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--- calc_spatial_lag [2015/10/11 23:51]
admin
+++ calc_spatial_lag [2026/08/28 03:11] (current)
hermann Sync from local documentation review
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 ====== Calc Spatial Lag ======
 ===== Description =====
-This functor iteratively solves a spatial lag regression.
+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]]  | pLag is the autoregressive coefficient.   |
+| P Lag  | [[Real Value Type]]  | Spatial autoregressive coefficient (p) used in the regression.  |
-| W Neighborhoods  | [[Neighborhood Table Type]]  | The neighborhood matrix.  |
+| W Neighborhoods  | [[Neighborhood Table Type]]  | Spatial weight matrix (W) used in the regression.  |
-| X1  | [[Lookup Table Type]]  | x1 is the autoregressive term. When y is not known, x1 is used instead. In this case, a lookup table with same number of records and values equal to zero must be reported.  |
+| 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]]  | Coefficients for independent variables x2, x3, x4... xn.  |
+| 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]]  | Regression random error term.  |
+| E Error  | [[Real Value Type]]  | Random error term (E) of the regression.  |
-===== Output =====
+===== Optional Inputs =====
-^ Name               ^ Type                                  ^ Description                                 ^
+None.
-| Y Result           | [[Lookup Table Type|Lookup Table  ]]  | A lookup table with Y results.              |
-| Y Predicted Result | [[Lookup Table Type|Lookup Table  ]]  | A lookup table with the predicted results.  |
+===== 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 =====
@@ Line 26: / Line 30: @@
 ===== Notes =====
-The lag spatial model is represented as follows:
+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.
-<m>y = {rho W y}+{X beta}+ varepsilon</m>
+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).
-where <m>rho</m> is the autoregressive coefficient; W is the spatial weight matrix; y is the dependent variable; X is co-variables' information matrix; <m>beta</m> is the regression coefficients and <m>varepsilon</m> is a random error term. W can be understood as the representation of the spatial interaction of a phenomenon. In a binary matrix, unit i is unit j’s neighbor if the spatial weight matrix cell, a<sub>ij</sub>, is equal to 1.
+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 ====
+**References**
-ANSELIN, L. SpaceStat TUTORIAL. Urbana-Champaign, University of Illinois, 1992.
+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.