This thesis develops new models and inference methods for network structures, and contains two parts. In the first part, we develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. Our saddlepoint density approximation features relative error of order O(1/(n(T-1))) with n being the cross-sectional dimension and T the time-series dimension. Monte Carlo experiments illustrate the good performance of our approximation over first-order asymptotics and Edgeworth expansions. In the second part, we derive Laplace-approximated maximum likelihood estimators (GLAMLEs) of parameters in our Graph Generalized Linear Latent Variable Models. Then, we study the statistical properties of GLAMLEs and display the estimation results in a Monte Carlo simulation considering different numbers of latent variables. Moreover, we make a comparison between Laplace and variational approximations for inference of our model.