贝叶斯空间计量模型1

贝叶斯空间计量模型一、采用贝叶斯空间计量模型的原因残差项可能存在异方差，而ML估计 方法 快递客服问题件处理详细方法山木方法pdf计算方法pdf华与华方法下载八字理论方法下载 的前提是同方差，因此，当残差项存在异方差时，采用ML方法估计出的参数结果不具备稳健性。二、贝叶斯空间计量模型的估计方法(一)待估参数对于空间计量模型(以空间自回归模型为例)y=pWy+£假设残差项是异方差的，即£~N(0,o2V)V=diag(v,v,・・・v)12n上述模型需要估计的参数有：POvv…v12n共计n+2个参数，存在自由度问题，难以进行参数检验。为此根据大数定律，增加了新的假设：vi服从自由度为r的卡方分布。如此以来，待估参数将减少为3个。(二)参数估计方法采用MCMC(MarkovChainMonteCarlo)参数估计 思想 教师资格思想品德鉴定表下载浅论红楼梦的主题思想员工思想动态调查问卷论语教育思想学生思想教育讲话稿 ，具体的抽样方法选择吉布斯抽样方法(Gibbssamplingapproach)在随意给定待估参数一个初始值之后，开始生成参数的新数值，并根据新数值生成其他参数的新数值，如此往复，对每一个待估参数，将得到一组生成的数值，根据该组数值，计算其均值，即为待估参数的贝叶斯估计值。三、贝叶斯空间计量模型的类型空间自回归模型far_g()空间滞后模型(空间回归自回归混合模型)sar_g()空间误差模型sem_g()广义空间模型(空间自相关模型)sac_g()四、贝叶斯空间模型与普通空间模型的选择 标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 首先按照参数显著性，以及极大似然值，确定普通空间计量模型的具体类型，之后对于该确定的类型，再判断是否需要进一步采用贝叶斯估计方法。标准一：对普通空间计量模型的残差项做图，观察参数项是否是正态分布，若非正态分布，则考虑使用贝叶斯方法估计。技巧：r=30的贝叶斯估计等价于普通空间计量模型估计，此时可以做出v的分布图，观察其是否基本等于1,若否，则应采用贝叶斯估计方法。标准二：若按标准一发现存在异方差，采用贝叶斯估计后，如果参数结果与普通空间计量方法存在较大差异，则说明采用贝叶斯估计是必要的。例1：选举投票率普通SAR与贝叶斯SAR对比：loadelect.dat;loadford.dat;y=elect(:,7)./elect(:,8);x1=elect(:,9)./elect(:,8);x2=elect(:,10)./elect(:,8);x3=elect(:,11)./elect(:,8);w=sparse(ford(:,1),ford(:,2),ford(:,3));x=[ones(3107,1)x1x2x3];res1=sar(y,x,w);res2=sar_g(y,x,w,2100,100);Vnames=strvcat('voter',‘const'，‘educ’，‘home’，‘income’)；prt(res1);prt(res2);SpatialautoregressiveModelEstimatesDependentVariable=voterR-squared=0.4605Rbar-squared=0.4600sigmaA2=0.0041Nobs,Nvars=3107,4log-likelihood=5091.6196ofiterations=11minandmaxrho=-1.0000,1.0000totaltimeinsecs=1.0530timeforlndet=0.2330timefort-stats=0.0220timeforx-impacts=0.7380drawsx-impacts=1000PaceandBarry,1999MClndetapproximationusedorderforMCappr=50iterforMCappr=30VariableCoefficientAsymptott-statz-probabilityconst-0.100304-8.4062990.000000educ0.33570421.9010990.000000home0.75406028.2122110.000000income-0.008135-8.5352120.000000rho0.527962335.7243590.000000DirectCoefficientt-statt-problower01upper99educ0.36279519.8269370.0000000.3123650.411283home0.81307027.4488840.0000000.7423420.889356income-0.008836-8.5093820.000000-0.011871-0.006258IndirectCoefficientt-statt-problower01upper99educ0.34968018.5555790.0000000.3037290.398939home0.78486314.5658870.0000000.6534110.943592income-0.008511-8.8202210.000000-0.011142-0.006208TotalCoefficientt-statt-problower01upper99educ0.71247522.9896440.0000000.6307820.785895home1.59793321.5123550.0000001.4063091.809108income-0.017348-8.9415620.000000-0.022571-0.012650检验是否存在异方差是否存在遗漏变量：贝叶斯对列向量做柱状图。bar(res.vmean);BayesianspatialautoregressivemodelHeteroscedasticmodelDependentVariable=voterR-squared=0.4425Rbar-squared=0.4419meanofsigedraws=0.0023sige,epe/(n-k)=0.0065TOC\o"1-5"\h\zr-value=4Nobs,Nvars=3107,4ndraws,nomit=2100,100totaltimeinsecs=20.6420timeforlndet=0.2370timeforsampling=19,2790PaceandBarry,1999MClndetapproximationusedorderforMCappr=50iterforMCappr=30minandmaxrho=-1.0000,1.0000PosteriorEstimatesVariableCoefficientStdDeviationp-levelconst-0.1078630.0127290.000000educ0.3484160.0180720.000000home0.7277990.0264160.000000income-0.0096030.0010500.000000rho0.5610540.0133130.000000Directlower01lower05Coefficientupper95upper99educ0.3282560.3411550.3804310.4188020.431102home0.7216090.7362560.7946800.8523520.865360income-0.013430-0.012833-0.010486-0.008285-0.007535Indirectlower01lower05Coefficientupper95upper99educ0.3401420.3548940.4140590.4770480.496021home0.7301080.7595030.8649660.9853691.023184income-0.015080-0.014207-0.011413-0.008841-0.008030Totallower01lower05Coefficientupper95upper99educ0.6716150.7023640.7944900.8896450.918055home1.4646461.5109931.6596461.8226761.878911income-0.028283-0.026981-0.021899-0.017254-0.015491对遗漏变量的测量:loadelect.dat;lat=elect(:,5);lon=elect(:,6);[lonsli]=sort(lon);lats=lat(li,1);elects=elect(li,:);y=elects(:,7)./elects(:,8);x1=elects(:,9)./elects(:,8);x2=elecrs(:,10)./elects(:,8);x2=elects(:,10)./elects(:,8);x3=elects(:,11)./elects(:,8);x=[ones(3107,1)x1x2x3];[w1ww2]=xy2cont(lons,lats);vnames=strvcat('voters','const','educ','home','income');res=sar(y,x,w,2100,100);res=sar_g(y,x,w,2100,100);prt(res,vnames);BayesianspatialautoregressivemodelHeteroscedasticmodelDependentVariable=votersR-squared=0.4402Rbar-squared=0.4396meanofsigedraws=0.0022sige,epe/(n-k)=0.0065TOC\o"1-5"\h\zr-value=4Nobs,Nvars=3107,4ndraws,nomit=2100,100totaltimeinsecs=20,3230timeforIndet=0.2460timeforsampling=18,9770PaceandBarry,1999MCIndetapproximationusedorderforMCappr=50iterforMCappr=30minandmaxrho=-1.0000,1.0000*1**1**1**1**1*vt**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1**1*vt**1*k1****************************************************************PosteriorEstimatesVariableCoefficientStdDeviationp-levelconst-0.1331820.0126330.000000educ0.3006530.0179860.000000home0.7252020.0259440.000000income-0.0082190.0010090.000000rho0.6284070.0141160.000000Directlower01lower05Coefficientupper95upper99educ0.2788640.2916610.3308810.3699910.380129home0.7197880.7409180.7981160.8546850.871987income-0.011823-0.011255-0.009045-0.006332-0.006066Indirectlower01lower05Coefficientupper95upper99educ0.3753000.4013400.4793630.5572330.582751home0.9642150.9994991.1562891.3198061.378247income-0.017674-0.016599-0.013104-0.009689-0.008661Totallower01lower05Coefficientupper95upper99educ0.6603220.6983390.8102440.9228390.954496home1.7054561.7615181.9544052.1593642.235497income-0.029407-0.027676-0.022149-0.016642-0.014568例2：elect数据2个权重矩阵——亚1W2W2=slag（W1,2）bressar（sem/sac）_gSAR（2个）SEM（2个）SAC（4个）普通*贝叶斯共计16个模型（注：可对变量统一取对数）