Spatial interaction models are a special case of a general model of spatial autocorrelation\cite{Getis_2008}. Recent attention has turned to network autocorrelation, one of the previously neglected
components of spatial interaction models (e.g., Griffith 2007; LeSage and Pace 2008; LeSage and Fischer 2010; Chun and Griffith 2011; Novak et al. 2011).
Gravity models typically rely on three types of factors to explain mean interaction frequencies: Origin-specific variables that characterise the ability of origin locations to produce or generate flows; destination-specific variables that attempt to capture the attractiveness of destination locations; and a separation function that reflects the way spatial separation of origins from destinations constrains or impedes the interaction \cite{Fischer_2011}. Spatial dependence in a flow setting refers to a situation where flows from nearby locations (either origins or destinations) are similar in magnitude. A failure to incorporate spatial dependence in model specifications leads to biased parameter estimates and incorrect conclusions. Numbers of migrants moving from one location to another is a count data is assumed to have Poisson distribution.
Poisson regression is one special case of the Generalized Linear Model (GLM). GLM allows one to fit models to a dependent variable that is a member of the exponential distribution family. GLM is characterized by three components: the distribution of the dependent variable, a linear function of a set of independent variables, and a link function between the dependent variable and its expectation as expressed by the linear function of independent variables. When the logarithm is applied as a link function, the Poisson regression has a log-linear form. In this context, the gravity model can be written as