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. 2026 Aug 19;13:1908801. doi: 10.3389/fnut.2026.1908801

Table 8.

Spatial heterogeneity and robustness tests.

Panel A. Regional and socioeconomic heterogeneity
Subsample HP-DFE → SEI HP-DFE × SA → SEI RE-DFE → UE RE-DFE × FL → UE SEI_t − 1 → NR
Eastern China 0.142*** 0.061* 0.246*** −0.096** −0.116**
Central China 0.119** 0.074** 0.218*** −0.081* −0.128**
Western China 0.086* 0.093** 0.192** −0.068* −0.109*
Northeastern China 0.073 0.052 0.176* −0.044 −0.087
High-income provinces 0.138*** 0.058* 0.251*** −0.104** −0.121**
Low-income provinces 0.094** 0.096** 0.203*** −0.071* −0.112*
High-urbanization provinces 0.146*** 0.055* 0.263*** −0.101** −0.119**
Low-urbanization provinces 0.091** 0.089** 0.198** −0.073* −0.107*
Panel B. Robustness checks
Robustness specification HP-DFE → SEI HP-DFE × SA → SEI RE-DFE → UE RE-DFE × FL → UE SEI_t − 1 → NR
Equal-weighted indices 0.108** 0.069** 0.207*** −0.083** −0.118***
PCA-based indices 0.121*** 0.076** 0.223*** −0.079** −0.127***
Excluding municipalities 0.101** 0.071** 0.196*** −0.075* −0.113**
Excluding 2020–2022 0.118** 0.068* 0.201*** −0.081** −0.109**
Non-interpolated sample 0.097** 0.064* 0.189*** −0.072* −0.105**
Lagged exposure model 0.104** 0.066* 0.193*** −0.078** −0.116**
Panel C. GWR/MGWR local coefficient ranges
Local coefficient Minimum Median Maximum
HP-DFE → SEI 0.061 0.118 0.196
RE-DFE → UE 0.135 0.221 0.284
SA → SEI 0.041 0.092 0.143
FL → SEI 0.072 0.126 0.183
SEI → NR −0.168 −0.112 −0.061