Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding the range and realism of exponential-family approaches to network modelling. In this paper we develop a theory of inference for ERN models when only part of the network is observed, as well as specific methodology for missing data, including non-ignorable mechanisms for network-based sampling designs and for latent class models. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health.

Networked populations consist of inhomogeneous individuals connected via relational ties. The individuals typically vary in multivariate attributes. In some cases primary interest focuses on individual attributes and in others the understanding of the social structure of the ties. In many circumstances both are of interest, as is their relationship. In this paper we consider this last, most general, case. We model the joint distribution of social ties and individual attributes when the population is only partially observed. Of central interest is when the population is surveyed using a network sampling design. A second situation is when data about a subset of the ties and/or the individual attributes is unintentionally missing. Exponential-family random network models (ERNM)s are capable of specifying a joint statistical representation of both the ties of a network and individual attributes. This class of models allow the nodal attributes to be modeled as stochastic processes, expanding the range and realism of exponential-family approaches to network modeling. In this paper we develop a theory of inference for ERNMs when only part of the network is observed, as well as specific methodology for partially observed networks, including non-ignorable mechanisms for network-based sampling designs. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health.

Efforts to identify differential or core cognitive deficits in schizophrenia have been made for several decades, with limited success. Part of the difficulty in establishing a cognitive profile in schizophrenia is the considerable inter-patient heterogeneity in the level of cognitive impairment. Thus, it may be useful to examine the presence of relative cognitive weaknesses on an intra-person level. In the present study we examined the rates of significant intra-person differences between crystallized verbal ability versus five other cognitive abilities among 127 persons with schizophrenia or schizoaffective disorder and 127 demographically matched normal comparison (NC) subjects. We found that the rates of significant discrepancies above the NC group base-rates was significantly greater in reference to those discrepancies involving visual memory relative to those associated with auditory memory, working memory, processing speed, and perceptual organization. The findings conflict with prior suggestions that working memory or auditory episodic memory are differential or core deficits in schizophrenia, and highlight the importance of considering visual memory in characterizing the cognitive effects of this condition.