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Spatial econometric panel model

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In this study, the Spatial Lag Panel Model (SLPM), Spatial Error Panel Model (SEPM), and Spatial Durbin Panel Model (SDPM) were introduced to reveal the relationship between the HMFD and meteorological factors based on the following model derived from the measurement of variables . The logarithm of the variable would not change the nature and correlation of the data, but it would compress the scale of the variable. After taking the logarithm of the variables, the data was more stable, and the collinearity and heteroscedasticity of the model were also weakened. In this article, the logarithm of waterfall played an important in weakening the heteroscedasticity. Besides, the temperature had negative number and the unit of humidity is percentage, which is not suitable for logarithm change, so the final model was as follows:

Where the i represents the 107 county-units (i = 1, 2…107); t means the time variable (t = 2009, 2010…2018); α denotes the constant term and εij represents the error term. The SLPM is used to analyse the influence of dependent variables from the neighbouring counties by adding the spatial lag term of the dependent variable into the independent variable. The spatial dependence can be reflected as an error term, namely, missing variables in the model have a spatial correlation with HMFD, or unobservable random variables have spatial correlations with HMFD. The SEPM is applied in such circumstances. The SDPM is useful in reflecting the influence on specific regions from surrounding regions. However, although the SDPM can reveal the relationship between dependent and independent variables inside and outside the local region, the coefficients of SDPM cannot be directly explained, as the effects due to the derivative of y correspondence to x usually do not equal βk. Hence, the effects of the coefficient can be decomposed into direct and spill-over effects.

After understanding the functions of all the spatial econometric panel models, a standard model selection strategy is established. The procedures can be divided into four steps. In the first step, the Moran’s I or LM test is introduced to examine the spatial autocorrelation, namely, the availability of conducting spatial analysis methods. In the second step, the Wald test and the LR test are used to choose the SLPM, SEPM or SPDM. In the third step, the Hausman test is applied to determine whether a fixed effect model or a random effect model should be used. If a fixed effect model is used, the last step is introduced to determine the application of fixed effects (time, individual or both). If it is fixed effect model, the last step were introduced to determine individual fixed effects (controlling the “space-specific, time-invariant” variables, which are excluded from the model) or time effects (controlling the “time-specific, space-invariant” variables, which are excluded from the model) or both fixed effects (controlling the above two), and it would be chosen according to the sample size and time.

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