Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

Previous nutrient demand and consumption analyses show that several economic and sociodemographic variables are often associated with intakes. However, most of the literature does not account for differences among individuals within households. This study reviewed possible definitions of nutrient differences with respect to nutritional needs. Nutrient levels defined by the Thrifty Food Plan were used as subsistence levels for households in the 1977-78 Nationwide Food Consumption Survey. Probit analysis showed that the usual variables found related to nutrient intakes did not differentiate among subsistence groups. Household life cycle and working female heads influenced whether the household was under its requirement level.

Consumer behavior with respect to purchase regularity, satisfaction, origin, and willingness to pay for selected local versus non-Tennessee grown fresh produce is examined. Except for origin, consumer behavior with respect to the above is affected by income, household size and age distribution, race, age of respondent, college education, and occupation. The pattern of significant variables changed by commodity. Tomatoes, followed by peaches, had the greatest local market potential. Local promotion of other products may be more difficult. Results suggested consumers have no strong preferences for or against locally grown fresh produce. The prices of locally grown commodities in Knoxville should be less than or equal to those of comparable quality non-Tennessee commodities.