Geographically and Temporally Regression (GTWR), the p-value of Local regression coefficients

Question

Hi! I have recently been puzzled by the p-values of the local regression coefficients of the GTWR model, which are rarely mentioned in related research publications, where people only report the R-squared, Ajusted R-squared, and AICc of the OLS, GWR, TWR, and GTWR to show how well the models are fitted. However, when the temporal variation of the local regression coefficients is discussed, there is no mention of the P-value, which seems to be difficult to account for the explanatory power of the local regression coefficients. In addition, in the GTWR model, is it necessary to satisfy that the p-value of the regression coefficients of all explanatory variables at each observation is less than 0.05. When the p-value of an explanatory variable in the model is less than 0.05 at only a few observations, but the model as a whole fits very well, and the model fits worse after deleting the explanatory variable, should the variable be deleted or not? Is it reasonable for some studies to set the proportion of observations with a p-value of less than 0.05 at more than 50% to consider the model as having a strong explanatory effect, and to discuss the local regression coefficients in this way? Hope someone can help with the question, thanks a lot. 😊

finmarkk · Answer

@ZhichengZhong wrote:Hi! I have recently been puzzled by the p-values of the local regression coefficients of the GTWR model, which are rarely mentioned in related research publications, where people only report the R-squared, Ajusted R-squared, and AICc of the OLS, GWR, TWR, and GTWR to show how well the models are fitted. However, when the temporal variation of the local regression coefficients is discussed, there is no mention of the P-value, which seems to be difficult to account for the explanatory power of the local regression coefficients. In addition, in the GTWR model, is it necessary to satisfy that the p-value of the regression coefficients of all explanatory variables at each observation is less than 0.05. When the p-value of an explanatory variable in the model is less than 0.05 at only a few observations, but the model as a whole fits very well, and the model fits worse after deleting the explanatory variable, should the variable be deleted or not? Is it reasonable for some studies to set the proportion of observations with a p-value of less than 0.05 at more than 50% to consider the model as having a strong explanatory effect, and to discuss the local regression coefficients in this way? Hope someone can help with the question, thanks a lot. 😊

Local p-values in GTWR vary naturally, so keep variables that improve the model and make sense rather than forcing strict significance everywhere.

ZhichengZhong · Answer

Many thanks for your reply! I'm confused because they visualize all the local regression coefficients spatially and even discuss time trends, but shouldn't so much of that discussion be predicated on the fact that all the local regression coefficients satisfy the significance test? Their practice of not showing p-values seems non-transparent. What if some observations are not significant? Would it make sense to set a significance ratio similar to the one I mentioned?

ZhichengZhong · Answer

Thank you very much for your reply. I actually performed the construction of the OLS regression and verified the linear relationship before performing the GTWR regression, and then transformed the selected explanatory variables to ensure a better linear relationship. However, except for the explanatory variables having high Beta values which have good significance of local regression coefficients across observations in the GTWR model, the other explanatory variables having low Beta values have very poor significance of local regression coefficients across observations, but the adjusted R-squared and the AICc of the GTWR model are very good, so are these results usable for discussion? My aim is to compare the effects of the same set of explanatory variables on two dependent variables, the first of which has achieved the desired effect, but the results of the model for the second dependent variable produce the above problem. This already includes explanatory variables that are simultaneously linear and significant for both dependent variables.

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