Analysis Of Mixed Spatial Autoregressive Model With Missing Data

In this era of huge amount of data and information,many biological data,medical data,and economic data are spatially correlated.Therefore,traditional regression models cannot be simply used for modeling and analysis.So we need to find new methods,and the spatial autoregressive model is just suitable for this type of data modeling analysis.However,in the actual research process,the missing situation is inevitable.Many statistical methods are used by scholars to deal with the problem of missing data.In the process of research,it is found that different imputation methods will result in different data sets,which will lead to different analysis results.Aiming at the spatial autoregressive model with missing data,this article first selects six methods for processing missing values: mean imputation,random forest imputation,regression imputation,nearest neighbor imputation,multiple imputation and adversarial generative network imputation（GAIN）,and set the missing rate of simulated data to 5%,10%,20%,30%,and 40%,respectively.By comparing the imputed value and the average absolute error and mean square error of the model parameter estimation to research different effects of different interpolation method.The study found that: when a single variable is missing,regression imputation and GAIN can achieve better results.When multiple variables are missing,GAIN,multiple imputation and nearest neighbor imputation can achieve relatively good results;with the missing rate with the increase of,the effect of various interpolation methods gradually deteriorates.Then,according to the characteristics of the adversarial generative network interpolation,this article proposes an improved adversarial generative network interpolation method,and this method is called GAIN-MUL.Through comparative analysis with other methods,it is found that It can show relatively good results at 20%from the perspective of interpolation error;from the perspective of model parameter errors,GAIN-MUL can also achieve good results,which provides researchers with more choices when dealing with missing data.Finally,this paper studies the mixed space autoregressive model with component data,and also considers the missing cases,and uses the regression and interpolation method to fill in the data and then estimate the parameters.And through experiments to verify the effectiveness of the two estimation methods MLE and 2SLS.From the experimental results,it is found that for the mixed spatial autoregressive model with component data,both MLE and 2SLE can obtain good parameter estimation results;for the missing cases,compared to directly deleting the missing samples,the regression interpolation After supplementing,the effect of parameter estimation is obviously better.