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. 2025 Jul 16;15:25771. doi: 10.1038/s41598-025-04719-5

Table 6.

Selection results of spatial econometric model types.

Test type Null Hypothesis Test Statistic P-value Result
Livser Infser Livser Infser Livser Infser
LM test SEM 73.719 3.192 0.000 0.074 Selecting SDM Selecting SDM
SEM (robust) 42.759 12.259 0.000 0.000
SAR 50.559 7.438 0.000 0.023
SAR (robust) 19.599 9.141 0.000 0.002
Hausman test Random effect 22.480 19.797 0.0000 0.0710 Rejecting the null hypothesis, fixed effects are selected Rejecting the null hypothesis, fixed effects are selected
LR test SDM can be simplified to SAR 53.84 24.74 0.0047 0.0161 Rejecting the null hypothesis, Selecting SDM Rejecting the null hypothesis, Selecting SDM
SDM can be simplified to SEM 66.21 23.67 0.0042 0.0225 Rejecting the null hypothesis, Selecting SDM Rejecting the null hypothesis, Selecting SDM
Fixed effect test Individual fixed effects are preferred over both fixed effects 44.89 36.24 0.0000 0.0873 Rejecting the null hypothesis, the two-way fixed effects model is selected Rejecting the null hypothesis, the two-way fixed effects model is selected
Time fixed effects are preferred over both fixed effects 1429.25 1344.40 0.0000 0.0000 Rejecting the null hypothesis, the two-way fixed effects model is selected Rejecting the null hypothesis, the two-way fixed effects model is selected