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Laboratório Regressão Espacial

Laboratório Regressão Espacial. Análise Espacial de Dados Geográficos SER-303 Novembro/2009. Regra de decisão. Multiplicadores de Lagrange para teste de autocorrelação espacial columbus.lagrange. Permite distinguir entre os modelos spatial lag e o spatial error.

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Laboratório Regressão Espacial

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  1. Laboratório Regressão Espacial Análise Espacial de Dados Geográficos SER-303 Novembro/2009

  2. Regra de decisão

  3. Multiplicadores de Lagrange para teste de autocorrelação espacial columbus.lagrange • Permite distinguir entre os modelos spatial lag e o spatial error. lm(formula = CRIME ~ INC + HOVAL, data = columbus) Matriz de pesos: weights: col.listw * = robusto Nesse exemplo o LMerr e o LMlag foram significantes verificando-se então suas versões robustas – opção: RMlag mais significante – rodar o spatial lag

  4. lagsarlm(CRIME~INC+HOVAL,data=columbus,listw=col.listw) • > summary(columbus.lag) • Call: • lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = col.listw) • Residuals: • Min 1Q Median 3Q Max • -37.4497095 -5.4565566 0.0016389 6.7159553 24.7107975 • Type: lag • Coefficients: (asymptotic standard errors) • Estimate Std. Error z value Pr(>|z|) • (Intercept) 46.851429 7.314754 6.4051 1.503e-10 • INC -1.073533 0.310872 -3.4533 0.0005538 • HOVAL -0.269997 0.090128 -2.9957 0.0027381 • Rho: 0.40389, LR test value:8.4179, p-value:0.0037154 • Asymptotic standard error: 0.12071 • z-value: 3.3459, p-value: 0.00082027 • Wald statistic: 11.195, p-value: 0.00082027 • Log likelihood: -183.1683 for lag model • ML residual variance (sigma squared): 99.164, (sigma: 9.9581) • Number of observations: 49 • Number of parameters estimated: 5 • AIC: 376.34, (AIC for lm: 382.75) • LM test for residual autocorrelation • test value: 0.19184, p-value: 0.66139

  5. errorsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = col.listw) • summary(columbus.err) • Call: • errorsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = col.listw) • Residuals: • Min 1Q Median 3Q Max • -34.45950 -6.21730 -0.69775 7.65256 24.23631 • Type: error • Coefficients: (asymptotic standard errors) • Estimate Std. Error z value Pr(>|z|) • (Intercept) 61.053618 5.314875 11.4873 < 2.2e-16 • INC -0.995473 0.337025 -2.9537 0.0031398 • HOVAL -0.307979 0.092584 -3.3265 0.0008794 • Lambda: 0.52089, LR test value: 6.4441, p-value: 0.011132 • Asymptotic standard error: 0.14129 • z-value: 3.6868, p-value: 0.00022713 • Wald statistic: 13.592, p-value: 0.00022713 • Log likelihood: -184.1552 for error model • ML residual variance (sigma squared): 99.98, (sigma: 9.999) • Number of observations: 49 • Number of parameters estimated: 5 • AIC: 378.31, (AIC for lm: 382.75)

  6. Comparação • O modelo SAR, spatial lag model, foi o escolhido de acordo com o diagrama do Anselin. • Pode-se comparar também, dado que os dois modelos foram rodados, o valor do log da verossimilhança – o que apresenta menor valor é pior. Nesse CAR é pior que o SAR • Os dois são melhores que o linear cujo valor de AIC é maior. • Não se compara o CAR e SAR usando o AIC.

  7. Mapas resíduos Regressão espacial SAR Regressão linear simples

  8. GWR • Largura da banda • bw <- gwr.sel ( crime~income+housing, data=columbus, coords=cbind(columbus$x, columbus$y), adapt = TRUE ) adapt=FALSE (default) - largura de banda fixa adapt=TRUE - adaptativa

  9. GWR > gwr_columbus Call: gwr(formula = crime ~ income + housing, data = columbus, coords = cbind(columbus$x, columbus$y), bandwidth = bw, gweight = gwr.Gauss, hatmatrix = TRUE) Kernel function: gwr.Gauss Fixed bandwidth: 2.275032 Summary of GWR coefficient estimates: Min. 1st Qu. Median 3rd Qu. Max. Global X.Intercept. 23.23000 54.13000 63.90000 68.76000 80.90000 68.6189 income -3.13100 -1.91300 -0.98440 -0.36860 1.29100 -1.5973 housing -1.05300 -0.37670 -0.09739 0.03006 0.79460 -0.2739 Number of data points: 49 Effective number of parameters: 29.61664 Effective degrees of freedom: 19.38336 Sigma (full EDF): 8.027396 Approximate effective # parameters (tr(S)): 23.92826 Approximate EDF (GWR p. 55, 92, tr(S)): 25.07174 Sigma (approximate EDF, tr(S)): 7.058251 Sigma (ML): 5.048836 AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21): 403.6193 AIC (GWR p. 96, eq. 4.22): 321.6617 Residual sum of squares: 1249.046 Obs: gwr.Gauss é default a outra opção é gwr.bisquare()

  10. Mapas dos coeficientes

  11. Mapa dos coeficientes

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