Loading the rstan package
library(rstan)
Loading required package: ggplot2
Loading required package: StanHeaders
rstan (Version 2.17.3, 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)
Creating a data object containing observed responses (y)
## Reading in the job placement data
dat <- read.csv(file.path(ddir, "job_placement.csv"), header = FALSE)
## Assigning variable names
colnames(dat) <- c("id", "wjcalc", "wjspl",
"wratspl", "wratcalc", "waiscalc",
"waisspl", "edlevel", "newschl",
"suspend", "expelled", "haveld", "female", "age")
summary(dat)
id wjcalc wjspl wratspl
Min. : 1.00 Min. : 13.0 Min. :19.00 Min. : 19.00
1st Qu.: 89.25 1st Qu.: 20.0 1st Qu.:37.00 1st Qu.: 32.00
Median :173.50 Median : 24.0 Median :42.00 Median : 36.00
Mean :170.57 Mean : 644.8 Mean :41.67 Mean : 346.93
3rd Qu.:253.75 3rd Qu.: 27.0 3rd Qu.:47.00 3rd Qu.: 41.75
Max. :335.00 Max. :99999.0 Max. :57.00 Max. :99999.00
wratcalc waiscalc waisspl edlevel
Min. :23.00 Min. : 6.0 Min. : 16.0 Min. : 7.0
1st Qu.:34.00 1st Qu.: 8.0 1st Qu.: 33.0 1st Qu.: 10.0
Median :38.00 Median : 10.0 Median : 38.0 Median : 12.0
Mean :38.92 Mean : 632.1 Mean : 658.1 Mean : 632.1
3rd Qu.:43.00 3rd Qu.: 13.0 3rd Qu.: 42.0 3rd Qu.: 12.0
Max. :54.00 Max. :99999.0 Max. :99999.0 Max. :99999.0
newschl suspend expelled haveld
Min. : 0 Min. : 0 Min. : 0 Min. : 0.0
1st Qu.: 0 1st Qu.: 0 1st Qu.: 0 1st Qu.: 0.0
Median : 1 Median : 1 Median : 0 Median : 0.0
Mean : 2174 Mean : 1864 Mean : 1863 Mean : 310.7
3rd Qu.: 1 3rd Qu.: 1 3rd Qu.: 0 3rd Qu.: 0.0
Max. :99999 Max. :99999 Max. :99999 Max. :99999.0
female age
Min. :0.0000 Min. :16.0
1st Qu.:0.0000 1st Qu.:18.0
Median :0.0000 Median :19.0
Mean :0.3137 Mean :19.7
3rd Qu.:1.0000 3rd Qu.:21.0
Max. :1.0000 Max. :27.0
## Extracting variables for the current example
dat.2 <- dat[ , c("wratcalc", "wjcalc", "waiscalc",
"wratspl", "wjspl", "waisspl")]
## Recoding 99999 to NA
dat.2[dat.2 == 99999] <- NA
## Creating a data set without NAs
dat.3 <- na.omit(dat.2)
## The data set containing observed responses (y) for the current example
summary(dat.3)
wratcalc wjcalc waiscalc wratspl wjspl
Min. :23.00 Min. :13.00 Min. : 6.00 Min. :19.00 Min. :19.0
1st Qu.:34.00 1st Qu.:20.00 1st Qu.: 8.00 1st Qu.:32.00 1st Qu.:37.0
Median :38.00 Median :24.00 Median :10.00 Median :36.00 Median :42.0
Mean :38.89 Mean :23.81 Mean :11.03 Mean :36.53 Mean :41.7
3rd Qu.:43.00 3rd Qu.:27.00 3rd Qu.:13.00 3rd Qu.:42.00 3rd Qu.:47.0
Max. :54.00 Max. :36.00 Max. :21.00 Max. :57.00 Max. :57.0
waisspl
Min. :16.0
1st Qu.:33.0
Median :38.0
Mean :37.2
3rd Qu.:42.0
Max. :52.0
Bayesian MCMC estimation using rstan in three steps
This three-step approach is recommended for debug purposes
Step 1 - Using the stanc() function to translate Stan code to C++
## The tr_01 object contains C++ translation for cfa-01.stan
tr_01 <- stanc("cfa-01.stan")
Step 2 - Using the stan_model() function to create an S4 class model object
## The so_01 is an S4 class model object created for tr_01
## Warnings will show up - move to the next step if the warnings are nonfatal
so_01 <- stan_model(stanc_ret = tr_01, verbose=FALSE)
In file included from fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/math/tools/config.hpp:13:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/config.hpp:39:
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
# define BOOST_NO_CXX11_RVALUE_REFERENCES
^
<command line>:6:9: note: previous definition is here
#define BOOST_NO_CXX11_RVALUE_REFERENCES 1
^
In file included from fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:1:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Core:531:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:2:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/LU:47:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:3:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Cholesky:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Jacobi:29:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:3:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Cholesky:43:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/QR:17:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Householder:27:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:5:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/SVD:48:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Geometry:58:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Dense:7:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Eigenvalues:58:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:36:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/operator_unary_plus.hpp:7:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/scal/fun/constants.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/math/constants/constants.hpp:13:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/math/tools/convert_from_string.hpp:15:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/lexical_cast.hpp:32:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/lexical_cast/try_lexical_convert.hpp:42:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/lexical_cast/detail/converter_lexical.hpp:52:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/container/container_fwd.hpp:61:
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/container/detail/std_fwd.hpp:27:1: warning: inline namespaces are a C++11 feature [-Wc++11-inline-namespace]
BOOST_MOVE_STD_NS_BEG
^
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/move/detail/std_ns_begin.hpp:18:34: note: expanded from macro 'BOOST_MOVE_STD_NS_BEG'
#define BOOST_MOVE_STD_NS_BEG _LIBCPP_BEGIN_NAMESPACE_STD
^
/Library/Developer/CommandLineTools/usr/include/c++/v1/__config:439:52: note: expanded from macro '_LIBCPP_BEGIN_NAMESPACE_STD'
#define _LIBCPP_BEGIN_NAMESPACE_STD namespace std {inline namespace _LIBCPP_NAMESPACE {
^
In file included from fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:83:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Sparse:26:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/SparseCore:66:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:83:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Sparse:27:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/OrderingMethods:71:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:83:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Sparse:29:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/SparseCholesky:43:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:83:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Sparse:32:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/SparseQR:35:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:83:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/Sparse:33:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/RcppEigen/include/Eigen/IterativeLinearSolvers:46:
/Library/Frameworks/R.framework/Versions/3.4/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 fileb1277ab9d216.cpp:743:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/rstan/include/rstan/rstaninc.hpp:3:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/rstan/include/rstan/stan_fit.hpp:36:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/services/optimize/bfgs.hpp:11:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/optimization/bfgs.hpp:9:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/optimization/lbfgs_update.hpp:6:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/circular_buffer.hpp:54:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/circular_buffer/details.hpp:20:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/move/move.hpp:30:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/move/iterator.hpp:27:
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/move/detail/iterator_traits.hpp:29:1: warning: inline namespaces are a C++11 feature [-Wc++11-inline-namespace]
BOOST_MOVE_STD_NS_BEG
^
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/BH/include/boost/move/detail/std_ns_begin.hpp:18:34: note: expanded from macro 'BOOST_MOVE_STD_NS_BEG'
#define BOOST_MOVE_STD_NS_BEG _LIBCPP_BEGIN_NAMESPACE_STD
^
/Library/Developer/CommandLineTools/usr/include/c++/v1/__config:439:52: note: expanded from macro '_LIBCPP_BEGIN_NAMESPACE_STD'
#define _LIBCPP_BEGIN_NAMESPACE_STD namespace std {inline namespace _LIBCPP_NAMESPACE {
^
In file included from fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:44:
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
static void set_zero_all_adjoints() {
^
In file included from fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:45:
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
static void set_zero_all_adjoints_nested() {
^
In file included from fileb1277ab9d216.cpp:8:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math.hpp:4:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
In file included from /Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
/Library/Frameworks/R.framework/Versions/3.4/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: 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) {
^
19 warnings generated.
Step 3 - Using the sampling() function for MCMC sampling/estimation
post_01 <- sampling(object = so_01, ## the S4 model object created in Step 2
data = data_for_stan, ## the data input (an list object)
chains = 2, ## number of MCMC chains
iter = 4000, ## total number of MCMC draws per chain
warmup = 1500) ## number of warmup draws per chain
SAMPLING FOR MODEL 'cfa-01' NOW (CHAIN 1).
Gradient evaluation took 0.000435 seconds
1000 transitions using 10 leapfrog steps per transition would take 4.35 seconds.
Adjust your expectations accordingly!
Iteration: 1 / 4000 [ 0%] (Warmup)
Iteration: 400 / 4000 [ 10%] (Warmup)
Iteration: 800 / 4000 [ 20%] (Warmup)
Iteration: 1200 / 4000 [ 30%] (Warmup)
Iteration: 1501 / 4000 [ 37%] (Sampling)
Iteration: 1900 / 4000 [ 47%] (Sampling)
Iteration: 2300 / 4000 [ 57%] (Sampling)
Iteration: 2700 / 4000 [ 67%] (Sampling)
Iteration: 3100 / 4000 [ 77%] (Sampling)
Iteration: 3500 / 4000 [ 87%] (Sampling)
Iteration: 3900 / 4000 [ 97%] (Sampling)
Iteration: 4000 / 4000 [100%] (Sampling)
Elapsed Time: 10.5965 seconds (Warm-up)
10.8877 seconds (Sampling)
21.4842 seconds (Total)
SAMPLING FOR MODEL 'cfa-01' NOW (CHAIN 2).
Gradient evaluation took 0.000124 seconds
1000 transitions using 10 leapfrog steps per transition would take 1.24 seconds.
Adjust your expectations accordingly!
Iteration: 1 / 4000 [ 0%] (Warmup)
Iteration: 400 / 4000 [ 10%] (Warmup)
Iteration: 800 / 4000 [ 20%] (Warmup)
Iteration: 1200 / 4000 [ 30%] (Warmup)
Iteration: 1501 / 4000 [ 37%] (Sampling)
Iteration: 1900 / 4000 [ 47%] (Sampling)
Iteration: 2300 / 4000 [ 57%] (Sampling)
Iteration: 2700 / 4000 [ 67%] (Sampling)
Iteration: 3100 / 4000 [ 77%] (Sampling)
Iteration: 3500 / 4000 [ 87%] (Sampling)
Iteration: 3900 / 4000 [ 97%] (Sampling)
Iteration: 4000 / 4000 [100%] (Sampling)
Elapsed Time: 10.0005 seconds (Warm-up)
11.1349 seconds (Sampling)
21.1353 seconds (Total)
Alternatively, MCMC can be done in one step using the stan() function
post_02 <- stan(file = "cfa-01.stan", ## the Stan syntax file
data = data_for_stan, ## data input for rstan
chains = 2, ## number of MCMC chains
iter = 4000, ## total number of MCMC draws per chain
warmup = 1500) ## number of warmup draws per chain
Examining the posterior distributions (MCMC draws)
The standardized factor loadings
## Trace plot for visualizing MCMC convergence
plot(post_01, plotfun = "trace", pars = c("loading_std"), inc_warmup = TRUE)
## Density plot for factor loadings
plot(post_01, pars = "loading_std", show_density = TRUE, ci_level = 0.5)
ci_level: 0.5 (50% intervals)
outer_level: 0.95 (95% intervals)
## Descriptive table for summarizing the posterior distribution
print(post_01, pars = "loading_std", probs = c(.025, .975),
digits = 2, mode = TRUE, use_cache = FALSE)
Inference for Stan model: cfa-01.
2 chains, each with iter=4000; warmup=1500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=5000.
mean se_mean sd 2.5% 97.5% n_eff Rhat
loading_std[1] 0.95 0 0.04 0.87 1.04 714 1
loading_std[2] 0.91 0 0.04 0.82 1.00 1039 1
loading_std[3] 0.72 0 0.05 0.63 0.82 2132 1
loading_std[4] 0.95 0 0.04 0.87 1.04 953 1
loading_std[5] 0.96 0 0.04 0.88 1.05 860 1
loading_std[6] 0.95 0 0.04 0.87 1.04 932 1
Samples were drawn using NUTS(diag_e) at Wed May 16 14:49:30 2018.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
The factor correlation
## Trace plot for visualizing MCMC convergence
## factor_cor[1,1] and factor_cor[2,2] were fixed to 1 for model identification
plot(post_01, plotfun = "trace", pars = c("factor_cor"), inc_warmup = TRUE)
## Descriptive table for summarizing the posterior distribution
print(post_01, pars = "factor_cor", probs = c(.025, .975),
digits = 2, mode = TRUE, use_cache = FALSE)
Inference for Stan model: cfa-01.
2 chains, each with iter=4000; warmup=1500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=5000.
mean se_mean sd 2.5% 97.5% n_eff Rhat
factor_cor[1,1] 1.00 0 0.00 1.00 1.00 5000 NaN
factor_cor[1,2] 0.56 0 0.04 0.47 0.63 696 1
factor_cor[2,1] 0.56 0 0.04 0.47 0.63 696 1
factor_cor[2,2] 1.00 0 0.00 1.00 1.00 3002 1
Samples were drawn using NUTS(diag_e) at Wed May 16 14:49:30 2018.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
Unstandardized indicator intercept
## Trace plot for visualizing MCMC convergence
plot(post_01, plotfun = "trace", pars = c("intercept_unstd"), inc_warmup = TRUE)
## Descriptive table for summarizing the posterior distribution
print(post_01, pars = 'intercept_unstd', probs = c(.025,.975),
digits = 2, use_cache = FALSE)
Inference for Stan model: cfa-01.
2 chains, each with iter=4000; warmup=1500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=5000.
mean se_mean sd 2.5% 97.5% n_eff Rhat
intercept_unstd[1] 38.90 0.01 0.35 38.20 39.56 588 1
intercept_unstd[2] 23.82 0.01 0.25 23.33 24.30 631 1
intercept_unstd[3] 11.03 0.01 0.19 10.65 11.40 914 1
intercept_unstd[4] 36.55 0.02 0.38 35.80 37.30 630 1
intercept_unstd[5] 41.72 0.02 0.40 40.96 42.51 628 1
intercept_unstd[6] 37.22 0.01 0.38 36.49 37.95 631 1
Samples were drawn using NUTS(diag_e) at Wed May 16 14:49:30 2018.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
Unstandardized indicator residuals
## Trace plot for visualizing MCMC convergence
plot(post_01, plotfun = "trace", pars = c("residual_unstd"), inc_warmup = TRUE)
## Trace plot for visualizing MCMC convergence
print(post_01, pars = 'residual_unstd', probs = c(.025,.975),
digits = 2, use_cache = FALSE)
Inference for Stan model: cfa-01.
2 chains, each with iter=4000; warmup=1500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=5000.
mean se_mean sd 2.5% 97.5% n_eff Rhat
residual_unstd[1] 1.99 0.02 0.28 1.40 2.49 206 1.01
residual_unstd[2] 1.98 0.01 0.14 1.69 2.27 550 1.01
residual_unstd[3] 2.33 0.00 0.10 2.14 2.54 5000 1.00
residual_unstd[4] 2.27 0.00 0.14 2.00 2.56 5000 1.00
residual_unstd[5] 2.16 0.00 0.15 1.87 2.45 3392 1.00
residual_unstd[6] 2.29 0.00 0.14 2.03 2.56 5000 1.00
Samples were drawn using NUTS(diag_e) at Wed May 16 14:49:30 2018.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
