====== Calc Spatial Lag ======

===== Description =====

Container that iteratively solves a spatial lag regression, y = pLag * W * y + X * B + E, over independent variables registered inside it.

===== Inputs =====

^ Name  ^ Type  ^ Description  ^
| P Lag  | [[Real Value Type]]  | Spatial autoregressive coefficient (p) used in the regression.  |
| W Neighborhoods  | [[Neighborhood Table Type]]  | Spatial weight matrix (W) used in the regression.  |
| X1  | [[Lookup Table Type]]  | Values of the observed dependent variable (X1) for each region. When the observed result is not yet known, X1 stands in for it; in that case, supply a lookup table with the same number of records and every value set to zero.  |
| B Coefficients  | [[Lookup Table Type]]  | Regression coefficients (B): the coefficient of the observed variable (index 0), followed by the coefficient of each independent variable registered in this container.  |
| E Error  | [[Real Value Type]]  | Random error term (E) of the regression.  |

===== Optional Inputs =====

None.

===== Outputs =====

^ Name  ^ Type  ^ Description  ^
| Y Result  | [[Lookup Table Type]]  | Result (y) of the equation y = pLag * W * y + X * B + E, solved iteratively until convergence.  |
| Y Predicted Result  | [[Lookup Table Type]]  | Predicted result (y^) of the equation y^ = pLag * W * X1 + X * B + E.  |

===== Group =====

[[Functor List#Statistics | Statistics]]

===== Notes =====

The independent variables (X) used in the regression are registered inside this container by functors representing a numbered table (Number Table), each identified by a sequential number starting at 1.

The number of coefficients supplied in B Coefficients must equal the number of independent variables registered in this container, plus one for the observed variable's own coefficient (index 0).

W represents the spatial interaction of a phenomenon: in a binary weight matrix, unit i is a neighbor of unit j when the corresponding matrix cell is 1.

**References**

ANSELIN, L. SpaceStat Tutorial. Urbana-Champaign, University of Illinois, 1992.

ANSELIN, L. Spatial Externalities, Spatial Multipliers and Spatial Econometrics. Urbana-Champaign, University of Illinois, 2002.

===== Internal Name =====

CalcSpatialLag