#first plot our data
ggplot()+
geom_sf(data = chicago, aes(fill=as.numeric(poverty)))+
scale_fill_steps(
name = "poverty",
low = "white",
high = "maroon",
n.breaks = 5,
show.limits = T)+
theme_void()
##
## Call:
## lm(formula = poverty ~ unemployed + without_hs, data = model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.9658 -5.0431 0.1463 4.2113 15.9993
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.30152 2.02635 1.629 0.1082
## unemployed 1.03616 0.12222 8.478 5.23e-12 ***
## without_hs 0.13101 0.07166 1.828 0.0722 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.614 on 63 degrees of freedom
## Multiple R-squared: 0.6146, Adjusted R-squared: 0.6024
## F-statistic: 50.24 on 2 and 63 DF, p-value: 9.007e-14
##
## Global Moran I for regression residuals
##
## data:
## model: lm(formula = poverty ~ unemployed + without_hs, data = model)
## weights: chicago_list
##
## Moran I statistic standard deviate = 5.4579, p-value = 2.409e-08
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I Expectation Variance
## 0.407123871 -0.034255539 0.006539907
#Lagrange multiplier test
lm.RStests(lm, chicago_list, test = "all")
##
## Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
## dependence
##
## data:
## model: lm(formula = poverty ~ unemployed + without_hs, data = model)
## test weights: chicago_list
##
## RSerr = 22.405, df = 1, p-value = 2.208e-06
##
##
## Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
## dependence
##
## data:
## model: lm(formula = poverty ~ unemployed + without_hs, data = model)
## test weights: chicago_list
##
## RSlag = 10.447, df = 1, p-value = 0.001229
##
##
## Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
## dependence
##
## data:
## model: lm(formula = poverty ~ unemployed + without_hs, data = model)
## test weights: chicago_list
##
## adjRSerr = 12.374, df = 1, p-value = 0.0004354
##
##
## Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
## dependence
##
## data:
## model: lm(formula = poverty ~ unemployed + without_hs, data = model)
## test weights: chicago_list
##
## adjRSlag = 0.41501, df = 1, p-value = 0.5194
##
##
## Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
## dependence
##
## data:
## model: lm(formula = poverty ~ unemployed + without_hs, data = model)
## test weights: chicago_list
##
## SARMA = 22.82, df = 2, p-value = 1.108e-05
# here we see that three out of the five lagrange multiplier tests (Rserr, RSlag, SARMA) are significant since their p-value's are <0.05. This is evidence of spatial dependence. Because the spatial error model is significant for both tests, we will use that.
lm_error <- errorsarlm(poverty ~ unemployed + without_hs,
data = model,
listw = chicago_list,
zero.policy = TRUE,
na.action = na.omit)
summary(lm_error)
##
## Call:errorsarlm(formula = poverty ~ unemployed + without_hs, data = model,
## listw = chicago_list, na.action = na.omit, zero.policy = TRUE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.3775 -3.5106 -1.0496 2.6220 12.4427
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.595454 2.916467 0.8899 0.3735
## unemployed 0.827768 0.140147 5.9064 3.496e-09
## without_hs 0.335110 0.075589 4.4333 9.280e-06
##
## Lambda: 0.71704, LR test value: 24.683, p-value: 6.7583e-07
## Asymptotic standard error: 0.090613
## z-value: 7.9133, p-value: 2.4425e-15
## Wald statistic: 62.62, p-value: 2.5535e-15
##
## Log likelihood: -204.461 for error model
## ML residual variance (sigma squared): 24.56, (sigma: 4.9558)
## Number of observations: 66
## Number of parameters estimated: 5
## AIC: 418.92, (AIC for lm: 441.6)
#Here we see the lamda value is .71704, which is statistically significant and suggests spatial autocorrelation in the residuals.
#We can see from the model that unemployment and no highschool degree has a positive statistically significant impact on poverty