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Abstract Latent space models are often used to model network data by embedding a network’s nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, we begin by formalizing a class of latent space models we call generalized linear network eigenmodels that can model various edge types (binary, ordinal, nonnegative continuous) found in scientific applications. This model class subsumes the traditional eigenmodel by embedding it in a generalized linear model with an exponential dispersion family random component and fixes identifiability issues that hindered interpretability. We propose a Bayesian approach to dimension selection for generalized linear network eigenmodels based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. We show that the model’s posterior is consistent and concentrates on low-dimensional models near the truth. We demonstrate our approach’s consistent dimension selection on simulated networks, and we use generalized linear network eigenmodels to study the effect of covariates on the formation of networks from biology, ecology, and economics and the existence of residual latent structure. 

Objectives:Hearing loss affects the emotional well-being of adults and is sometimes associated with clinical depression. Chronic tinnitus is highly comorbid with hearing loss and separately linked with depression. In this article, the authors investigated the combined effects of hearing loss and tinnitus on depression in the presence of other moderating influences such as demographic, lifestyle, and health factors. Design:The authors used the National Health and Nutrition Examination Survey data (2011–2012 and 2015–2016) to determine the effects of hearing loss and tinnitus on depression in a population of US adults (20 to 69 years). The dataset included the Patient Health Questionnaire-9 for depression screening, hearing testing using pure-tone audiometry, and information related to multiple demographic, lifestyle, and health factors (n = 5845). Results:The statistical analysis showed moderate to high associations between depression and hearing loss, tinnitus, and demographic, lifestyle, and health factors, separately. Results of logistic regression analysis revealed that depression was significantly influenced by hearing loss (adjusted odds ratios [OR] = 3.0), the functional impact of tinnitus (adjusted OR = 2.4), and their interaction, both in the absence or presence of the moderating influences. The effect of bothersome tinnitus on depression was amplified in the presence of hearing loss (adjusted OR = 2.4 in the absence of hearing loss to adjusted OR = 14.9 in the presence of hearing loss). Conversely, the effect of hearing loss on depression decreased when bothersome tinnitus was present (adjusted OR = 3.0 when no tinnitus problem was present to adjusted OR = 0.7 in the presence of bothersome tinnitus). Conclusions:Together, hearing loss and bothersome tinnitus had a significant effect on self-reported depression symptoms, but their relative effect when comorbid differed. Tinnitus remained more salient than hearing loss and the latter’s contribution to depression was reduced in the presence of tinnitus, but the presence of hearing loss significantly increased the effects of tinnitus on depression, even when the effects of the relevant demographic, lifestyle, or health factors were controlled. Treatment strategies that target depression should screen for hearing loss and bothersome tinnitus and provide management options for the conditions.