基于权重的空间网格抽样：按倾向分配观测值至网格单元

核心思路是基于sim_spatial的sim_1值构建分配权重，让success=1的观测以与sim_1正相关的概率被分配到网格单元，success=0的观测可采用均匀分配或弱相关权重（根据需求调整）。以下是具体实现步骤和代码示例：

步骤1：预处理空间网格的权重 #

首先将sim_spatial中的sim_1转换为可用于抽样的概率权重，避免极端值导致权重失衡：

• 对sim_1做min-max缩放，将值映射到[0,1]区间
• 若sim_1存在负值，先偏移至非负区间（如加上最小值的绝对值）
• 将缩放后的值归一化，确保权重总和为1

步骤2：分组分配观测 #

将sim_data按success分为两组，分别采用不同抽样策略：

• success=1组：使用sim_1对应的权重进行加权随机抽样
• success=0组：可使用均匀权重（无空间偏好）或自定义弱相关权重（如sim_1的倒数）

R语言示例（假设用sf处理空间网格） #

library(dplyr)
library(sf)

# 预处理空间网格，生成概率权重
sim_spatial <- sim_spatial %>%
  mutate(
    sim_1_scaled = (sim_1 - min(sim_1)) / (max(sim_1) - min(sim_1)),
    weight = sim_1_scaled / sum(sim_1_scaled)
  )

# 提取网格ID和对应权重
grid_ids <- sim_spatial$grid_id
success1_weights <- sim_spatial$weight
success0_weights <- rep(1/length(grid_ids), length(grid_ids)) # 均匀权重

# 为每个观测分配网格
sim_data <- sim_data %>%
  mutate(
    grid_id = case_when(
      success == 1 ~ sample(grid_ids, n(), replace = TRUE, prob = success1_weights),
      success == 0 ~ sample(grid_ids, n(), replace = TRUE, prob = success0_weights)
    )
  )

# 可选：关联空间网格属性
sim_data_spatial <- sim_data %>%
  left_join(sim_spatial %>% st_drop_geometry(), by = "grid_id")

Python语言示例（用geopandas处理空间网格） #

import pandas as pd
import numpy as np
import geopandas as gpd

# 预处理空间网格，生成概率权重
sim_spatial['sim_1_scaled'] = (sim_spatial['sim_1'] - sim_spatial['sim_1'].min()) / (sim_spatial['sim_1'].max() - sim_spatial['sim_1'].min())
sim_spatial['weight'] = sim_spatial['sim_1_scaled'] / sim_spatial['sim_1_scaled'].sum()

# 提取网格ID和对应权重
grid_ids = sim_spatial['grid_id'].values
success1_weights = sim_spatial['weight'].values
success0_weights = np.full(len(grid_ids), 1/len(grid_ids)) # 均匀权重

# 定义分配函数
def assign_grid(row):
    if row['success'] == 1:
        return np.random.choice(grid_ids, p=success1_weights)
    else:
        return np.random.choice(grid_ids, p=success0_weights)

# 执行分配
sim_data['grid_id'] = sim_data.apply(assign_grid, axis=1)

# 可选：关联空间网格属性
sim_data_spatial = sim_data.merge(sim_spatial.drop(columns='geometry'), on='grid_id')

优化与验证 #

• 若需要更强的空间自相关性，可对sim_1_scaled做幂变换（如sim_1_scaled ** 2），放大高值单元的权重占比
• 若网格有容量限制，可采用迭代抽样：每次分配后减少对应网格的剩余容量，重新计算权重
• 分配完成后，可统计不同sim_1区间内success=1观测的占比，验证空间自相关性是否符合预期

内容的提问来源于stack exchange，提问作者Peter MacPherson