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README.md
In catalytic: Tools for Applying Catalytic Priors in Statistical Modeling
catalytic
The catalytic package enhances the stability and accuracy of
Generalized Linear Models (GLMs) and Cox proportional hazards models
(COX) in R, especially in high-dimensional or sparse data settings
where traditional methods struggle. By employing catalytic prior
distributions, this package integrates observed data with synthetic data
generated from simpler models, effectively reducing issues like
overfitting. This approach provides more robust parameter estimation,
making catalytic a valuable tool for complex and limited-data
scenarios.
Installation
You can install the released version of catalytic from
CRAN with:
install.packages("catalytic")
## Installing package into '/private/var/folders/j5/bktz8wt94hv7m_wtcc0k6ymh0000gn/T/RtmpNJNjW2/temp_libpath107b87e07f100'
## (as 'lib' is unspecified)
## Warning: package 'catalytic' is not available for this version of R
##
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
library(catalytic)
Example
set.seed(1)
data <- data.frame(
X1 = stats::rnorm(10),
X2 = stats::rnorm(10),
Y = stats::rnorm(10)
)
# Step 1: Initialization
cat_init <- cat_glm_initialization(
formula = Y ~ 1, # Formula for a simple model to generate synthetic response
family = gaussian,
data = data,
syn_size = 100 # Synthetic data size
)
print(cat_init)
## cat_glm_initialization
## formula: Y ~ 1
## model: Unknown Variance
## custom variance: NULL
## family: gaussian [identity]
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## ------
## Observation Data Information:
## covariates dimention: 10 rows with 2 column(s)
## head(data) :
## [only show the head of first 10 columns]
##
## X1 X2 Y
## 1 -0.6264538 1.51178117 0.91897737
## 2 0.1836433 0.38984324 0.78213630
## 3 -0.8356286 -0.62124058 0.07456498
## 4 1.5952808 -2.21469989 -1.98935170
## 5 0.3295078 1.12493092 0.61982575
## 6 -0.8204684 -0.04493361 -0.05612874
##
## ------
## Synthetic Data Information:
## covariates dimention: 100 rows with 2 column(s)
## head(data):
## [only show the head of first 10 columns]
##
## X1 X2 Y
## 1 -0.8356286 0.5953590 -0.1336732
## 2 -0.3053884 0.6855034 -0.1336732
## 3 -0.8204684 0.3898432 -0.1336732
## 4 0.7383247 0.5939013 -0.1336732
## 5 0.1836433 0.7523157 -0.1336732
## 6 0.1836433 -0.7461351 -0.1336732
##
## data generation process:
## [only show the first 10 columns]
##
## Covariate Type Process
## 1 X1 Continuous Coordinate
## 2 X2 Continuous Coordinate->Deskewing
##
## ------
## * For help interpreting the printed output see ?print.cat_initialization
# Step 2: Choose Method(s)
## Method 1 - Estimation with fixed tau
cat_glm_model <- cat_glm(
formula = Y ~ ., # Formula for model fitting
cat_init = cat_init, # Output object from `cat_glm_initialization`
tau = 10 # Down-weight factor for synthetic data
)
print(cat_glm_model)
## cat_glm
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## tau: 10
## family: gaussian [identity]
## ------
## coefficients' information:
## (Intercept) X1 X2
## -0.199 -0.402 0.250
##
## ------
## * For help interpreting the printed output see ?print.cat
print(predict(cat_glm_model))
## 1 2 3 4 5 6
## 0.43141012 -0.17506574 -0.01774890 -1.39427971 -0.04996112 0.12024636
## 7 8 9 10
## -0.39882013 -0.25973457 -0.22499036 0.07272498
## Method 2 - Estimation with selective tau
cat_glm_tune_model <- cat_glm_tune(
formula = Y ~ .,
cat_init = cat_init,
tau_seq = seq(1, 10) # Vector of values for downweighting synthetic data
)
print(cat_glm_tune_model)
## cat_glm_tune
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## tau sequnce: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
## family: gaussian
## risk estimate method: parametric_bootstrap
## discrepancy method: mean_square_error
##
## optimal tau: 10
## minimun risk estimate: 1.539
## ------
## coefficients' information:
##
## (Intercept) X1 X2
## -0.199 -0.402 0.250
##
## ------
## * For help interpreting the printed output see ?print.cat_tune
print(predict(cat_glm_tune_model))
## 1 2 3 4 5 6
## 0.43141012 -0.17506574 -0.01774890 -1.39427971 -0.04996112 0.12024636
## 7 8 9 10
## -0.39882013 -0.25973457 -0.22499036 0.07272498
plot(cat_glm_tune_model, text_pos = 2)
## Method 3 - Bayesian posterior sampling with fixed tau
cat_glm_bayes_model <- cat_glm_bayes(
formula = Y ~ .,
cat_init = cat_init,
tau = 10
)
##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.5e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
## Chain 1: Adjust your expectations accordingly!
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## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
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print(cat_glm_bayes_model)
## cat_glm_bayes
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## tau: 10
## family: gaussian [identity]
## stan algorithm: NUTS
## stan chain: 4
## stan iter: 2000
## stan warmup: 1000
## ------
## coefficients' information:
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5%
## (Intercept) -0.196 0.003 0.156 -0.504 -0.298 -0.197 -0.093 0.118
## X1 -0.405 0.003 0.198 -0.813 -0.536 -0.405 -0.277 -0.017
## X2 0.247 0.003 0.153 -0.053 0.146 0.247 0.351 0.554
## sigma 0.648 0.002 0.103 0.483 0.575 0.636 0.703 0.888
## lp__ -18.429 0.039 1.550 -22.281 -19.198 -18.074 -17.319 -16.535
## n_eff Rhat
## (Intercept) 3547.056 1.003
## X1 3928.271 0.999
## X2 3583.399 1.001
## sigma 2780.931 1.000
## lp__ 1547.193 1.000
##
## ------
## * For help interpreting the printed output see ?print.cat_bayes
print(predict(cat_glm_bayes_model))
## [1] 0.43217093 -0.17392884 -0.01089480 -1.39082785 -0.05115094 0.12558130
## [7] -0.39757973 -0.26171856 -0.22616132 0.07484400
traceplot(cat_glm_bayes_model)
## Method 4 - Bayesian posterior sampling with adaptive tau
cat_glm_bayes_joint_model <- cat_glm_bayes_joint(
formula = Y ~ .,
cat_init = cat_init
)
##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
## Chain 4:
## Chain 4: Gradient evaluation took 9e-06 seconds
## Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
## Chain 4: Adjust your expectations accordingly!
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print(cat_glm_bayes_joint_model)
## cat_glm_bayes_joint
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## family: gaussian [identity]
## stan algorithm: NUTS
## stan chain: 4
## stan iter: 2000
## stan warmup: 1000
## ------
## coefficients' information:
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5%
## (Intercept) -0.141 0.004 0.259 -0.658 -0.308 -0.141 0.028 0.385
## X1 -0.647 0.006 0.348 -1.331 -0.876 -0.647 -0.422 0.053
## X2 0.334 0.005 0.257 -0.179 0.171 0.335 0.497 0.864
## tau 0.963 0.011 0.684 0.122 0.470 0.798 1.310 2.623
## sigma 0.777 0.003 0.167 0.527 0.658 0.752 0.867 1.167
## lp__ -14.090 0.045 1.801 -18.409 -15.022 -13.716 -12.755 -11.682
## n_eff Rhat
## (Intercept) 3607.756 1.000
## X1 3361.235 1.000
## X2 3098.601 1.001
## tau 4149.713 1.001
## sigma 2964.667 1.001
## lp__ 1588.695 1.002
##
## ------
## * For help interpreting the printed output see ?print.cat_bayes
print(predict(cat_glm_bayes_joint_model))
## [1] 0.7690212 -0.1300890 0.1918019 -1.9138229 0.0210847 0.3745221
## [7] -0.4623462 -0.3040014 -0.2397665 0.2545836
traceplot(cat_glm_bayes_joint_model)
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catalytic
The catalytic package enhances the stability and accuracy of
Generalized Linear Models (GLMs) and Cox proportional hazards models
(COX) in R, especially in high-dimensional or sparse data settings
where traditional methods struggle. By employing catalytic prior
distributions, this package integrates observed data with synthetic data
generated from simpler models, effectively reducing issues like
overfitting. This approach provides more robust parameter estimation,
making catalytic a valuable tool for complex and limited-data
scenarios.
Installation
You can install the released version of catalytic from CRAN with:
install.packages("catalytic")
## Installing package into '/private/var/folders/j5/bktz8wt94hv7m_wtcc0k6ymh0000gn/T/RtmpNJNjW2/temp_libpath107b87e07f100'
## (as 'lib' is unspecified)
## Warning: package 'catalytic' is not available for this version of R
##
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
library(catalytic)
Example
set.seed(1)
data <- data.frame(
X1 = stats::rnorm(10),
X2 = stats::rnorm(10),
Y = stats::rnorm(10)
)
# Step 1: Initialization
cat_init <- cat_glm_initialization(
formula = Y ~ 1, # Formula for a simple model to generate synthetic response
family = gaussian,
data = data,
syn_size = 100 # Synthetic data size
)
print(cat_init)
## cat_glm_initialization
## formula: Y ~ 1
## model: Unknown Variance
## custom variance: NULL
## family: gaussian [identity]
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## ------
## Observation Data Information:
## covariates dimention: 10 rows with 2 column(s)
## head(data) :
## [only show the head of first 10 columns]
##
## X1 X2 Y
## 1 -0.6264538 1.51178117 0.91897737
## 2 0.1836433 0.38984324 0.78213630
## 3 -0.8356286 -0.62124058 0.07456498
## 4 1.5952808 -2.21469989 -1.98935170
## 5 0.3295078 1.12493092 0.61982575
## 6 -0.8204684 -0.04493361 -0.05612874
##
## ------
## Synthetic Data Information:
## covariates dimention: 100 rows with 2 column(s)
## head(data):
## [only show the head of first 10 columns]
##
## X1 X2 Y
## 1 -0.8356286 0.5953590 -0.1336732
## 2 -0.3053884 0.6855034 -0.1336732
## 3 -0.8204684 0.3898432 -0.1336732
## 4 0.7383247 0.5939013 -0.1336732
## 5 0.1836433 0.7523157 -0.1336732
## 6 0.1836433 -0.7461351 -0.1336732
##
## data generation process:
## [only show the first 10 columns]
##
## Covariate Type Process
## 1 X1 Continuous Coordinate
## 2 X2 Continuous Coordinate->Deskewing
##
## ------
## * For help interpreting the printed output see ?print.cat_initialization
# Step 2: Choose Method(s)
## Method 1 - Estimation with fixed tau
cat_glm_model <- cat_glm(
formula = Y ~ ., # Formula for model fitting
cat_init = cat_init, # Output object from `cat_glm_initialization`
tau = 10 # Down-weight factor for synthetic data
)
print(cat_glm_model)
## cat_glm
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## tau: 10
## family: gaussian [identity]
## ------
## coefficients' information:
## (Intercept) X1 X2
## -0.199 -0.402 0.250
##
## ------
## * For help interpreting the printed output see ?print.cat
print(predict(cat_glm_model))
## 1 2 3 4 5 6
## 0.43141012 -0.17506574 -0.01774890 -1.39427971 -0.04996112 0.12024636
## 7 8 9 10
## -0.39882013 -0.25973457 -0.22499036 0.07272498
## Method 2 - Estimation with selective tau
cat_glm_tune_model <- cat_glm_tune(
formula = Y ~ .,
cat_init = cat_init,
tau_seq = seq(1, 10) # Vector of values for downweighting synthetic data
)
print(cat_glm_tune_model)
## cat_glm_tune
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## tau sequnce: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
## family: gaussian
## risk estimate method: parametric_bootstrap
## discrepancy method: mean_square_error
##
## optimal tau: 10
## minimun risk estimate: 1.539
## ------
## coefficients' information:
##
## (Intercept) X1 X2
## -0.199 -0.402 0.250
##
## ------
## * For help interpreting the printed output see ?print.cat_tune
print(predict(cat_glm_tune_model))
## 1 2 3 4 5 6
## 0.43141012 -0.17506574 -0.01774890 -1.39427971 -0.04996112 0.12024636
## 7 8 9 10
## -0.39882013 -0.25973457 -0.22499036 0.07272498
plot(cat_glm_tune_model, text_pos = 2)
## Method 3 - Bayesian posterior sampling with fixed tau
cat_glm_bayes_model <- cat_glm_bayes(
formula = Y ~ .,
cat_init = cat_init,
tau = 10
)
##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.5e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1:
## Chain 1:
## Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
## Chain 1: Iteration: 200 / 2000 [ 10%] (Warmup)
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## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
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print(cat_glm_bayes_model)
## cat_glm_bayes
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## tau: 10
## family: gaussian [identity]
## stan algorithm: NUTS
## stan chain: 4
## stan iter: 2000
## stan warmup: 1000
## ------
## coefficients' information:
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5%
## (Intercept) -0.196 0.003 0.156 -0.504 -0.298 -0.197 -0.093 0.118
## X1 -0.405 0.003 0.198 -0.813 -0.536 -0.405 -0.277 -0.017
## X2 0.247 0.003 0.153 -0.053 0.146 0.247 0.351 0.554
## sigma 0.648 0.002 0.103 0.483 0.575 0.636 0.703 0.888
## lp__ -18.429 0.039 1.550 -22.281 -19.198 -18.074 -17.319 -16.535
## n_eff Rhat
## (Intercept) 3547.056 1.003
## X1 3928.271 0.999
## X2 3583.399 1.001
## sigma 2780.931 1.000
## lp__ 1547.193 1.000
##
## ------
## * For help interpreting the printed output see ?print.cat_bayes
print(predict(cat_glm_bayes_model))
## [1] 0.43217093 -0.17392884 -0.01089480 -1.39082785 -0.05115094 0.12558130
## [7] -0.39757973 -0.26171856 -0.22616132 0.07484400
traceplot(cat_glm_bayes_model)
## Method 4 - Bayesian posterior sampling with adaptive tau
cat_glm_bayes_joint_model <- cat_glm_bayes_joint(
formula = Y ~ .,
cat_init = cat_init
)
##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 0.000251 seconds
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## Chain 2: Elapsed Time: 0.055 seconds (Warm-up)
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##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 9e-06 seconds
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## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
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print(cat_glm_bayes_joint_model)
## cat_glm_bayes_joint
## formula: Y ~ .
## covariates dimention: 10 (Observation) + 100 (Synthetic) = 110 rows with 2 column(s)
## family: gaussian [identity]
## stan algorithm: NUTS
## stan chain: 4
## stan iter: 2000
## stan warmup: 1000
## ------
## coefficients' information:
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5%
## (Intercept) -0.141 0.004 0.259 -0.658 -0.308 -0.141 0.028 0.385
## X1 -0.647 0.006 0.348 -1.331 -0.876 -0.647 -0.422 0.053
## X2 0.334 0.005 0.257 -0.179 0.171 0.335 0.497 0.864
## tau 0.963 0.011 0.684 0.122 0.470 0.798 1.310 2.623
## sigma 0.777 0.003 0.167 0.527 0.658 0.752 0.867 1.167
## lp__ -14.090 0.045 1.801 -18.409 -15.022 -13.716 -12.755 -11.682
## n_eff Rhat
## (Intercept) 3607.756 1.000
## X1 3361.235 1.000
## X2 3098.601 1.001
## tau 4149.713 1.001
## sigma 2964.667 1.001
## lp__ 1588.695 1.002
##
## ------
## * For help interpreting the printed output see ?print.cat_bayes
print(predict(cat_glm_bayes_joint_model))
## [1] 0.7690212 -0.1300890 0.1918019 -1.9138229 0.0210847 0.3745221
## [7] -0.4623462 -0.3040014 -0.2397665 0.2545836
traceplot(cat_glm_bayes_joint_model)
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