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calc_spatial_lag [2011/07/26 18:52]
hermann created 		calc_spatial_lag [2026/08/28 03:11] (current)
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-====== Calc Spatial Lag ====== ​+====== Calc Spatial Lag ======
  
 ===== Description ===== ===== 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 ===== ===== Inputs =====
  
-^ Name            ^ Type                                              ^ Description ​                              ​^ +^ Name  ^ Type  ^ Description ​ ^ 
-| P Lag           ​| [[Double ​Type|Double  ​]]                          | pLag is the autoregressive coefficient. ​  ​| +| P Lag  | [[Real Value Type]] ​ | Spatial ​autoregressive coefficient ​(p) used in the regression.  | 
-| W Neighborhoods | [[Neighborhood Table Type|Neighborhood Table  ​]]  | The neighborhood ​matrix. ​                 | +| W Neighborhoods ​ | [[Neighborhood Table Type]] ​ | Spatial weight ​matrix ​(W) used in the regression.  | 
-| X1              | [[Lookup Table Type|Lookup Table  ​]]              | 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|Lookup Table  ​]]              | 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         ​| [[Double ​Type|Double  ​]]                          | 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 ===== ===== Group =====
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 ===== Notes ===== ===== 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. ANSELIN, L. Spatial Externalities,​ Spatial Multipliers and Spatial Econometrics. Urbana-Champaign,​ University of Illinois, 2002.