Homework4 Dem 7473
Craig, Scott
11/3/2018
For this assignment, I used the 2016 ACS 5 yr data set.
I filtered my data to contain working (>35 hrs/week) immigrants, between the ages of 18 and 65. The idea for the models is to evaluate the effects of some independent variables on immigrnats (to the US) income.
Dependent variable: Income. I used the z-scale of the natural log of income. Independent Variables:
1st model: z-scaled age. Dummy variable education (1 for greater than high school or zero for less than) and gender.
2nd model: added z scaled SEI (socioeconomic index from country of origin) and z-scaled years living in the US.
usa_00005 <- read_csv("usa_00005.csv")
acs <- as.tibble(usa_00005)
acs <- acs %>%
filter(BPL > 120) %>%
filter( AGE >= 18 & AGE <+ 65) %>%
filter(UHRSWORK >= 35) %>%
mutate(
income = log(INCWAGE),
zage = scale(AGE),
edu = ifelse(EDUC >= 6, 1, 0),#at least high school educ
sex = SEX - 1
) %>%
filter(income <= 20 & income >= -20)
acs <- acs %>%
filter(SPEAKENG >=1 & SPEAKENG <= 7) %>%
mutate(
zinc = scale(income),
zyrsusa = scale(YRSUSA1),
speakeng = ifelse(SPEAKENG >= 2 & SPEAKENG <= 6,1,0),# 1 if speak english, else 0
zsei = scale(SEI)
)
outliers <- acs %>%
filter(zinc >= 4 | zinc <= -4)
#print(outliers$zinc)
acs[complete.cases(acs),]## # A tibble: 805,835 x 42
## YEAR DATANUM SERIAL HHWT GQ PERNUM PERWT NCHILD SEX AGE RACE
## <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
## 1 2016 5 32 25 1 1 24 1 2 48 1
## 2 2016 5 47 12 1 1 12 1 2 31 6
## 3 2016 5 49 15 1 2 16 0 1 25 1
## 4 2016 5 59 23 1 2 24 1 1 45 1
## 5 2016 5 60 12 1 2 13 0 2 58 1
## 6 2016 5 64 43 1 2 59 3 1 27 7
## 7 2016 5 74 12 1 2 13 1 1 47 1
## 8 2016 5 80 13 1 1 13 0 1 39 1
## 9 2016 5 81 8 1 2 8 3 2 38 7
## 10 2016 5 92 15 1 1 15 2 1 28 1
## # ... with 805,825 more rows, and 31 more variables: RACED <int>,
## # BPL <int>, BPLD <int>, CITIZEN <int>, YRSUSA1 <int>, SPEAKENG <int>,
## # EDUC <int>, EDUCD <int>, EMPSTAT <int>, EMPSTATD <int>, OCC <int>,
## # OCC2010 <int>, IND <int>, OCCSOC <chr>, INDNAICS <chr>,
## # UHRSWORK <int>, INCTOT <int>, INCWAGE <int>, POVERTY <int>,
## # OCCSCORE <int>, SEI <int>, PRENT <dbl>, EDSCOR90 <dbl>, income <dbl>,
## # zage <dbl>, edu <dbl>, sex <dbl>, zinc <dbl>, zyrsusa <dbl>,
## # speakeng <dbl>, zsei <dbl>rm(usa_00005); gc()## used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
## Ncells 2184006 116.7 3665610 195.8 NA 3665610 195.8
## Vcells 25524018 194.8 90797206 692.8 16384 113343863 864.8index <- sample(1:nrow(acs), 10000)
acs.sample <- acs[index,]
priors1 <- c(set_prior("normal(0,1)", class = "b"),
set_prior("normal(0,1)", class = "Intercept"),
set_prior("inv_gamma(.5,.5)", class = "sigma"))
priors2 <- c(set_prior("normal(0,2)", class = "b"),
set_prior("normal(0,2)", class = "Intercept"),
set_prior("inv_gamma(.75,.75)", class = "sigma"))
options(mc.cores = parallel::detectCores())
fit.1 <- brm(zinc|weights(PERWT) ~ zage + edu + sex, data = acs.sample, family = gaussian(),
prior = priors1,
warmup = 1500,
iter = 6000, chains = 2,
cores = 2, seed = 1230, refresh=0)## In file included from filefca699a5c97.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:18:8: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
## size_t fft_next_good_size(size_t N) {
## ^
## 15 warnings generated.out1 <- as.data.frame(fit.1)
#print(summary(fit.1),digits=4)
mysum <- function(x){
mu=mean(x,na.rm=T)
sdev = sd(x, na.rm = T)
lci = quantile(x, p = 0.025, na.rm = T)
lci.5 = quantile(x, p = 0.05, na.rm = T)
lci.95 = quantile(x, p = .95, na.rm = T)
uci = quantile(x, p = .975, na.rm = T)
list(mu=mu, sd=sdev, lci=lci, lci.5 = lci.5, lci.95 = lci.95, uci=uci)
}
sapply(out1,mysum)## b_Intercept b_zage b_edu b_sex sigma lp__
## mu -0.5404309 0.1956962 0.7402886 -0.2744528 0.9033936 -320028.4
## sd 0.004309835 0.00181907 0.00463605 0.003843368 0.001293743 1.628919
## lci -0.5488204 0.1921656 0.731346 -0.2819636 0.9008442 -320032.5
## lci.5 -0.5475589 0.1927901 0.7327038 -0.2807811 0.9012731 -320031.5
## lci.95 -0.5334053 0.198691 0.7478129 -0.2680061 0.9055041 -320026.4
## uci -0.5320742 0.1992708 0.7492153 -0.266862 0.9059133 -320026.2plot.zage <- ggplot()+geom_density(data = acs, aes(zage), col = "red", alpha = .5, lwd = 1.5)
plot.edu <- ggplot()+geom_density(data = acs, aes(edu), col = "red", alpha = .5, lwd = 1.5)
plot.sex <- ggplot()+geom_density(data = acs, aes(sex), col = "red", alpha = .5, lwd = 1.5)
plot.zsei <- ggplot()+geom_density(data = acs, aes(zsei), col = "red", alpha = .5, lwd = 1.5)
plot.zyrsusa <- ggplot()+geom_density(data = acs, aes(zyrsusa), col = "red", alpha = .5, lwd = 1.5)
#plot(fit.1, N=2)
#####Bayesian p-values
bayespval <- function(x){
if(mean(x ) < 0){
pval = mean(x < 0)
}
else{
pval = mean(x > 0)
}
list(pval = pval)
}
b.pval.out1 <- sapply(out1, bayespval)
#save(fit.1, file = "fit_1.rda")
#save(fit.1.p2, file = "fit_1_p2.rda")
#save(fit.2, file = "fit_2.rda")
####same model, different priors
fit.1.p2 <- brm(zinc|weights(PERWT) ~ zage + edu + sex, data = acs.sample, family = gaussian(),
prior = priors2,
warmup = 1000,#using default priors as the different distributions
iter = 5000, chains = 2,
cores = 2, seed = 1230, refresh=0)## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Core:531:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:2:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/LU:47:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:3:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Cholesky:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Jacobi:29:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:3:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Cholesky:43:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/QR:17:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Householder:27:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SVD:48:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Geometry:58:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Eigenvalues:58:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:26:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseCore:66:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:27:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/OrderingMethods:71:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseCholesky:43:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:32:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseQR:35:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:33:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/IterativeLinearSolvers:46:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:44:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:13: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
## static void set_zero_all_adjoints() {
## ^
## In file included from filefca3a1a57f5.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:70:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:18:8: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
## size_t fft_next_good_size(size_t N) {
## ^
## 15 warnings generated.out1.p2 <- as.data.frame(fit.1.p2)
#plot(fit.1.p2, N=2)
#print(summary(fit.1.p2,digits=3))
b.pval.out1.p2 <- sapply(out1.p2, bayespval)
#####adding covariates
#tried to add two covariates but it didn't work out so well, so just added one
#Sys.setenv(USE_CXX14 = 1)
fit.2 <- brm(zinc|weights(PERWT) ~ zage + edu + sex + zsei + zyrsusa, data = acs.sample, family = gaussian(),
prior = priors1,
warmup = 1500,
iter = 6000, chains = 2,
cores = 2, seed = 1230, refresh=0)## In file included from filefca3bf23931.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from filefca3bf23931.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:13: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
## static void set_zero_all_adjoints() {
## ^
## In file included from filefca3bf23931.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
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## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:18:8: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
## size_t fft_next_good_size(size_t N) {
## ^
## 15 warnings generated.out2 <- as.data.frame(fit.2)
#plot(fit.2, N=2)
#print(summary(fit.2),digits=4)
b.pval.out2 <- sapply(out2, bayespval)
#waic1 <- WAIC(fit.1)
#waic2 <- WAIC(fit.2)
waic.hw4 <- waic(fit.1,fit.2, compare = T)
#loo.hw4 <- loo(fit.1,fit.2, reloo = T)#This isn't working well for me. Making the executive decision to not run it
#####inla
library(INLA)
inla.setOption("enable.inla.argument.weights", TRUE)
mod1 <- inla(zinc ~ zage + edu + sex, weights = acs.sample$PERWT,
data = acs.sample,
control.compute = list(waic = T),
family = "gaussian",
num.threads = 2)
#summary((mod1))
mod1.rob <- inla(zinc ~ zage + edu + sex, weights = acs.sample$PERWT,
data = acs.sample,
family = "t",
control.compute = list(waic = T),
control.family = list(hyper=list(dof=list(initial=3, fixed=T))),
num.threads = 2)
#summary(mod1.rob)
mod2 <- inla(zinc ~ zage + edu + sex + zsei + zyrsusa, weights = acs.sample$PERWT,
data = acs.sample,
control.compute = list(waic = T),
family = "gaussian",
num.threads = 2)
#summary(mod2)The variables
Looking at the distributions of the 5 variables that will be used:
Z scaled AGE
plot.zage
Dichotomous Education variable (1 for HS education 0 for less than):
plot.edu
Gender
plot.edu
Z scaled socioeconomic index (This distribution looks odd, but I believe it is because of the sheer difference in number of immigrants from various countries)
plot.zsei
And the last is the Z scaled number of years each immigrant has spent in the US
plot.zyrsusa
The Results
basic
The results for the first model (3 regressors) with MCMC and INLA are:
The MCMC can be summarized as follows:
print(summary(fit.1),digits=4) #MCMC## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: zinc | weights(PERWT) ~ zage + edu + sex
## Data: acs.sample (Number of observations: 10000)
## Samples: 2 chains, each with iter = 6000; warmup = 1500; thin = 1;
## total post-warmup samples = 9000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.5404 0.0043 -0.5488 -0.5321 8820 1.0000
## zage 0.1957 0.0018 0.1922 0.1993 11051 0.9999
## edu 0.7403 0.0046 0.7313 0.7492 7856 1.0001
## sex -0.2745 0.0038 -0.2820 -0.2669 8631 1.0000
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 0.9034 0.0013 0.9008 0.9059 13499 0.9999
##
## 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).print(summary(mod1),digits=4)#INLA##
## Call:
## c("inla(formula = zinc ~ zage + edu + sex, family = \"gaussian\", ", " data = acs.sample, weights = acs.sample$PERWT, control.compute = list(waic = T), ", " num.threads = 2)")
##
## Time used:
## Pre-processing Running inla Post-processing Total
## 0.9755 4.4635 0.4588 5.8978
##
## Fixed effects:
## mean sd 0.025quant 0.5quant 0.975quant mode kld
## (Intercept) -0.5404 0.0043 -0.5488 -0.5404 -0.5320 -0.5404 0
## zage 0.1957 0.0018 0.1922 0.1957 0.1993 0.1957 0
## edu 0.7402 0.0046 0.7311 0.7402 0.7494 0.7402 0
## sex -0.2745 0.0038 -0.2818 -0.2745 -0.2671 -0.2745 0
##
## The model has no random effects
##
## Model hyperparameters:
## mean sd 0.025quant 0.5quant
## Precision for the Gaussian observations 1.226 0.0035 1.219 1.226
## 0.975quant mode
## Precision for the Gaussian observations 1.233 1.226
##
## Expected number of effective parameters(std dev): 5.828(0.0053)
## Number of equivalent replicates : 1715.77
##
## Watanabe-Akaike information criterion (WAIC) ...: 639500.79
## Effective number of parameters .................: 284.32
##
## Marginal log-Likelihood: -320035.79
## Posterior marginals for linear predictor and fitted values computedand can be summarized as follows:
sapply(out1,mysum)## b_Intercept b_zage b_edu b_sex sigma lp__
## mu -0.5404309 0.1956962 0.7402886 -0.2744528 0.9033936 -320028.4
## sd 0.004309835 0.00181907 0.00463605 0.003843368 0.001293743 1.628919
## lci -0.5488204 0.1921656 0.731346 -0.2819636 0.9008442 -320032.5
## lci.5 -0.5475589 0.1927901 0.7327038 -0.2807811 0.9012731 -320031.5
## lci.95 -0.5334053 0.198691 0.7478129 -0.2680061 0.9055041 -320026.4
## uci -0.5320742 0.1992708 0.7492153 -0.266862 0.9059133 -320026.2From these results we can see that Rhat’s are all near one (good), estimated errors are all fairly low and non-zero, zero is not contained in any of the bayesian credible intervals and both age and education have positive correlations while gender has a negative (women) correlation on income. We also see that education is the most dominant covariate among these three covariates more than doubling the effect of gender.
Robusticity
Checking for Robusticity with both MCMC and INLA. Note that the MCMC model was checked by changing the parameters of the normal distribution and the INLA model was tested with a different distribution (T with 2 df).
print(summary(fit.1.p2,digits=4))#MCMC## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: zinc | weights(PERWT) ~ zage + edu + sex
## Data: acs.sample (Number of observations: 10000)
## 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 -0.54 0.00 -0.55 -0.53 6519 1.00
## zage 0.20 0.00 0.19 0.20 10830 1.00
## edu 0.74 0.00 0.73 0.75 5648 1.00
## sex -0.27 0.00 -0.28 -0.27 6254 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 0.90 0.00 0.90 0.91 12030 1.00
##
## 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).summary(mod1.rob)##
## Call:
## c("inla(formula = zinc ~ zage + edu + sex, family = \"t\", data = acs.sample, ", " weights = acs.sample$PERWT, control.compute = list(waic = T), ", " control.family = list(hyper = list(dof = list(initial = 3, ", " fixed = T))), num.threads = 2)")
##
## Time used:
## Pre-processing Running inla Post-processing Total
## 0.8889 14.7290 0.3736 15.9915
##
## Fixed effects:
## mean sd 0.025quant 0.5quant 0.975quant mode kld
## (Intercept) -0.5283 0.0041 -0.5363 -0.5283 -0.5204 -0.5283 0
## zage 0.1868 0.0018 0.1834 0.1868 0.1903 0.1868 0
## edu 0.7372 0.0044 0.7285 0.7372 0.7458 0.7372 0
## sex -0.2722 0.0036 -0.2793 -0.2722 -0.2650 -0.2722 0
##
## The model has no random effects
##
## Model hyperparameters:
## mean sd 0.025quant 0.5quant
## precision for the student-t observations 1.295 0.004 1.287 1.295
## 0.975quant mode
## precision for the student-t observations 1.303 1.295
##
## Expected number of effective parameters(std dev): 5.959(0.0056)
## Number of equivalent replicates : 1678.12
##
## Watanabe-Akaike information criterion (WAIC) ...: 631633.27
## Effective number of parameters .................: 258.27
##
## Marginal log-Likelihood: -315873.92
## Posterior marginals for linear predictor and fitted values computedThese results match almost exactly the results of our original result. Its not until the third decimal in any category that we begin to see differences, so our check for robusticity is satisfied. ####Added ZSEI and ZYRSUSA results for both MCMC and INLA:
print(summary(fit.2),digits=4)#MCMC## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: zinc | weights(PERWT) ~ zage + edu + sex + zsei + zyrsusa
## Data: acs.sample (Number of observations: 10000)
## Samples: 2 chains, each with iter = 6000; warmup = 1500; thin = 1;
## total post-warmup samples = 9000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.1280 0.0041 -0.1361 -0.1199 9442 1.0001
## zage 0.1372 0.0019 0.1335 0.1410 11253 0.9999
## edu 0.3128 0.0044 0.3039 0.3214 8327 1.0000
## sex -0.3474 0.0034 -0.3538 -0.3408 10630 0.9998
## zsei 0.4332 0.0018 0.4297 0.4368 13027 1.0001
## zyrsusa 0.0954 0.0019 0.0915 0.0991 11336 0.9999
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 0.8045 0.0012 0.8022 0.8067 16496 0.9999
##
## 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).summary(mod2)##
## Call:
## c("inla(formula = zinc ~ zage + edu + sex + zsei + zyrsusa, family = \"gaussian\", ", " data = acs.sample, weights = acs.sample$PERWT, control.compute = list(waic = T), ", " num.threads = 2)")
##
## Time used:
## Pre-processing Running inla Post-processing Total
## 0.9531 4.5912 0.4651 6.0094
##
## Fixed effects:
## mean sd 0.025quant 0.5quant 0.975quant mode kld
## (Intercept) -0.1280 0.0041 -0.1361 -0.1280 -0.1198 -0.1280 0
## zage 0.1372 0.0019 0.1334 0.1372 0.1409 0.1372 0
## edu 0.3128 0.0045 0.3040 0.3128 0.3215 0.3128 0
## sex -0.3474 0.0034 -0.3540 -0.3474 -0.3408 -0.3474 0
## zsei 0.4332 0.0018 0.4297 0.4332 0.4367 0.4332 0
## zyrsusa 0.0954 0.0020 0.0915 0.0954 0.0992 0.0954 0
##
## The model has no random effects
##
## Model hyperparameters:
## mean sd 0.025quant 0.5quant
## Precision for the Gaussian observations 1.546 0.0044 1.538 1.546
## 0.975quant mode
## Precision for the Gaussian observations 1.555 1.546
##
## Expected number of effective parameters(std dev): 8.305(0.0067)
## Number of equivalent replicates : 1204.08
##
## Watanabe-Akaike information criterion (WAIC) ...: 582283.95
## Effective number of parameters .................: 398.69
##
## Marginal log-Likelihood: -291867.34
## Posterior marginals for linear predictor and fitted values computedAs we can see the results of all three models (basic, robusticity check and added variables) are fairly similar (almost exactly so) whether looking at the results of MCMC or INLA.
When the extra two variables are added the results differ quite a bit. First we note that all of the Rhats are near one and zero is not contained in any of the CI’s. All correlations but gender are positive, and like the first result, gender remains a negative correlation when determining income. The Z-scaled SEI score becomes the most dominant covariate, followed by gender when evaluating among these five covariates. Education falls to third place at about half the importance of ZSEI.
When looking at the WAICs,
waic.hw4## WAIC SE
## fit.1 640257.66 7588.73
## fit.2 583998.40 8061.03
## fit.1 - fit.2 56259.27 2795.64we see that the WAIc for the the model with five variables has a smaller waic by almost 6000 although it does have a slightly higher SE. Overall, including thee extra two variables makes a stronger model.
We also note that using INLA produced very similar results as the MCMC in a much shorter time.