neighborhood of a specified rank-one alternative. Fixed-dimensional lattice local limits make the conditioning and availability requirements explicit.
ER -