The article introduces a new class of models for social network analysis, focusing on the probability of relationships between individuals based on their positions in an unobserved "social space." The authors develop maximum likelihood and Bayesian inference methods to estimate the latent positions and the effects of observed covariates. They propose Markov chain Monte Carlo (MCMC) procedures for these inferences and present analyses of three standard social network datasets, comparing their method to stochastic blockmodeling. The proposed method improves model fit, provides a visual and interpretable spatial representation of social relationships, and allows for quantifying statistical uncertainty in the social space. The article discusses the advantages of the proposed model over existing methods, including its flexibility, interpretability, and ability to handle missing data.The article introduces a new class of models for social network analysis, focusing on the probability of relationships between individuals based on their positions in an unobserved "social space." The authors develop maximum likelihood and Bayesian inference methods to estimate the latent positions and the effects of observed covariates. They propose Markov chain Monte Carlo (MCMC) procedures for these inferences and present analyses of three standard social network datasets, comparing their method to stochastic blockmodeling. The proposed method improves model fit, provides a visual and interpretable spatial representation of social relationships, and allows for quantifying statistical uncertainty in the social space. The article discusses the advantages of the proposed model over existing methods, including its flexibility, interpretability, and ability to handle missing data.