Spatial Multiplier Effects Analyzer

Build a tool that estimates spatial multiplier effects to decompose how changes in independent variables propagate through spatially connected observations. The tool should fit a spatial model and compute direct, indirect, and total effects.

Requirements

Input Data

Your implementation must accept:

• A dependent variable (y) as a numeric array
• Independent variables (X) as a 2D numeric array
• A spatial weights matrix (W) representing spatial connections between observations

Model Estimation

Estimate a spatial lag model that includes a spatially lagged dependent variable. The model should:

• Include an intercept term automatically
• Estimate coefficients for the independent variables
• Estimate the spatial autoregressive parameter

Multiplier Decomposition

Compute spatial multipliers that decompose the total effect into:

• Direct effects: The impact of a unit change in an independent variable on the same observation
• Indirect effects: The spillover impact on other spatially connected observations
• Total effects: The sum of direct and indirect effects

Calculate these multipliers using at least two different computational methods and verify they produce consistent results.

Output

Return a data structure containing:

• Direct, indirect, and total effects for each independent variable
• Results from multiple computation methods for comparison
• The estimated spatial autoregressive parameter

Test Cases

Test Case 1: Basic Multiplier Computation @test

Given a 5-observation dataset with y=[1,2,3,4,5], X=[[1,2],[2,3],[3,4],[4,5],[5,6]], and a row-standardized spatial weights matrix with nearest-neighbor connections:

• Verify that direct, indirect, and total effects are all computed and returned
• Verify that total effects equal direct effects plus indirect effects (within numerical precision)

Test Case 2: Method Comparison @test

Using the same dataset from Test Case 1:

• Verify that at least two different computation methods are used
• Verify that results from different methods are numerically similar (within 0.01 tolerance for each effect type)

Test Case 3: Spatial Parameter Validation @test

Using the fitted model from Test Case 1:

• Verify that the estimated spatial autoregressive parameter (rho) is returned
• Verify that rho is between -1.0 and 1.0

@generates

API

def analyze_spatial_multipliers(y, X, W):
    """
    Estimate spatial multipliers from a spatial lag model.

    Parameters:
    -----------
    y : array-like
        Dependent variable (n x 1)
    X : array-like
        Independent variables (n x k)
    W : array-like or sparse matrix
        Spatial weights matrix (n x n)

    Returns:
    --------
    dict
        Dictionary containing:
        - 'direct': array of direct effects for each variable
        - 'indirect': array of indirect effects for each variable
        - 'total': array of total effects for each variable
        - 'methods': dict with results from different computation methods
        - 'rho': estimated spatial autoregressive parameter
    """
    pass

Dependencies { .dependencies }

spreg { .dependency }

Provides spatial econometric regression models and multiplier computation.