The ordinalbayes R package was developed for fitting
ordinal Bayesian models when there is a high-dimensional covariate
space, such as when high-throughput genomic data are used in modeling
the ordinal outcome. This package depends on the runjags R
package and JAGS (version >=4.x.x) must be installed as well. See the
JAGS and
[runjags] (https://CRAN.R-project.org/package=runjags) for
installation instructions. The package includes the function
ordinalbayes which can be used to fit LASSO
(model = "lasso"), normal spike-and-slab
(model = "normalss"), double exponential spike-and-slab
(model = "dess"), and regression-based variable inclusion
indicator Bayesian models (model = "regressvi"). Variable
selection can be performed using Bayes factor or using the posterior
distributions of the variable inclusion indicators directly. This
vignette describes the syntax required for each of our Bayesian
models.
library("ordinalbayes")
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#> 'S4Vectors::setequal' when loading 'DESeq2'The package includes a two subsets of The Cancer Genome Atlas
Cervical Squamous Cell Carcinoma and Endocervical Adenocarcinoma
(TCGA-CESC) dataset: finalSet includes 2,009 transcripts
while reducedSet includes 41 transcripts. Both datasets
include the same set of subjects who belong to FIGO stages I (N = 124), II (N = 61), and III-IV (N = 57). Additionally, the
cesc data.frame is an object that combines the phenotypic
and gene expression data into one object. To shorten run time, all
illustrations will use cesc.
head(cesc)
#> age_at_index cigarettes_per_day race Stage
#> TCGA-VS-A950-01A-11R-A42T-07 42 0.00000000 not reported 3
#> TCGA-Q1-A73Q-01A-21R-A32P-07 46 0.18082192 white 1
#> TCGA-EK-A2H1-01A-11R-A180-07 20 0.00000000 white 1
#> TCGA-EA-A44S-01A-12R-A26T-07 31 0.00000000 white 3
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 85 0.03123288 white 2
#> TCGA-EA-A97N-01A-11R-A38B-07 38 0.00000000 white 1
#> ENSG00000076344 ENSG00000077274 ENSG00000101888
#> TCGA-VS-A950-01A-11R-A42T-07 5.678609 6.720300 10.414790
#> TCGA-Q1-A73Q-01A-21R-A32P-07 2.624350 6.743087 10.320279
#> TCGA-EK-A2H1-01A-11R-A180-07 4.429953 6.716512 9.863641
#> TCGA-EA-A44S-01A-12R-A26T-07 7.021206 6.768850 10.330866
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 4.278489 6.863422 10.332698
#> TCGA-EA-A97N-01A-11R-A38B-07 4.743899 6.748497 10.677080
#> ENSG00000115548 ENSG00000122884 ENSG00000125430
#> TCGA-VS-A950-01A-11R-A42T-07 12.34056 11.67348 6.970051
#> TCGA-Q1-A73Q-01A-21R-A32P-07 13.03217 11.69802 6.694007
#> TCGA-EK-A2H1-01A-11R-A180-07 11.88161 11.91802 9.736960
#> TCGA-EA-A44S-01A-12R-A26T-07 12.29227 11.47830 7.820151
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 12.26797 10.52209 8.599117
#> TCGA-EA-A97N-01A-11R-A38B-07 12.69808 11.62760 7.292076
#> ENSG00000131370 ENSG00000135443 ENSG00000136457
#> TCGA-VS-A950-01A-11R-A42T-07 7.773317 0.2365704 4.474246
#> TCGA-Q1-A73Q-01A-21R-A32P-07 7.940475 2.8509120 4.224641
#> TCGA-EK-A2H1-01A-11R-A180-07 6.840253 0.1340269 4.000747
#> TCGA-EA-A44S-01A-12R-A26T-07 6.248571 1.9650794 2.658386
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 7.377230 2.4958251 4.158171
#> TCGA-EA-A97N-01A-11R-A38B-07 8.462590 0.8706077 6.069735
#> ENSG00000138398 ENSG00000150636 ENSG00000161277
#> TCGA-VS-A950-01A-11R-A42T-07 11.96366 6.951354 8.397064
#> TCGA-Q1-A73Q-01A-21R-A32P-07 12.19146 7.057087 8.616144
#> TCGA-EK-A2H1-01A-11R-A180-07 12.03228 5.994565 7.664759
#> TCGA-EA-A44S-01A-12R-A26T-07 11.49463 6.076752 8.229867
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 11.62506 6.153901 8.164465
#> TCGA-EA-A97N-01A-11R-A38B-07 11.91054 5.766807 7.599969
#> ENSG00000163510 ENSG00000164485 ENSG00000164651
#> TCGA-VS-A950-01A-11R-A42T-07 10.81206 5.523265 1.232149
#> TCGA-Q1-A73Q-01A-21R-A32P-07 10.87095 6.572502 7.002737
#> TCGA-EK-A2H1-01A-11R-A180-07 10.91258 5.190466 3.773971
#> TCGA-EA-A44S-01A-12R-A26T-07 10.14616 5.230594 4.125903
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 10.51710 7.611485 4.626328
#> TCGA-EA-A97N-01A-11R-A38B-07 10.65186 6.434868 3.245165
#> ENSG00000166091 ENSG00000166342 ENSG00000171121
#> TCGA-VS-A950-01A-11R-A42T-07 -0.04265304 3.8745245 5.513192
#> TCGA-Q1-A73Q-01A-21R-A32P-07 -0.09322960 0.9864192 8.369090
#> TCGA-EK-A2H1-01A-11R-A180-07 0.46102302 3.5160175 6.690186
#> TCGA-EA-A44S-01A-12R-A26T-07 1.48172747 0.3112567 7.179220
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 -0.02222228 3.6285145 6.507039
#> TCGA-EA-A97N-01A-11R-A38B-07 0.98318046 3.3422185 7.321927
#> ENSG00000177173 ENSG00000180229 ENSG00000188817
#> TCGA-VS-A950-01A-11R-A42T-07 4.446792 5.221334 -0.3054604
#> TCGA-Q1-A73Q-01A-21R-A32P-07 3.806744 5.043258 2.8640614
#> TCGA-EK-A2H1-01A-11R-A180-07 2.511395 3.628166 -0.4096528
#> TCGA-EA-A44S-01A-12R-A26T-07 3.072081 4.242614 -0.4280007
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 3.435647 4.987061 -0.2773388
#> TCGA-EA-A97N-01A-11R-A38B-07 3.787959 5.867989 2.1377124
#> ENSG00000197360 ENSG00000203601 ENSG00000225449
#> TCGA-VS-A950-01A-11R-A42T-07 -0.9218773 0.6578841 0.8891913
#> TCGA-Q1-A73Q-01A-21R-A32P-07 0.1096139 1.3319538 2.0622014
#> TCGA-EK-A2H1-01A-11R-A180-07 -1.0322035 -0.2522735 0.1200411
#> TCGA-EA-A44S-01A-12R-A26T-07 -0.3961578 4.6452716 2.3121313
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 -0.8921010 -0.1027297 1.6885515
#> TCGA-EA-A97N-01A-11R-A38B-07 -0.9470927 1.4453662 1.8141608
#> ENSG00000230201 ENSG00000233996 ENSG00000236138
#> TCGA-VS-A950-01A-11R-A42T-07 0.45515752 -0.8005787 2.39181764
#> TCGA-Q1-A73Q-01A-21R-A32P-07 -0.01038494 -0.8460940 -0.02090517
#> TCGA-EK-A2H1-01A-11R-A180-07 -0.04845732 -0.8570974 0.90786314
#> TCGA-EA-A44S-01A-12R-A26T-07 -0.56658738 0.2505256 0.87490415
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 -0.50968290 -0.7739022 0.72861666
#> TCGA-EA-A97N-01A-11R-A38B-07 -0.53019894 -0.2257776 1.77938002
#> ENSG00000236819 ENSG00000250602 ENSG00000253923
#> TCGA-VS-A950-01A-11R-A42T-07 0.6838114 1.405047 0.47003057
#> TCGA-Q1-A73Q-01A-21R-A32P-07 6.4898812 3.254435 0.33945673
#> TCGA-EK-A2H1-01A-11R-A180-07 -0.6782753 3.336353 0.02637618
#> TCGA-EA-A44S-01A-12R-A26T-07 -0.6916469 2.931575 0.44931341
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 -0.5467389 3.602136 0.23578770
#> TCGA-EA-A97N-01A-11R-A38B-07 -0.6117338 3.057354 -0.79423073
#> ENSG00000256980 ENSG00000259083 ENSG00000259134
#> TCGA-VS-A950-01A-11R-A42T-07 3.212629 2.073511 1.9863973
#> TCGA-Q1-A73Q-01A-21R-A32P-07 3.131681 2.553974 0.9570086
#> TCGA-EK-A2H1-01A-11R-A180-07 3.408530 2.962731 1.7540029
#> TCGA-EA-A44S-01A-12R-A26T-07 2.265136 2.087338 2.1799799
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 1.691849 3.295767 1.5173814
#> TCGA-EA-A97N-01A-11R-A38B-07 1.590774 3.163264 2.2831056
#> ENSG00000260484 ENSG00000263612 ENSG00000264049
#> TCGA-VS-A950-01A-11R-A42T-07 -0.7171493 -0.06975943 1.0613205
#> TCGA-Q1-A73Q-01A-21R-A32P-07 -0.7653965 1.08025444 1.9822718
#> TCGA-EK-A2H1-01A-11R-A180-07 -0.1380986 6.20400949 1.1402154
#> TCGA-EA-A44S-01A-12R-A26T-07 2.4260667 0.49979689 0.8579997
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 -0.6844628 0.79342833 0.1272949
#> TCGA-EA-A97N-01A-11R-A38B-07 -0.7394679 5.90066262 1.0206188
#> ENSG00000264954 ENSG00000265579 ENSG00000271711
#> TCGA-VS-A950-01A-11R-A42T-07 -0.58860794 2.8046547 0.157358427
#> TCGA-Q1-A73Q-01A-21R-A32P-07 -0.01342846 -0.1233080 -0.818584845
#> TCGA-EK-A2H1-01A-11R-A180-07 0.32064622 2.4109333 -0.001821686
#> TCGA-EA-A44S-01A-12R-A26T-07 -0.64840554 0.4594487 0.214261241
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 -0.55822181 2.4464137 -0.747553857
#> TCGA-EA-A97N-01A-11R-A38B-07 -0.60127115 2.5372659 -0.242044960
#> ENSG00000272071 ENSG00000276517
#> TCGA-VS-A950-01A-11R-A42T-07 3.504165 4.384537
#> TCGA-Q1-A73Q-01A-21R-A32P-07 1.179076 5.068678
#> TCGA-EK-A2H1-01A-11R-A180-07 1.124490 5.115981
#> TCGA-EA-A44S-01A-12R-A26T-07 3.398700 5.139583
#> TCGA-ZJ-AAX4-01A-11R-A42T-07 1.348471 4.523211
#> TCGA-EA-A97N-01A-11R-A38B-07 1.259106 4.805752The primary function for model fitting in the
ordinalbayes package is ordinalbayes. The
function arguments are
args(ordinalbayes)
#> function (formula, data, x = NULL, subset, center = TRUE, scale = TRUE,
#> a = 0.1, b = 0.1, model = "regressvi", gamma.ind = "fixed",
#> pi.fixed = 0.05, c.gamma = NULL, d.gamma = NULL, alpha.var = 10,
#> sigma2.0 = NULL, sigma2.1 = NULL, coerce.var = 10, lambda0 = NULL,
#> nChains = 3, adaptSteps = 5000, burnInSteps = 5000, numSavedSteps = 9999,
#> thinSteps = 3, parallel = TRUE, seed = NULL, quiet = FALSE)
#> NULLThe ordinalbayes function accepts a model
formula that specifies the ordinal outcome on the left-hand
side of the equation and any unpenalized predictor variable(s) from the
phenotypic dataset on the right-hand side of the ∼ equation; if no unpenalized predictor
variables are included, the model formula includes 1 (the intercept) on
the right-hand side of the equation. Unpenalized predictors are those
that we want to coerce into the model (e.g., age) so that no penalty is
applied. When unpenalized predictors are included (or coerced) into the
model, the user can specify the variance associated with those model
parameters (default coerce.var=10).
For example, this call fits a regression-based variable inclusion
indicator Bayesian model to predict the ordinal outcome
Stage where cigarettes_per_day+age_at_index
and age_at_index are included as unpenalized predictors
(coerced into the model) and the expression of 41 genes are included as
penalized predictors. The user should pass to x the genomic
feature data (e.g., expression of genes from high-throughput assays) to
be penalized in the fitted model, which are in columns 5-45 of the
cesc data.frame. Here a fixed constant prior for πj is set to
0.05. To shorten run time for demonstration purposes, we reduced the
number of iterations for adaptation (adaptSteps), the
number of iterations of the Markov chain to run
(burnInSteps), and the number of saved steps per chain
(numSavedSteps) for all examples.
fit<-ordinalbayes(Stage~cigarettes_per_day+age_at_index, data=cesc,x=cesc[, 5:45], model="regressvi", gamma.ind="fixed", pi.fixed=0.05, adaptSteps=500, burnInSteps=500, numSavedSteps=999)
#> Welcome to JAGS 4.3.2 on Fri Nov 8 05:16:40 2024
#> JAGS is free software and comes with ABSOLUTELY NO WARRANTY
#> Loading module: basemod: ok
#> Loading module: bugs: ok
#> . . Reading data file data.txt
#> . Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 242
#> Unobserved stochastic nodes: 87
#> Total graph size: 13583
#> . Reading parameter file inits1.txt
#> . Initializing model
#> . Adapting 500
#> -------------------------------------------------| 500
#> ++++++++++++++++++++++++++++++++++++++++++++++++++ 100%
#> Adaptation successful
#> . Updating 500
#> -------------------------------------------------| 500
#> ************************************************** 100%
#> . . . . . . Updating 2997
#> -------------------------------------------------| 2950
#> ************************************************** 99%
#> * 100%
#> . . . . Updating 0
#> . Deleting model
#> .By default the genomic features are centered
(center=TRUE) and scaled (scale=TRUE) and
three chains are run (nChains). The user can
subset the data set prior to model fitting, for example,
subset=(race=="white").
The LASSO Bayesian ordinal model can be fit by specifying
model="lasso" which assumes the penalized coefficients
βj for
j = 1, …, P are from
independent Laplace (or double exponential) distributions with parameter
λ which is from a Gamma
distribution with parameters a and b. The
default parameters are a=0.01 and b=0.01.
Like the LASSO model, the regression-based variable inclusion
indicator model assumes the penalized coefficients βj for j = 1, …, P are from
independent Laplace (or double exponential) distributions with parameter
λ which is from a Gamma
distribution with parameters a and b.
Additionally, a variable inclusion indicator γj is assumed to
follow a Bernoulli distribution with parameter πj. The user can
use either a fixed (gamma.ind="fixed") or random
(gamma.ind="random") prior for πj. When
gamma.ind="fixed", the user can specify
pi.fixed as the constant prior to be some value the (0, 1)
interval (default is 0.05). Here there are no unpenalized covariates
included in the model so the right-hand side of the model formula is
1.
fit.regressvi.fixed<-ordinalbayes(Stage~1, data=cesc,x=cesc[, 5:45], model="regressvi", gamma.ind="fixed", pi.fixed=0.05, adaptSteps=500, burnInSteps=500, numSavedSteps=999)When gamma.ind="random", the user must specify parameter
values for the Beta distribution c.gamma (e.g., 0.01) and
d.gamma (e.g. 0.19).
The normal spike-and-slab Bayesian ordinal model can be fit by
specifying model="normalss". When fitting this model the
user is required to specify the variance for the spike by setting
sigma2.0 to a small positive value (e.g., 0.01) and
variance for the slab by setting sigma2.1 to a large
positive value (e.g., 10). Additionally, a variable inclusion indicator
γj is
assumed to follow a Bernoulli distribution with parameter πj. The user can
use either a fixed (gamma.ind="fixed") or random
(gamma.ind="random") prior for πj. When
gamma.ind="fixed", the user can specify
pi.fixed as the constant prior to be some value the (0, 1)
interval (default is 0.05). Here there are no unpenalized covariates
included in the model so the right-hand side of the model formula is
1.
fit.normalss.fixed<-ordinalbayes(Stage~1, data=cesc,x=cesc[, 5:45], model="normalss", gamma.ind="fixed", pi.fixed = 0.05, sigma2.0=0.01, sigma2.1=10, adaptSteps=500, burnInSteps=500, numSavedSteps=999)When gamma.ind="random", the user must specify parameter
values for the Beta distribution c.gamma (e.g., 0.01) and
d.gamma (e.g. 0.19).
The double exponential spike-and-slab ordinal model can be fit by
specifying model="dess". Like LASSO and , the slab is taken
to be a double exponential distribution with parameter λ which follows a Gamma distribution
with parameters a and b. When fitting this
model the user is required to specify the parameter for the spike (λ0) using
lambda0 (e.g., 20). Additionally, a variable inclusion
indicator γj is assumed to
follow a Bernoulli distribution with parameter πj. The user can
use either a fixed (gamma.ind="fixed") or random
(gamma.ind="random") prior for πj. When
gamma.ind="fixed", the user can specify
pi.fixed as the constant prior to be some value the (0, 1)
interval (default is 0.05). Here there are no unpenalized covariates
included in the model so the right-hand side of the model formula is
1.
fit.dess.fixed<-ordinalbayes(Stage~1, data=cesc,x=cesc[, 5:45], model="dess", gamma.ind="fixed", pi.fixed = 0.05, lambda0=20, adaptSteps=500, burnInSteps=500, numSavedSteps=999)When gamma.ind="random", the user must specify parameter
values for the Beta distribution c.gamma (e.g., 0.01) and
d.gamma (e.g. 0.19).
Generic functions for the resulting ordinalbayes object
are available for extracting meaningful results from the resulting MCMC
chain. The print function returns several summaries from
the MCMC output for each parameter monitored including: the 95th lower
confidence limit for the highest posterior density (HPD) credible
interval (Lower95), the median value (Median), the 95th upper confidence
limit for the HPD credible interval (Upper95), the mean value (Mean),
the sample standard deviation (SD), the mode of the variable (Mode), the
Monte Carlo standard error (MCerr,) percent of SD due to MCMC (MC%ofSD),
effective sample size (SSeff), autocorrelation at a lag of 30 (AC.30),
and the potential scale reduction factor (psrf).
print(fit)
#> Lower95 Median Upper95 Mean
#> alpha0[1] -0.433475000 0.9298580 2.26676e+00 0.91275616
#> alpha0[2] 2.018540000 3.4247800 4.94128e+00 3.41229646
#> gamma.ENSG00000076344 0.000000000 0.0000000 1.00000e+00 0.32866200
#> gamma.ENSG00000077274 0.000000000 1.0000000 1.00000e+00 0.50984318
#> gamma.ENSG00000101888 0.000000000 1.0000000 1.00000e+00 0.70503837
#> gamma.ENSG00000115548 1.000000000 1.0000000 1.00000e+00 0.98298298
#> gamma.ENSG00000122884 0.000000000 0.0000000 1.00000e+00 0.05839173
#> gamma.ENSG00000125430 0.000000000 0.0000000 1.00000e+00 0.34367701
#> gamma.ENSG00000131370 0.000000000 0.0000000 1.00000e+00 0.38438438
#> gamma.ENSG00000135443 0.000000000 0.0000000 1.00000e+00 0.15382049
#> gamma.ENSG00000136457 0.000000000 0.0000000 1.00000e+00 0.18184852
#> gamma.ENSG00000138398 1.000000000 1.0000000 1.00000e+00 0.95261929
#> gamma.ENSG00000150636 0.000000000 0.0000000 1.00000e+00 0.48548549
#> gamma.ENSG00000161277 0.000000000 1.0000000 1.00000e+00 0.93693694
#> gamma.ENSG00000163510 0.000000000 0.0000000 1.00000e+00 0.05672339
#> gamma.ENSG00000164485 0.000000000 1.0000000 1.00000e+00 0.54721388
#> gamma.ENSG00000164651 0.000000000 1.0000000 1.00000e+00 0.54454454
#> gamma.ENSG00000166091 0.000000000 0.0000000 1.00000e+00 0.45812479
#> gamma.ENSG00000166342 0.000000000 0.0000000 1.00000e+00 0.14414414
#> gamma.ENSG00000171121 0.000000000 0.0000000 0.00000e+00 0.03970637
#> gamma.ENSG00000177173 1.000000000 1.0000000 1.00000e+00 0.95895896
#> gamma.ENSG00000180229 0.000000000 0.0000000 1.00000e+00 0.15682349
#> gamma.ENSG00000188817 0.000000000 0.0000000 1.00000e+00 0.40707374
#> gamma.ENSG00000197360 0.000000000 0.0000000 1.00000e+00 0.06039373
#> gamma.ENSG00000203601 0.000000000 0.0000000 1.00000e+00 0.09209209
#> gamma.ENSG00000225449 0.000000000 0.0000000 1.00000e+00 0.07874541
#> gamma.ENSG00000230201 0.000000000 0.0000000 1.00000e+00 0.36803470
#> gamma.ENSG00000233996 0.000000000 1.0000000 1.00000e+00 0.59793126
#> gamma.ENSG00000236138 0.000000000 0.0000000 0.00000e+00 0.04471138
#> gamma.ENSG00000236819 0.000000000 1.0000000 1.00000e+00 0.93393393
#> gamma.ENSG00000250602 0.000000000 0.0000000 1.00000e+00 0.32599266
#> gamma.ENSG00000253923 0.000000000 1.0000000 1.00000e+00 0.68935602
#> gamma.ENSG00000256980 0.000000000 0.0000000 1.00000e+00 0.05605606
#> gamma.ENSG00000259083 0.000000000 0.0000000 1.00000e+00 0.05038372
#> gamma.ENSG00000259134 0.000000000 1.0000000 1.00000e+00 0.69803136
#> gamma.ENSG00000260484 0.000000000 0.0000000 0.00000e+00 0.04304304
#> gamma.ENSG00000263612 0.000000000 0.0000000 1.00000e+00 0.18785452
#> gamma.ENSG00000264049 0.000000000 0.0000000 1.00000e+00 0.15215215
#> gamma.ENSG00000264954 0.000000000 0.0000000 1.00000e+00 0.21488155
#> gamma.ENSG00000265579 0.000000000 0.0000000 1.00000e+00 0.11177845
#> gamma.ENSG00000271711 0.000000000 0.0000000 1.00000e+00 0.08842176
#> gamma.ENSG00000272071 0.000000000 0.0000000 1.00000e+00 0.22288956
#> gamma.ENSG00000276517 0.000000000 1.0000000 1.00000e+00 0.94461128
#> beta.ENSG00000076344 0.000000000 0.0000000 7.43305e-01 0.17478649
#> beta.ENSG00000077274 -3.888170000 -0.1467700 0.00000e+00 -0.93716400
#> beta.ENSG00000101888 -0.987420000 -0.5514100 0.00000e+00 -0.47259610
#> beta.ENSG00000115548 0.456972000 0.9350130 1.49592e+00 0.93016342
#> beta.ENSG00000122884 0.000000000 0.0000000 1.51175e-01 0.02118685
#> beta.ENSG00000125430 0.000000000 0.0000000 7.73057e-01 0.18336678
#> beta.ENSG00000131370 -0.830980000 0.0000000 0.00000e+00 -0.21829392
#> beta.ENSG00000135443 -0.539741000 0.0000000 0.00000e+00 -0.06578075
#> beta.ENSG00000136457 -0.647580000 0.0000000 0.00000e+00 -0.09333314
#> beta.ENSG00000138398 -1.284970000 -0.8598300 0.00000e+00 -0.84204652
#> beta.ENSG00000150636 0.000000000 0.0000000 9.63402e-01 0.31474352
#> beta.ENSG00000161277 0.000000000 0.6928520 1.05848e+00 0.67259456
#> beta.ENSG00000163510 -0.095404800 0.0000000 1.89061e-02 -0.02167887
#> beta.ENSG00000164485 -0.872001000 -0.3073360 0.00000e+00 -0.32036501
#> beta.ENSG00000164651 0.000000000 0.3045340 8.91599e-01 0.32890516
#> beta.ENSG00000166091 0.000000000 0.0000000 8.86686e-01 0.26970016
#> beta.ENSG00000166342 0.000000000 0.0000000 4.72876e-01 0.05983235
#> beta.ENSG00000171121 0.000000000 0.0000000 0.00000e+00 -0.01181109
#> beta.ENSG00000177173 0.231326000 0.7670510 1.32043e+00 0.74704148
#> beta.ENSG00000180229 0.000000000 0.0000000 5.74341e-01 0.07259595
#> beta.ENSG00000188817 -0.918385000 0.0000000 6.01200e-04 -0.25678571
#> beta.ENSG00000197360 -0.177786000 0.0000000 5.28925e-02 -0.02169836
#> beta.ENSG00000203601 -0.012203000 0.0000000 3.93316e-01 0.03440799
#> beta.ENSG00000225449 -0.320337000 0.0000000 0.00000e+00 -0.03102246
#> beta.ENSG00000230201 0.000000000 0.0000000 6.79358e-01 0.17816959
#> beta.ENSG00000233996 0.000000000 0.3746720 8.72514e-01 0.34556783
#> beta.ENSG00000236138 0.000000000 0.0000000 0.00000e+00 0.01276635
#> beta.ENSG00000236819 -1.350620000 -0.8553150 0.00000e+00 -0.82994589
#> beta.ENSG00000250602 -0.688813000 0.0000000 0.00000e+00 -0.16024025
#> beta.ENSG00000253923 0.000000000 0.4490010 8.10281e-01 0.38132075
#> beta.ENSG00000256980 -0.111667000 0.0000000 1.50226e-02 -0.01945728
#> beta.ENSG00000259083 -0.000288853 0.0000000 2.65257e-03 -0.01454637
#> beta.ENSG00000259134 0.000000000 0.5588050 1.04049e+00 0.48373660
#> beta.ENSG00000260484 0.000000000 0.0000000 0.00000e+00 0.01234166
#> beta.ENSG00000263612 -0.569360000 0.0000000 7.29816e-05 -0.08485093
#> beta.ENSG00000264049 0.000000000 0.0000000 4.87576e-01 0.05984188
#> beta.ENSG00000264954 0.000000000 0.0000000 5.71368e-01 0.09499381
#> beta.ENSG00000265579 0.000000000 0.0000000 4.26671e-01 0.04332112
#> beta.ENSG00000271711 0.000000000 0.0000000 3.21571e-01 0.03133108
#> beta.ENSG00000272071 0.000000000 0.0000000 6.21315e-01 0.10270013
#> beta.ENSG00000276517 -1.199630000 -0.7801000 0.00000e+00 -0.76318384
#> lambda 0.651131000 1.4160400 2.35741e+00 1.46260996
#> cigarettes_per_day -0.426335000 0.1025620 6.40773e-01 0.10095239
#> age_at_index -0.011089100 0.0162206 4.23585e-02 0.01579986
#> SD Mode MCerr MC%ofSD SSeff AC.30
#> alpha0[1] 0.70262118 NA 0.061420785 8.7 131 4.040236e-01
#> alpha0[2] 0.75225406 NA 0.058550590 7.8 165 3.602857e-01
#> gamma.ENSG00000076344 0.46980521 0 0.020462713 4.4 527 1.045383e-01
#> gamma.ENSG00000077274 0.49998652 1 0.017777370 3.6 791 9.320344e-03
#> gamma.ENSG00000101888 0.45610161 1 0.024188016 5.3 356 1.358860e-01
#> gamma.ENSG00000115548 0.12935618 1 0.005109442 3.9 641 -4.052177e-03
#> gamma.ENSG00000122884 0.23452182 0 0.005461579 2.3 1844 2.032965e-02
#> gamma.ENSG00000125430 0.47501412 0 0.014968710 3.2 1007 -2.641471e-02
#> gamma.ENSG00000131370 0.48653059 0 0.020969202 4.3 538 5.610135e-02
#> gamma.ENSG00000135443 0.36083679 0 0.010944534 3.0 1087 1.974260e-02
#> gamma.ENSG00000136457 0.38578400 0 0.013444387 3.5 823 3.498624e-02
#> gamma.ENSG00000138398 0.21248729 1 0.012978779 6.1 268 2.716031e-01
#> gamma.ENSG00000150636 0.49987269 0 0.026435989 5.3 358 1.354807e-01
#> gamma.ENSG00000161277 0.24311692 1 0.009949310 4.1 597 5.165609e-02
#> gamma.ENSG00000163510 0.23135191 0 0.012065727 5.2 368 1.563362e-01
#> gamma.ENSG00000164485 0.49784892 1 0.020051600 4.0 616 8.233079e-02
#> gamma.ENSG00000164651 0.49809494 1 0.023571667 4.7 447 1.100634e-01
#> gamma.ENSG00000166091 0.49832653 0 0.022140968 4.4 507 1.240225e-01
#> gamma.ENSG00000166342 0.35129444 0 0.011021039 3.1 1016 1.471610e-02
#> gamma.ENSG00000171121 0.19530106 0 0.004733622 2.4 1702 4.494977e-03
#> gamma.ENSG00000177173 0.19841827 1 0.006197586 3.1 1025 -9.843752e-03
#> gamma.ENSG00000180229 0.36369495 0 0.011842343 3.3 943 -5.967982e-03
#> gamma.ENSG00000188817 0.49137081 0 0.020860697 4.2 555 9.661498e-02
#> gamma.ENSG00000197360 0.23825462 0 0.005182162 2.2 2114 -1.987087e-02
#> gamma.ENSG00000203601 0.28920416 0 0.008400792 2.9 1185 -1.286431e-02
#> gamma.ENSG00000225449 0.26938594 0 0.006999707 2.6 1481 4.508945e-03
#> gamma.ENSG00000230201 0.48235132 0 0.019704967 4.1 599 7.748766e-02
#> gamma.ENSG00000233996 0.49039750 1 0.022160180 4.5 490 9.492323e-02
#> gamma.ENSG00000236138 0.20670396 0 0.003993517 1.9 2679 4.189357e-03
#> gamma.ENSG00000236819 0.24843900 1 0.008728489 3.5 810 -1.260635e-02
#> gamma.ENSG00000250602 0.46882276 0 0.017193371 3.7 744 2.956125e-02
#> gamma.ENSG00000253923 0.46283450 1 0.019218596 4.2 580 6.061405e-02
#> gamma.ENSG00000256980 0.23006833 0 0.005440116 2.4 1789 1.103046e-02
#> gamma.ENSG00000259083 0.21877195 0 0.004419061 2.0 2451 -1.815343e-02
#> gamma.ENSG00000259134 0.45918834 1 0.024053126 5.2 364 1.764363e-01
#> gamma.ENSG00000260484 0.20298790 0 0.005152464 2.5 1552 -1.869395e-02
#> gamma.ENSG00000263612 0.39066114 0 0.010803767 2.8 1308 -4.700062e-03
#> gamma.ENSG00000264049 0.35922825 0 0.007486523 2.1 2302 3.402771e-02
#> gamma.ENSG00000264954 0.41080869 0 0.010826344 2.6 1440 5.426163e-02
#> gamma.ENSG00000265579 0.31514626 0 0.008325438 2.6 1433 -2.187072e-02
#> gamma.ENSG00000271711 0.28395467 0 0.006774902 2.4 1757 -2.008992e-03
#> gamma.ENSG00000272071 0.41625427 0 0.015910626 3.8 684 2.510316e-02
#> gamma.ENSG00000276517 0.22877560 1 0.008995935 3.9 647 7.038137e-02
#> beta.ENSG00000076344 0.27545182 NA 0.012747159 4.6 467 9.511276e-02
#> beta.ENSG00000077274 1.41669821 NA 0.062732731 4.4 510 8.087368e-02
#> beta.ENSG00000101888 0.35554978 NA 0.018770439 5.3 359 1.392913e-01
#> beta.ENSG00000115548 0.27431244 NA 0.009891473 3.6 769 -2.786978e-02
#> beta.ENSG00000122884 0.10297305 NA 0.002690444 2.6 1465 5.548370e-03
#> beta.ENSG00000125430 0.28356615 NA 0.010916030 3.8 675 -2.065471e-02
#> beta.ENSG00000131370 0.30968049 NA 0.014447889 4.7 459 4.965376e-02
#> beta.ENSG00000135443 0.17447576 NA 0.005856099 3.4 888 7.014074e-02
#> beta.ENSG00000136457 0.22033576 NA 0.007887998 3.6 780 7.115097e-02
#> beta.ENSG00000138398 0.30004735 NA 0.016354751 5.5 337 1.911974e-01
#> beta.ENSG00000150636 0.36437043 NA 0.020641486 5.7 312 1.700882e-01
#> beta.ENSG00000161277 0.26488946 NA 0.009287531 3.5 813 3.373874e-02
#> beta.ENSG00000163510 0.11887246 NA 0.007776245 6.5 234 2.653924e-01
#> beta.ENSG00000164485 0.33036993 NA 0.013893643 4.2 565 1.014205e-01
#> beta.ENSG00000164651 0.34032661 NA 0.016851767 5.0 408 1.309196e-01
#> beta.ENSG00000166091 0.33254468 NA 0.017099486 5.1 378 1.361102e-01
#> beta.ENSG00000166342 0.16326897 NA 0.005313827 3.3 944 -7.578358e-05
#> beta.ENSG00000171121 0.07220400 NA 0.001938587 2.7 1387 2.977390e-02
#> beta.ENSG00000177173 0.26274186 NA 0.008128530 3.1 1045 1.509765e-02
#> beta.ENSG00000180229 0.19029833 NA 0.006804792 3.6 782 4.409283e-03
#> beta.ENSG00000188817 0.34617478 NA 0.015648911 4.5 489 9.317959e-02
#> beta.ENSG00000197360 0.10346679 NA 0.002497440 2.4 1716 -1.300475e-02
#> beta.ENSG00000203601 0.12756907 NA 0.004482872 3.5 810 3.506626e-03
#> beta.ENSG00000225449 0.12468281 NA 0.003594500 2.9 1203 4.730983e-03
#> beta.ENSG00000230201 0.25853009 NA 0.010907662 4.2 562 1.095835e-01
#> beta.ENSG00000233996 0.32464712 NA 0.016420794 5.1 391 1.241967e-01
#> beta.ENSG00000236138 0.07335294 NA 0.001712755 2.3 1834 4.658866e-03
#> beta.ENSG00000236819 0.34651100 NA 0.013774235 4.0 633 4.639616e-02
#> beta.ENSG00000250602 0.25416918 NA 0.009952624 3.9 652 4.187546e-02
#> beta.ENSG00000253923 0.29531999 NA 0.011780088 4.0 628 6.499906e-02
#> beta.ENSG00000256980 0.09790173 NA 0.002288114 2.3 1831 -6.266798e-04
#> beta.ENSG00000259083 0.07436149 NA 0.001745832 2.3 1814 -7.809889e-03
#> beta.ENSG00000259134 0.37337270 NA 0.020512857 5.5 331 1.792189e-01
#> beta.ENSG00000260484 0.06829827 NA 0.001804714 2.6 1432 -3.442721e-02
#> beta.ENSG00000263612 0.19762962 NA 0.005877525 3.0 1131 -6.527597e-03
#> beta.ENSG00000264049 0.15801594 NA 0.003378146 2.1 2188 3.442352e-02
#> beta.ENSG00000264954 0.20159813 NA 0.005570215 2.8 1310 5.387916e-02
#> beta.ENSG00000265579 0.13953408 NA 0.004193964 3.0 1107 -1.658003e-02
#> beta.ENSG00000271711 0.11335734 NA 0.002821477 2.5 1614 -1.293232e-03
#> beta.ENSG00000272071 0.21480477 NA 0.009355345 4.4 527 4.264340e-02
#> beta.ENSG00000276517 0.29458176 NA 0.011540368 3.9 652 5.260914e-02
#> lambda 0.44499403 NA 0.017943188 4.0 615 1.038871e-01
#> cigarettes_per_day 0.27636237 NA 0.006482322 2.3 1818 -1.333869e-02
#> age_at_index 0.01402138 NA 0.001193205 8.5 138 4.131138e-01
#> psrf
#> alpha0[1] 1.0113915
#> alpha0[2] 1.0154169
#> gamma.ENSG00000076344 1.0013954
#> gamma.ENSG00000077274 1.0005987
#> gamma.ENSG00000101888 0.9997783
#> gamma.ENSG00000115548 1.0561920
#> gamma.ENSG00000122884 1.0012792
#> gamma.ENSG00000125430 1.0068505
#> gamma.ENSG00000131370 1.0011319
#> gamma.ENSG00000135443 1.0101614
#> gamma.ENSG00000136457 1.0029154
#> gamma.ENSG00000138398 1.0029560
#> gamma.ENSG00000150636 1.0034633
#> gamma.ENSG00000161277 1.0046685
#> gamma.ENSG00000163510 1.0019082
#> gamma.ENSG00000164485 1.0038864
#> gamma.ENSG00000164651 0.9998362
#> gamma.ENSG00000166091 1.0010285
#> gamma.ENSG00000166342 1.0006914
#> gamma.ENSG00000171121 1.0134976
#> gamma.ENSG00000177173 1.0152291
#> gamma.ENSG00000180229 1.0061620
#> gamma.ENSG00000188817 1.0100037
#> gamma.ENSG00000197360 1.0037385
#> gamma.ENSG00000203601 1.0019510
#> gamma.ENSG00000225449 1.0015737
#> gamma.ENSG00000230201 1.0032263
#> gamma.ENSG00000233996 1.0011983
#> gamma.ENSG00000236138 1.0048129
#> gamma.ENSG00000236819 1.0183495
#> gamma.ENSG00000250602 1.0019062
#> gamma.ENSG00000253923 1.0012277
#> gamma.ENSG00000256980 1.0061124
#> gamma.ENSG00000259083 1.0017067
#> gamma.ENSG00000259134 1.0027180
#> gamma.ENSG00000260484 1.0003839
#> gamma.ENSG00000263612 1.0019489
#> gamma.ENSG00000264049 1.0007694
#> gamma.ENSG00000264954 0.9998891
#> gamma.ENSG00000265579 1.0030010
#> gamma.ENSG00000271711 1.0042908
#> gamma.ENSG00000272071 1.0109562
#> gamma.ENSG00000276517 1.0144901
#> beta.ENSG00000076344 1.0010221
#> beta.ENSG00000077274 1.0019150
#> beta.ENSG00000101888 0.9998463
#> beta.ENSG00000115548 1.0046313
#> beta.ENSG00000122884 1.0085651
#> beta.ENSG00000125430 1.0083874
#> beta.ENSG00000131370 1.0011497
#> beta.ENSG00000135443 1.0152429
#> beta.ENSG00000136457 1.0066863
#> beta.ENSG00000138398 1.0000278
#> beta.ENSG00000150636 1.0024666
#> beta.ENSG00000161277 1.0013281
#> beta.ENSG00000163510 1.0040441
#> beta.ENSG00000164485 1.0051341
#> beta.ENSG00000164651 1.0005512
#> beta.ENSG00000166091 1.0010422
#> beta.ENSG00000166342 1.0012695
#> beta.ENSG00000171121 1.0249745
#> beta.ENSG00000177173 1.0020057
#> beta.ENSG00000180229 1.0067688
#> beta.ENSG00000188817 1.0145703
#> beta.ENSG00000197360 1.0123973
#> beta.ENSG00000203601 1.0017999
#> beta.ENSG00000225449 1.0002578
#> beta.ENSG00000230201 1.0029182
#> beta.ENSG00000233996 1.0024614
#> beta.ENSG00000236138 1.0158148
#> beta.ENSG00000236819 1.0044316
#> beta.ENSG00000250602 1.0019545
#> beta.ENSG00000253923 1.0006083
#> beta.ENSG00000256980 1.0346782
#> beta.ENSG00000259083 1.0007234
#> beta.ENSG00000259134 1.0056051
#> beta.ENSG00000260484 1.0010880
#> beta.ENSG00000263612 1.0027956
#> beta.ENSG00000264049 0.9999775
#> beta.ENSG00000264954 1.0001266
#> beta.ENSG00000265579 1.0033739
#> beta.ENSG00000271711 1.0059616
#> beta.ENSG00000272071 1.0161004
#> beta.ENSG00000276517 1.0079891
#> lambda 1.0065106
#> cigarettes_per_day 0.9998849
#> age_at_index 1.0120707The summary function provides the following output: *
alphamatrix, the MCMC output for the threshold parameters;
* betamatrix, the MCMC output for the penalized parameters;
* zetamatrix, The MCMC output for the unpenalized
parameters (if included); * gammamatrix, the MCMC output
for the variable inclusion parameters (not available when
model = "lasso");
* gammamean, the posterior mean of the variable inclusion
indicators (not available when model = "lasso"); *
gamma.BayesFactor, Bayes factor for the variable inclusion
indicators (not available when model = "lasso"); *
Beta.BayesFactor, Bayes factor for the penalized
parameters; and * lambdamatrix, the MCMC output for the
penalty parameter (not available when
model="normalss").
summary.fit<-summary(fit)
names(summary.fit)
#> [1] "alphamatrix" "betamatrix" "zetamatrix"
#> [4] "gammamatrix" "gammamean" "gamma.BayesFactor"
#> [7] "Beta.BayesFactor" "lambdamatrix"
head(summary.fit$gammamatrix)
#> gamma.ENSG00000076344 gamma.ENSG00000077274 gamma.ENSG00000101888
#> 1001 0 0 1
#> 1004 0 0 1
#> 1007 0 0 1
#> 1010 0 0 1
#> 1013 0 0 1
#> 1016 0 0 1
#> gamma.ENSG00000115548 gamma.ENSG00000122884 gamma.ENSG00000125430
#> 1001 1 0 0
#> 1004 1 0 0
#> 1007 1 0 0
#> 1010 1 0 0
#> 1013 1 0 1
#> 1016 1 0 0
#> gamma.ENSG00000131370 gamma.ENSG00000135443 gamma.ENSG00000136457
#> 1001 1 0 0
#> 1004 1 0 0
#> 1007 1 0 1
#> 1010 0 0 1
#> 1013 0 0 1
#> 1016 0 0 0
#> gamma.ENSG00000138398 gamma.ENSG00000150636 gamma.ENSG00000161277
#> 1001 1 1 1
#> 1004 1 1 1
#> 1007 1 1 1
#> 1010 1 1 1
#> 1013 1 1 1
#> 1016 1 1 1
#> gamma.ENSG00000163510 gamma.ENSG00000164485 gamma.ENSG00000164651
#> 1001 0 0 1
#> 1004 0 0 1
#> 1007 0 0 1
#> 1010 0 0 1
#> 1013 0 0 0
#> 1016 0 0 0
#> gamma.ENSG00000166091 gamma.ENSG00000166342 gamma.ENSG00000171121
#> 1001 0 0 0
#> 1004 0 0 0
#> 1007 1 0 0
#> 1010 1 0 0
#> 1013 0 0 0
#> 1016 1 0 0
#> gamma.ENSG00000177173 gamma.ENSG00000180229 gamma.ENSG00000188817
#> 1001 1 0 0
#> 1004 1 0 1
#> 1007 1 1 0
#> 1010 1 0 0
#> 1013 1 0 0
#> 1016 1 0 1
#> gamma.ENSG00000197360 gamma.ENSG00000203601 gamma.ENSG00000225449
#> 1001 0 0 0
#> 1004 0 0 0
#> 1007 0 0 0
#> 1010 0 0 0
#> 1013 0 0 0
#> 1016 0 0 0
#> gamma.ENSG00000230201 gamma.ENSG00000233996 gamma.ENSG00000236138
#> 1001 0 0 0
#> 1004 0 1 0
#> 1007 0 1 1
#> 1010 0 1 0
#> 1013 0 1 0
#> 1016 0 0 0
#> gamma.ENSG00000236819 gamma.ENSG00000250602 gamma.ENSG00000253923
#> 1001 1 1 1
#> 1004 1 1 1
#> 1007 1 0 1
#> 1010 1 0 0
#> 1013 1 0 1
#> 1016 1 1 1
#> gamma.ENSG00000256980 gamma.ENSG00000259083 gamma.ENSG00000259134
#> 1001 0 0 1
#> 1004 0 0 1
#> 1007 0 0 1
#> 1010 0 0 0
#> 1013 0 0 0
#> 1016 0 0 0
#> gamma.ENSG00000260484 gamma.ENSG00000263612 gamma.ENSG00000264049
#> 1001 0 0 0
#> 1004 0 0 0
#> 1007 0 0 1
#> 1010 0 0 0
#> 1013 0 0 0
#> 1016 0 0 0
#> gamma.ENSG00000264954 gamma.ENSG00000265579 gamma.ENSG00000271711
#> 1001 1 0 0
#> 1004 0 1 1
#> 1007 0 0 0
#> 1010 0 0 0
#> 1013 0 0 0
#> 1016 1 0 0
#> gamma.ENSG00000272071 gamma.ENSG00000276517
#> 1001 0 1
#> 1004 0 1
#> 1007 0 1
#> 1010 1 1
#> 1013 0 1
#> 1016 0 1To identify which penalized features using Bayes factor at a given threshold (e.g., 5):
names(which(summary.fit$Beta.BayesFactor>5))
#> [1] "ENSG00000076344" "ENSG00000077274" "ENSG00000101888" "ENSG00000115548"
#> [5] "ENSG00000125430" "ENSG00000131370" "ENSG00000138398" "ENSG00000150636"
#> [9] "ENSG00000161277" "ENSG00000164485" "ENSG00000164651" "ENSG00000166091"
#> [13] "ENSG00000177173" "ENSG00000188817" "ENSG00000230201" "ENSG00000233996"
#> [17] "ENSG00000236819" "ENSG00000250602" "ENSG00000253923" "ENSG00000259134"
#> [21] "ENSG00000264954" "ENSG00000272071" "ENSG00000276517"or
names(which(summary.fit$gamma.BayesFactor>5))
#> [1] "ENSG00000076344" "ENSG00000077274" "ENSG00000101888" "ENSG00000115548"
#> [5] "ENSG00000125430" "ENSG00000131370" "ENSG00000138398" "ENSG00000150636"
#> [9] "ENSG00000161277" "ENSG00000164485" "ENSG00000164651" "ENSG00000166091"
#> [13] "ENSG00000177173" "ENSG00000188817" "ENSG00000230201" "ENSG00000233996"
#> [17] "ENSG00000236819" "ENSG00000250602" "ENSG00000253923" "ENSG00000259134"
#> [21] "ENSG00000264954" "ENSG00000272071" "ENSG00000276517"Alternatively, a threshold for γ̄j could be used for variable selection.
names(which(summary.fit$gammamean>0.5))
#> [1] "ENSG00000077274" "ENSG00000101888" "ENSG00000115548" "ENSG00000138398"
#> [5] "ENSG00000161277" "ENSG00000164485" "ENSG00000164651" "ENSG00000177173"
#> [9] "ENSG00000233996" "ENSG00000236819" "ENSG00000253923" "ENSG00000259134"
#> [13] "ENSG00000276517"coefficients<-coef(fit)
coefficients$gamma[which(summary.fit$gamma.BayesFactor>5)]
#> ENSG00000076344 ENSG00000077274 ENSG00000101888 ENSG00000115548 ENSG00000125430
#> 0.3286620 0.5098432 0.7050384 0.9829830 0.3436770
#> ENSG00000131370 ENSG00000138398 ENSG00000150636 ENSG00000161277 ENSG00000164485
#> 0.3843844 0.9526193 0.4854855 0.9369369 0.5472139
#> ENSG00000164651 ENSG00000166091 ENSG00000177173 ENSG00000188817 ENSG00000230201
#> 0.5445445 0.4581248 0.9589590 0.4070737 0.3680347
#> ENSG00000233996 ENSG00000236819 ENSG00000250602 ENSG00000253923 ENSG00000259134
#> 0.5979313 0.9339339 0.3259927 0.6893560 0.6980314
#> ENSG00000264954 ENSG00000272071 ENSG00000276517
#> 0.2148815 0.2228896 0.9446113
coefficients$gamma[which(summary.fit$Beta.BayesFactor>5)]
#> ENSG00000076344 ENSG00000077274 ENSG00000101888 ENSG00000115548 ENSG00000125430
#> 0.3286620 0.5098432 0.7050384 0.9829830 0.3436770
#> ENSG00000131370 ENSG00000138398 ENSG00000150636 ENSG00000161277 ENSG00000164485
#> 0.3843844 0.9526193 0.4854855 0.9369369 0.5472139
#> ENSG00000164651 ENSG00000166091 ENSG00000177173 ENSG00000188817 ENSG00000230201
#> 0.5445445 0.4581248 0.9589590 0.4070737 0.3680347
#> ENSG00000233996 ENSG00000236819 ENSG00000250602 ENSG00000253923 ENSG00000259134
#> 0.5979313 0.9339339 0.3259927 0.6893560 0.6980314
#> ENSG00000264954 ENSG00000272071 ENSG00000276517
#> 0.2148815 0.2228896 0.9446113To obtain model predictions,
phat<-predict(fit)
table(phat$class, cesc$Stage)
#>
#> 1 2 3
#> 1 121 16 2
#> 2 3 31 14
#> 3 0 14 41The plot function provides a trace of the sampled output
and optionally the density estimate for each variable in the chain. This
function additionally adds the appropriate beta and
gamma labels for each penalized variable name.