Lagsarlm

Lagsarlm is a function in the R package spdep used to estimate spatial autoregressive models that include a spatially lagged dependent variable. It implements the SAR (spatial autoregressive) model where the dependent variable is influenced by its neighbors: y = ρ Wy + Xβ + ε, with y the observed vector, W the spatial weights matrix, ρ the spatial lag parameter, X a matrix of covariates, β the regression coefficients, and ε an error term typically assumed to be normally distributed with variance σ².

The function requires a data frame and a specification of the spatial structure, usually provided via a spatial weights object (commonly named listw) or an explicit W matrix. Users supply a formula describing the dependent variable and covariates, plus the data and the spatial weights. Options such as zero.policy control whether observations with no neighbors are included, and na.action handles missing values.

Estimation is typically performed by maximum likelihood under standard normal errors, jointly estimating ρ and β (as well as σ²). The likelihood is constructed to account for the endogeneity introduced by Wy, and the estimation yields parameter estimates, standard errors, and model fit statistics. The process can involve iterative optimization and may leverage different computational routines available within spdep.

Output from lagsarlm includes the estimated coefficients for X (β) and the spatial lag parameter (ρ), along with standard errors and test statistics. It also provides model diagnostics such as log-likelihood, AIC, BIC, fitted values, and residuals. The results support interpretation of both covariate effects and the strength and direction of spatial dependence in the dependent variable.

Related functions in spdep include errorsarlm for spatial error models and related tools for diagnostics, prediction, and hypothesis testing in spatial econometric models.