HW4_State_Tracts

Save your API key to your working directory

use census_api_key(key = "yourkeyhere", install = T)

one time to install your key for use in tidycensus

library(tidycensus)

census_api_key(key ="f67be5a86e696eebf0c84a5a20d85f2c04f7e9ef", overwrite= T  )

## To install your API key for use in future sessions, run this function with `install = TRUE`.

options(tigris_use_cache = TRUE)

Load libraries (new)

library (car)

## Loading required package: carData

library(brms)

## Loading required package: Rcpp

## Loading required package: ggplot2

## Loading 'brms' package (version 2.6.0). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').
## Run theme_set(theme_default()) to use the default bayesplot theme.

library(pscl)

## Classes and Methods for R developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University
## Simon Jackman
## hurdle and zeroinfl functions by Achim Zeileis

library(rstan)

## Loading required package: StanHeaders

## rstan (Version 2.18.1, GitRev: 2e1f913d3ca3)

## For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores()).
## To avoid recompilation of unchanged Stan programs, we recommend calling
## rstan_options(auto_write = TRUE)

library(haven)
library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:car':
## 
##     recode

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

Extract from ACS housing data for 2010 for TX Census Tracts that includes outcome variable (median housing value) and predictor variables (poverty, education, employment)

tx_acs<-get_acs(geography = "tract", state="TX", year = 2010,
                variables=c( "DP04_0080PE", "DP03_0002PE", "DP02_0061PE", "DP03_0119PE"), geometry = T, output = "wide")

## Getting data from the 2006-2010 5-year ACS
## Getting data from the 2006-2010 5-year ACS

## Using the ACS Data Profile

## Getting data from the 2006-2010 5-year ACS

## Using the ACS Data Profile

## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

## Using the ACS Data Profile

## Getting data from the 2006-2010 5-year ACS

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## Getting data from the 2006-2010 5-year ACS

## Using the ACS Data Profile

names(tx_acs)

##  [1] "GEOID"       "NAME"        "DP04_0080PE" "DP04_0080PM" "DP03_0002PE"
##  [6] "DP03_0002PM" "DP02_0061PE" "DP02_0061PM" "DP03_0119PE" "DP03_0119PM"
## [11] "geometry"

Regression model with 3 predictors

#create a county FIPS code - 5 digit

tx_acs$county<-substr(tx_acs$GEOID, 1, 5)

#rename variables and filter missing cases
tx_acs2<-tx_acs%>%
  mutate(homevalue=DP04_0080PE, laborforce=DP03_0002PE, hsgrad=DP02_0061PE, poverty= DP03_0119PE) %>%
#  st_transform(crs = 102740)%>%
  filter(complete.cases(homevalue, laborforce, hsgrad, poverty))

class(tx_acs2)

## [1] "sf"         "tbl_df"     "tbl"        "data.frame"

tx_acs2$homevaluez<-scale(tx_acs2$homevalue, center = T, scale = T)
fit1<-glm(homevaluez~laborforce+hsgrad+poverty, data=tx_acs2)
summary(fit1)

## 
## Call:
## glm(formula = homevaluez ~ laborforce + hsgrad + poverty, data = tx_acs2)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.1155  -0.4382  -0.0954   0.3192   5.2757  
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.6206761  0.0938537   6.613 4.14e-11 ***
## laborforce  -0.0259764  0.0011470 -22.648  < 2e-16 ***
## hsgrad       0.0252939  0.0011599  21.807  < 2e-16 ***
## poverty      0.0285581  0.0009438  30.257  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.5769714)
## 
##     Null deviance: 5149.0  on 5149  degrees of freedom
## Residual deviance: 2969.1  on 5146  degrees of freedom
## AIC: 11789
## 
## Number of Fisher Scoring iterations: 2

confint(fit1)

## Waiting for profiling to be done...

##                   2.5 %      97.5 %
## (Intercept)  0.43672619  0.80462601
## laborforce  -0.02822442 -0.02372835
## hsgrad       0.02302050  0.02756720
## poverty      0.02670824  0.03040804

options(mc.cores=parallel::detectCores())
fit2<-brm(homevaluez~laborforce+hsgrad+poverty, data=tx_acs2, family=gaussian(),
          warmup=1000, #burnin for 500 interations for each chain = 1000 burnin
              iter=5000, chains=2, #2*5000 = 10000 - 1000 burnin = 9000 total iterations
              cores=2,seed = 1115, #number of computer cores, 1 per chain is good.
            refresh = 0)

## Compiling the C++ model

## Start sampling

summary(fit1)

## 
## Call:
## glm(formula = homevaluez ~ laborforce + hsgrad + poverty, data = tx_acs2)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.1155  -0.4382  -0.0954   0.3192   5.2757  
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.6206761  0.0938537   6.613 4.14e-11 ***
## laborforce  -0.0259764  0.0011470 -22.648  < 2e-16 ***
## hsgrad       0.0252939  0.0011599  21.807  < 2e-16 ***
## poverty      0.0285581  0.0009438  30.257  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.5769714)
## 
##     Null deviance: 5149.0  on 5149  degrees of freedom
## Residual deviance: 2969.1  on 5146  degrees of freedom
## AIC: 11789
## 
## Number of Fisher Scoring iterations: 2

print(summary(fit2), digits = 3)

##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: homevaluez ~ laborforce + hsgrad + poverty 
##    Data: tx_acs2 (Number of observations: 5150) 
## Samples: 2 chains, each with iter = 5000; warmup = 1000; thin = 1;
##          total post-warmup samples = 8000
## 
## Population-Level Effects: 
##            Estimate Est.Error l-95% CI u-95% CI Eff.Sample  Rhat
## Intercept     0.620     0.093    0.438    0.802       8896 1.000
## laborforce   -0.026     0.001   -0.028   -0.024       8897 1.000
## hsgrad        0.025     0.001    0.023    0.028       9840 1.000
## poverty       0.029     0.001    0.027    0.030       9109 1.000
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Eff.Sample  Rhat
## sigma    0.760     0.007    0.746    0.774       4031 1.000
## 
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample 
## is a crude measure of effective sample size, and Rhat is the potential 
## scale reduction factor on split chains (at convergence, Rhat = 1).

There is similarity between the two models but the Bayesian shows more significant effects.

Specify alternative priors to gauge robusticity

prior1<-c(set_prior("normal(0,1)", class="b"),#prior for the beta's
         set_prior("normal(0,1)", class="Intercept"), #prior for the intercept
         set_prior("inv_gamma(.5,.5)", class="sigma"))#prior for the residual std. deviation
fit3<-brm(homevaluez~laborforce+hsgrad+poverty, data=tx_acs2, family=gaussian(),
              prior = prior1, 
              warmup=1000, #burnin for 1000 interations for each chain = 1000 burnin
              iter=5000, chains=2, #2*5000 = 10000 - 2000 burnin = 8000 total iterations
              cores=2,seed = 1115, #number of computer cores, 1 per chain is good.
              save_model="fit_lm_gamma_stan.txt", refresh = 0
            )

## Compiling the C++ model

## Start sampling

95% Bayesian credible interval

out1<-as.data.frame(fit2)
out2<-as.data.frame(fit3)

mysum<-function(x){
  mu=mean(x,na.rm=T)
  sdev=sd(x,na.rm=T)
  lci=quantile(x, p=.025,na.rm=T)
  uci=quantile(x, p=.975,na.rm=T)
list(mu=mu, sd=sdev, lci=lci, uci=uci)
  }

sapply(out1, mysum )

##     b_Intercept b_laborforce b_hsgrad    b_poverty    sigma      
## mu  0.6199188   -0.02596662  0.02530446  0.02855602   0.7597098  
## sd  0.09342329  0.001144094  0.001175192 0.0009483787 0.007366503
## lci 0.4376479   -0.02820969  0.022976    0.02668773   0.7455745  
## uci 0.802344    -0.02377191  0.02761464  0.03042585   0.7741612  
##     lp__     
## mu  -5898.08 
## sd  1.555595 
## lci -5901.918
## uci -5895.993

sapply(out2, mysum)

##     b_Intercept b_laborforce b_hsgrad    b_poverty   sigma       lp__     
## mu  0.6204675   -0.02598039  0.02529288  0.02856393  0.7596457   -5896.956
## sd  0.0915618   0.00111319   0.001155704 0.000924755 0.007553085 1.571746 
## lci 0.4370923   -0.02819525  0.02299183  0.02676528  0.7451818   -5900.851
## uci 0.803352    -0.02374401  0.02755481  0.03038992  0.7746515   -5894.889

90% Bayesian credible interval

out3<-as.data.frame(fit2)
out4<-as.data.frame(fit3)

mysum<-function(x){
  mu=mean(x,na.rm=T)
  sdev=sd(x,na.rm=T)
  lci=quantile(x, p=.05,na.rm=T)
  uci=quantile(x, p=.95,na.rm=T)
list(mu=mu, sd=sdev, lci=lci, uci=uci)
  }

sapply(out3, mysum )

##     b_Intercept b_laborforce b_hsgrad    b_poverty    sigma      
## mu  0.6199188   -0.02596662  0.02530446  0.02855602   0.7597098  
## sd  0.09342329  0.001144094  0.001175192 0.0009483787 0.007366503
## lci 0.4662746   -0.02785142  0.02338406  0.02698353   0.7478034  
## uci 0.7747336   -0.02406206  0.02725169  0.03010183   0.7717638  
##     lp__     
## mu  -5898.08 
## sd  1.555595 
## lci -5901.082
## uci -5896.167

sapply(out4, mysum)

##     b_Intercept b_laborforce b_hsgrad    b_poverty   sigma       lp__     
## mu  0.6204675   -0.02598039  0.02529288  0.02856393  0.7596457   -5896.956
## sd  0.0915618   0.00111319   0.001155704 0.000924755 0.007553085 1.571746 
## lci 0.4710233   -0.02781957  0.02338992  0.0270524   0.7473473   -5899.935
## uci 0.7702039   -0.02413734  0.02721156  0.03007382  0.7721869   -5895.047

Specify alterntive priors

#Student's T regression model
prior<-c(set_prior("normal(0,1)", class="b"),#prior for the beta's
         set_prior("cauchy(0,5)", class="sigma"),#prior for the residual std. deviation
         set_prior("gamma(1,1.5)", class="nu")) #prior for the t distribution d.f.

fit4<-brm(homevaluez~laborforce+hsgrad+poverty, data=tx_acs2, family=student(),
              prior = prior, 
              warmup=1000, 
              iter=5000, chains=2, 
              cores=2,seed = 1115,
              save_model="fit4_stan.txt", refresh=0)

## Compiling the C++ model

## Start sampling

print(summary(fit4), digits=3)

##  Family: student 
##   Links: mu = identity; sigma = identity; nu = identity 
## Formula: homevaluez ~ laborforce + hsgrad + poverty 
##    Data: tx_acs2 (Number of observations: 5150) 
## Samples: 2 chains, each with iter = 5000; warmup = 1000; thin = 1;
##          total post-warmup samples = 8000
## 
## Population-Level Effects: 
##            Estimate Est.Error l-95% CI u-95% CI Eff.Sample  Rhat
## Intercept     0.659     0.083    0.500    0.820      10359 1.000
## laborforce   -0.026     0.001   -0.028   -0.024      10362 1.000
## hsgrad        0.022     0.001    0.020    0.024       9522 1.000
## poverty       0.024     0.001    0.022    0.026       7963 1.000
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Eff.Sample  Rhat
## sigma    0.487     0.010    0.467    0.507       2597 1.000
## nu       2.903     0.153    2.618    3.220       2693 1.000
## 
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample 
## is a crude measure of effective sample size, and Rhat is the potential 
## scale reduction factor on split chains (at convergence, Rhat = 1).

WAIC1<-WAIC(fit2)
WAIC2<-WAIC(fit4)
compare_ic(WAIC1, WAIC2, ic=c("waic"))

##                 WAIC     SE
## fit2        11792.25 173.14
## fit4        10985.95 151.40
## fit2 - fit4   806.30  95.10

In this comparison, the normal is not preferred and the more complicated model is better.

WAIC(fit2, fit3, compare = T)

##                 WAIC     SE
## fit2        11792.25 173.14
## fit3        11792.06 173.23
## fit2 - fit3     0.19   0.12

HW4_State_Tracts

Monica Cruz

November 5, 2018

Save your API key to your working directory

Load libraries (new)

Extract from ACS housing data for 2010 for TX Census Tracts that includes outcome variable (median housing value) and predictor variables (poverty, education, employment)

Regression model with 3 predictors

There is similarity between the two models but the Bayesian shows more significant effects.

Specify alternative priors to gauge robusticity

95% Bayesian credible interval

90% Bayesian credible interval

Specify alterntive priors

In this comparison, the normal is not preferred and the more complicated model is better.