| Title: | Global, Parameterwise and Joint Shrinkage Factor Estimation |
|---|---|
| Description: | The predictive value of a statistical model can often be improved by applying shrinkage methods. This can be achieved, e.g., by regularized regression or empirical Bayes approaches. Various types of shrinkage factors can also be estimated after a maximum likelihood. While global shrinkage modifies all regression coefficients by the same factor, parameterwise shrinkage factors differ between regression coefficients. With variables which are either highly correlated or associated with regard to contents, such as several columns of a design matrix describing a nonlinear effect, parameterwise shrinkage factors are not interpretable and a compromise between global and parameterwise shrinkage, termed 'joint shrinkage', is a useful extension. A computational shortcut to resampling-based shrinkage factor estimation based on DFBETA residuals can be applied. Global, parameterwise and joint shrinkage for models fitted by lm(), glm(), coxph(), or mfp() is available. |
| Authors: | Daniela Dunkler [aut, cre], Georg Heinze [aut] |
| Maintainer: | Daniela Dunkler <[email protected]> |
| License: | GPL-3 |
| Version: | 1.2.3 |
| Built: | 2025-02-22 04:11:22 UTC |
| Source: | https://github.com/biometrician/shrink |
The predictive value of a statistical model can often be improved by applying
shrinkage methods. This can be achieved, e.g., by regularized regression or
empirical Bayes approaches. Various types of shrinkage factors can also be
estimated after a maximum likelihood. While global shrinkage modifies all
regression coefficients by the same factor, parameterwise shrinkage factors
differ between regression coefficients. With variables which are either highly
correlated or associated with regard to contents, such as several columns of
a design matrix describing a nonlinear effect or two main effects and their
pairwise interaction term, parameterwise shrinkage factors are not interpretable
and a compromise between global and parameterwise shrinkage, termed 'joint
shrinkage', is a useful extension.
A computational shortcut to resampling-based shrinkage factor estimation based
on DFBETA residuals can be applied.
Global, parameterwise and joint shrinkage for models fitted by lm,
glm, coxph, and mfp is available.
Functions included in the shrink-package:
shrink |
a function to compute global, parameterwise and joint post-estimation |
shrinkage factors of fit objects of class lm, glm, coxph, or mfp. |
|
coef.shrink |
returns shrunken regression coefficients from objects of class shrink. |
predict.shrink |
obtains predictions from shrunken regression coefficients from objects |
of class shrink. |
|
vcov.shrink |
returns the variance-covariance matrix of shrinkage factors. |
print.shrink |
prints objects of class shrink. |
summary.shrink |
summary of objects of class shrink. |
Data set included in the shrink-package:
deepvein |
deep vein thrombosis study |
GBSG |
German breast cancer study |
Sauerbrei (1999) suggested that before estimating parameterwise shrinkage factors, the data should be standardized to have a mean of 0 and unit variance.
Dunkler D, Sauerbrei W, Heinze G (2016). Global, Parameterwise and Joint
Shrinkage Factor Estimation. Journal of Statistical Software. 69(8), 1-19.
doi:10.18637/jss.v069.i08
Sauerbrei W (1999) The use of resampling methods to simplify regression
models in medial statistics. Applied Statistics 48(3): 313-329.
Verweij P, van Houwelingen J (1993) Cross-validation in survival analysis.
Statistics in Medicine 12(24): 2305-2314.
shrink, coef.shrink, predict.shrink,
print.shrink, summary.shrink, vcov.shrink,
deepvein
# with glm, family = binomial set.seed(888) intercept <- 1 beta <- c(0.5, 1.2) n <- 200 x1 <- rnorm(n, mean = 1, sd = 1) x2 <- rbinom(n, size = 1, prob = 0.3) linpred <- intercept + x1 * beta[1] + x2 * beta[2] prob <- exp(linpred) / (1 + exp(linpred)) runis <- runif(n, min = 0, max = 1) ytest <- ifelse(test = runis < prob, yes = 1, no = 0) simdat <- data.frame(cbind(y = ifelse(runis < prob, 1, 0), x1, x2)) fit <- glm(y ~ x1 + x2, family = binomial, data = simdat, x = TRUE) summary(fit) global <- shrink(fit, type = "global", method = "dfbeta") print(global) coef(global) shrink(fit, type = "parameterwise", method = "dfbeta") shrink(fit, type = "parameterwise", method = "dfbeta", join = list(c("x1", "x2"))) #shrink(fit, type = "global", method = "jackknife") #shrink(fit, type = "parameterwise", method = "jackknife") #shrink(fit, type = "parameterwise", method = "jackknife", # join = list(c("x1", "x2"))) # For more examples see shrink# with glm, family = binomial set.seed(888) intercept <- 1 beta <- c(0.5, 1.2) n <- 200 x1 <- rnorm(n, mean = 1, sd = 1) x2 <- rbinom(n, size = 1, prob = 0.3) linpred <- intercept + x1 * beta[1] + x2 * beta[2] prob <- exp(linpred) / (1 + exp(linpred)) runis <- runif(n, min = 0, max = 1) ytest <- ifelse(test = runis < prob, yes = 1, no = 0) simdat <- data.frame(cbind(y = ifelse(runis < prob, 1, 0), x1, x2)) fit <- glm(y ~ x1 + x2, family = binomial, data = simdat, x = TRUE) summary(fit) global <- shrink(fit, type = "global", method = "dfbeta") print(global) coef(global) shrink(fit, type = "parameterwise", method = "dfbeta") shrink(fit, type = "parameterwise", method = "dfbeta", join = list(c("x1", "x2"))) #shrink(fit, type = "global", method = "jackknife") #shrink(fit, type = "parameterwise", method = "jackknife") #shrink(fit, type = "parameterwise", method = "jackknife", # join = list(c("x1", "x2"))) # For more examples see shrink
shrink
This class of objects is returned by the shrink function. Objects of this
class have methods for the functions coef, predict, print,
summary, and vcov.
## S3 method for class 'shrink' coef(object, ...)## S3 method for class 'shrink' coef(object, ...)
object |
an object of class |
... |
further arguments. |
A vector with shrunken regression coefficients
shrink, print.shrink, predict.shrink,
summary.shrink, vcov.shrink
A data frame containing time to recurrence of thrombosis and several potential prognostic factors measured at baseline for 929 individuals with deep vein thrombosis or unprovoked pulmonary embolism. 147 events of recurrence were observed during a median follow-up time of 37.8 months.
deepveindeepvein
The data frame contains observations of 929 individuals and the following variables:
patient number.
time to recurrence of thrombosis or end of study in months.
= 1 recurrence of thrombosis.
gender.
factor II G20210A mutation.
factor V Leiden mutation.
log2-transformed D-dimer.
body mass index.
duration of anticoagulation therapy.
age in years.
location of first thrombosis: pulmonary embolism (PE), distal,
or proximal deep vein
thrombosis.
The data are a modified and partly simulated version of the data set used by Eichinger et al. (2010) and are available under a GPL-2 license.
M. Schumacher, G. Basert, H. Bojar, K. Huebner, M. Olschewski,
W. Sauerbrei, C. Schmoor, C. Beyerle, R.L.A. Neumann and H.F. Rauschecker
for the German Breast Cancer Study Group (1994).
Randomized trial evaluating hormonal treatment
and the duration of chemotherapy in node-positive breast cancer patients.
Journal of Clinical Oncology, 12, 2086–2093.
W. Sauerbrei and P. Royston (1999). Building multivariable prognostic
and diagnostic models: transformation of the predictors by using
fractional polynomials. Journal of the Royal Statistics Society
Series A, Volume 162(1), 71–94.
data("deepvein") summary(deepvein)data("deepvein") summary(deepvein)
A data frame containing the observations from the GBSG study.
GBSGGBSG
This data frame contains the observations of 686 women:
patient id.
hormonal therapy, a factor at two levels 0 (no) and 1 (yes).
of the patients in years.
menopausal status, a factor at two levels 1 (premenopausal) and 2 (postmenopausal).
tumor size (in mm).
tumor grade, a ordered factor at levels 1 < 2 < 3.
number of positive nodes.
progesterone receptor (in fmol).
estrogen receptor (in fmol).
recurrence free survival time (in days).
censoring indicator (0 censored, 1 event).
M. Schumacher, G. Basert, H. Bojar, K. Huebner, M. Olschewski,
W. Sauerbrei, C. Schmoor, C. Beyerle, R.L.A. Neumann and H.F. Rauschecker
for the German Breast Cancer Study Group (1994).
Randomized trial evaluating hormonal treatment
and the duration of chemotherapy in node-positive breast cancer patients.
Journal of Clinical Oncology, 12, 2086–2093.
W. Sauerbrei and P. Royston (1999). Building multivariable prognostic
and diagnostic models: transformation of the predictors by using
fractional polynomials. Journal of the Royal Statistics Society
Series A, Volume 162(1), 71–94.
data("GBSG") summary(GBSG)data("GBSG") summary(GBSG)
shrink
Obtains predictions from shrunken regression coefficients from an object of
class shrink.
This class of objects is returned by the shrink function. Objects of this
class have methods for the functions coef, predict, print,
summary, and vcov.
## S3 method for class 'shrink' predict( object, newdata = NULL, type = c("link", "response", "lp", "risk", "expected", "terms"), shrinktype = NULL, terms = NULL, na.action = na.pass, collapse, safe = FALSE, ... )## S3 method for class 'shrink' predict( object, newdata = NULL, type = c("link", "response", "lp", "risk", "expected", "terms"), shrinktype = NULL, terms = NULL, na.action = na.pass, collapse, safe = FALSE, ... )
object |
an object of class |
newdata |
a data frame for which predictions are obtained, otherwise
predictions are based on the data stored in |
type |
the type of prediction required. |
shrinktype |
the type of shrinkage requested, if the |
terms |
with |
na.action |
function determining what should be done with missing values
in |
collapse |
if |
safe |
option from |
... |
additional arguments to be passed to methods. |
A vector or matrix of predictions.
If object was obtained using type = "all", shrinktype
specifies for which type of shrinkage predictions are requested.
shrinktype will be ignored if object was obtained using
either type = "parameterwise" or type = "global".
shrink, coef.shrink, print.shrink,
summary.shrink, vcov.shrink
data("GBSG") library("mfp") fit <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05) + fp(prm, df = 4, select = 0.05), family = cox, data = GBSG) dfbeta.global <- shrink(fit, type = "global", method = "dfbeta") dfbeta.pw <- shrink(fit, type = "parameterwise", method = "dfbeta") dfbeta.join <- shrink(fit, type = "parameterwise", method = "dfbeta", join=list(c("age.1", "age.2"))) age <- 30:80 newdat <- data.frame(age = age, prm = 0) refdat <- data.frame(age = 50, prm = 0) # unshrunken plot(age, predict(fit, newdata = newdat, type = "lp") - predict(fit, newdata = refdat, type = "lp"), xlab = "Age", ylab = "Log hazard relative to 50 years", type = "l", lwd = 2) # globally shrunken lines(age, predict(dfbeta.global,newdata = newdat, type = "lp") - predict(dfbeta.global, newdata = refdat, type = "lp"), lty = 3, col = "red", lwd = 2) # jointly shrunken lines(age, predict(dfbeta.join, newdata = newdat, type = "lp") - predict(dfbeta.join, newdata = refdat, type = "lp"), lty = 4, col = "blue", lwd = 2) # parameterwise shrunken lines(age, predict(dfbeta.pw, newdata = newdat, type = "lp") - predict(dfbeta.pw, newdata =refdat, type = "lp"), lty = 2, col = "green", lwd = 2) legend("topright", lty = c(1, 3, 4, 2), title = "SHRINKAGE", legend = c("No", "Global", "Joint", "Parameterwise"), inset = 0.01, bty = "n", col = c("black", "red", "blue", "green"), lwd = 2)data("GBSG") library("mfp") fit <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05) + fp(prm, df = 4, select = 0.05), family = cox, data = GBSG) dfbeta.global <- shrink(fit, type = "global", method = "dfbeta") dfbeta.pw <- shrink(fit, type = "parameterwise", method = "dfbeta") dfbeta.join <- shrink(fit, type = "parameterwise", method = "dfbeta", join=list(c("age.1", "age.2"))) age <- 30:80 newdat <- data.frame(age = age, prm = 0) refdat <- data.frame(age = 50, prm = 0) # unshrunken plot(age, predict(fit, newdata = newdat, type = "lp") - predict(fit, newdata = refdat, type = "lp"), xlab = "Age", ylab = "Log hazard relative to 50 years", type = "l", lwd = 2) # globally shrunken lines(age, predict(dfbeta.global,newdata = newdat, type = "lp") - predict(dfbeta.global, newdata = refdat, type = "lp"), lty = 3, col = "red", lwd = 2) # jointly shrunken lines(age, predict(dfbeta.join, newdata = newdat, type = "lp") - predict(dfbeta.join, newdata = refdat, type = "lp"), lty = 4, col = "blue", lwd = 2) # parameterwise shrunken lines(age, predict(dfbeta.pw, newdata = newdat, type = "lp") - predict(dfbeta.pw, newdata =refdat, type = "lp"), lty = 2, col = "green", lwd = 2) legend("topright", lty = c(1, 3, 4, 2), title = "SHRINKAGE", legend = c("No", "Global", "Joint", "Parameterwise"), inset = 0.01, bty = "n", col = c("black", "red", "blue", "green"), lwd = 2)
shrink
This class of objects is returned by the shrink function. Objects of this
class have methods for the functions coef, predict, print,
summary, and vcov.
## S3 method for class 'shrink' print(x, ...)## S3 method for class 'shrink' print(x, ...)
x |
object of class |
... |
further arguments. |
shrink, coef.shrink, predict.shrink,
summary.shrink, vcov.shrink
Obtain global, parameterwise and joint post-estimation shrinkage factors for
regression coefficients from fit objects of class lm, glm,
coxph, or mfp.
shrink( fit, type = c("parameterwise", "global", "all"), method = c("jackknife", "dfbeta"), join = NULL, notes = TRUE, postfit = TRUE )shrink( fit, type = c("parameterwise", "global", "all"), method = c("jackknife", "dfbeta"), join = NULL, notes = TRUE, postfit = TRUE )
fit |
a fit object of class |
type |
of shrinkage, either |
method |
of shrinkage estimation, either |
join |
compute optional joint shrinkage factors for sets of specified columns
of the design matrix, if |
notes |
print notes. Default is TRUE. |
postfit |
obtain fit with shrunken regression coefficients. This option is only available for models without an intercept. Default is TRUE. |
While global shrinkage modifies all regression coefficients by the same factor, parameterwise shrinkage factors differ between regression coefficients. With variables which are either highly correlated or associated with regard to contents, such as several columns of a design matrix describing a nonlinear effect, parameterwise shrinkage factors are not interpretable. Joint shrinkage of a set of such associated design variables will give one common shrinkage factor for this set.
Joint shrinkage factors may be useful when analysing highly correlated and/or
such associated columns of the design matrix, e.g. dummy variables corresponding
to a categorical explanatory variable with more than two levels, two variables
and their pairwise interaction term, or several transformations of an explantory
variable enabling estimation of nonlinear effects. The analyst can define
'joint' shrinkage factors by specifing the join option if
type = "parameterwise". join expects a list with at least one character
vector including the names of the columns of the design matrix for which a joint
shrinkage factor is requested. For example the following specification of
join = list(c("dummy1", "dummy2", "dummy3"), c("main1",
"main2", "interaction"), c("varX.fp1", "varX.fp2")) requests
the joint shrinkage factors for a) "dummy1", "dummy2" and "dummy3",
b) "main1", "main2" and "interaction" and c) "varX.fp1"
and "varX.fp2".
rcs
shrink also works for models incorporating restricted cubic splines
computed with the rcs function from the rms package. A joint
shrinkage factor of explanatory variable varX transformed with rcs
can be obtained by join = list(c("rcs(varX)")) or by stating the names of the
rcs-transformed variables as given in the respective fit object. (These
two notations should not be mixed within one call to shrink.)
For linear regression models (lm or glm with family = "gaussian")
shrinkage factors obtained by Jackknife and the DFBETA approximation will be identical. For
all other types of regression, the computational effort of estimating shrinkage factors may
be greatly reduced by using method = "dfbeta" instead. However, for (very)
small data sets method = "jackknife" may be of advantage, as the use of DFBETA
residuals may underestimate the influence of some highly influential observations.
A shrunken intercept is estimated as follows: For all columns of the design matrix
except for the intercept the shrinkage factors are multiplied with the respective
regression coefficients and a linear predictor is computed. Then the shrunken
intercept is estimated by modeling fit$y ~ offset(linear predictor).
For regression models without an intercept, i.e., fit objects of class coxph,
the shrunken regression coefficients can be directly estimated. This postfit is retained
in the $postfit component of the shrink object.
shrink returns an object with the following components:
ShrinkageFactors |
a vector of shrinkage factors of regression coefficients. |
ShrinkageFactorsVCOV |
the covariance matrix of the shrinkage factors. |
ShrunkenRegCoef |
a vector with the shrunken regression coefficients. |
postfit |
an optional postfit model with shrunken regression coefficients and associated standard errors for models without an intercept. |
fit |
the original (unshrunken) fit object. |
type |
the requested shrinkage type. |
method |
the requested shrinkage method. |
join |
the requested joint shrinkage factors. |
call |
the function call. |
If type = "all" then the object returned by shrink additionally contains
global |
a list with the following elements: ShrinkageFactors,
ShrinkageFactorsVCOV and ShrunkenRegCoef. |
parameterwise |
a list with the following elements: ShrinkageFactors,
ShrinkageFactorsVCOV and ShrunkenRegCoef. |
joint |
an optional list with the following elements: ShrinkageFactors,
ShrinkageFactorsVCOV and ShrunkenRegCoef. |
For fit objects of class mfp with family != cox regression coefficients
of fit (obtained by coef(fit)) and fit$fit may not always be identical,
because of mfp's pretransformation applied to the explanatory variables in the model.
The shrink function uses a) the names as given in names(coef(fit)) and b) the
regression coefficients as given in summary(fit) which correspond to the pretransformed
explanatory variables.
Dunkler D, Sauerbrei W, Heinze G (2016). Global, Parameterwise and Joint
Shrinkage Factor Estimation. Journal of Statistical Software. 69(8), 1-19.
doi:10.18637/jss.v069.i08
Sauerbrei W (1999) The use of resampling methods to simplify regression
models in medial statistics. Applied Statistics 48(3): 313-329.
Verweij P, van Houwelingen J (1993) Cross-validation in survival analysis.
Statistics in Medicine 12(24): 2305-2314.
coef.shrink, predict.shrink, print.shrink,
summary.shrink, vcov.shrink
## Example with mfp (family = cox) data("GBSG") library("mfp") fit1 <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05) + fp(prm, df = 4, select = 0.05), family = cox, data = GBSG) shrink(fit1, type = "global", method = "dfbeta") dfbeta.pw <- shrink(fit1, type = "parameterwise", method = "dfbeta") dfbeta.pw dfbeta.pw$postfit # correlations between shrinkage factors and standard errors of shrinkage factors cov2cor(dfbeta.pw$ShrinkageFactorsVCOV) sqrt(diag(dfbeta.pw$ShrinkageFactorsVCOV)) shrink(fit1, type = "parameterwise", method = "dfbeta", join = list(c("age.1", "age.2"))) #shrink(fit1, type = "global", method = "jackknife") #shrink(fit1, type = "parameterwise", method = "jackknife") #shrink(fit1, type = "parameterwise", method = "jackknife", # join = list(c("age.1", "age.2"))) # obtain global, parameterwise and joint shrinkage with one call to 'shrink' shrink(fit1, type = "all", method = "dfbeta", join = list(c("age.1", "age.2"))) ## Example with rcs library("rms") fit2 <- coxph(Surv(rfst, cens) ~ rcs(age) + log(prm + 1), data = GBSG, x = TRUE) shrink(fit2, type = "global", method = "dfbeta") shrink(fit2, type = "parameterwise", method = "dfbeta") shrink(fit2, type = "parameterwise", method = "dfbeta", join = list(c("rcs(age)"))) shrink(fit2, type = "parameterwise", method = "dfbeta", join = list(c("rcs(age)"), c("log(prm + 1)"))) ## Examples with glm & mfp (family = binomial) set.seed(888) intercept <- 1 beta <- c(0.5, 1.2) n <- 1000 x1 <- rnorm(n, mean = 1, sd = 1) x2 <- rbinom(n, size = 1, prob = 0.3) linpred <- intercept + x1 * beta[1] + x2 * beta[2] prob <- exp(linpred) / (1 + exp(linpred)) runis <- runif(n, 0, 1) ytest <- ifelse(test = runis < prob, yes = 1, no = 0) simdat <- data.frame(cbind(y = ifelse(runis < prob, 1, 0), x1, x2)) fit3 <- glm(y ~ x1 + x2, family = binomial, data = simdat, x = TRUE) summary(fit3) shrink(fit3, type = "global", method = "dfbeta") shrink(fit3, type = "parameterwise", method = "dfbeta") shrink(fit3, type = "parameterwise", method = "dfbeta", join = list(c("x1", "x2"))) utils::data("Pima.te", package="MASS") utils::data("Pima.tr", package="MASS") Pima <- rbind(Pima.te, Pima.tr) fit4 <- mfp(type ~ npreg + glu + bmi + ped + fp(age, select = 0.05), family = binomial, data = Pima) summary(fit4) shrink(fit4, type = "global", method = "dfbeta") shrink(fit4, type = "parameterwise", method = "dfbeta") # fit objects of class mfp: for 'join' use variable names as given in 'names(coef(fit4))' shrink(fit4, type = "parameterwise", method = "dfbeta", join = list(c("age.1"))) ## Examples with glm & mfp (family = gaussian) and lm utils::data("anorexia", package = "MASS") contrasts(anorexia$Treat) <- contr.treatment(n = 3, base = 2) fit5 <- glm(Postwt ~ Prewt + Treat, family = gaussian, data = anorexia, x = TRUE) fit5 shrink(fit5, type = "global", method = "dfbeta") # which is identical to the more time-consuming jackknife approach: # shrink(fit5, type = "global", method = "jackknife") shrink(fit5, type = "parameterwise", method = "dfbeta") shrink(fit5, type = "parameterwise", method = "dfbeta", join = list(c("Treat1", "Treat3"))) fit6 <- lm(Postwt ~ Prewt + Treat, data = anorexia, x = TRUE, y = TRUE) fit6 shrink(fit6, type = "global", method = "dfbeta") shrink(fit6, type = "parameterwise", method = "dfbeta") shrink(fit6, type = "parameterwise", method = "dfbeta", join=list(c("Treat1", "Treat3"))) utils::data("GAGurine", package = "MASS") fit7 <- mfp(Age ~ fp(GAG, select = 0.05), family = gaussian, data = GAGurine) summary(fit7) shrink(fit7, type = "global", method = "dfbeta") shrink(fit7, type = "parameterwise", method = "dfbeta") # fit objects of class mfp: for 'join' use variable names as given in 'names(coef(fit7))' shrink(fit7, type = "parameterwise", method = "dfbeta", join = list(c("GAG.1", "GAG.2")))## Example with mfp (family = cox) data("GBSG") library("mfp") fit1 <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05) + fp(prm, df = 4, select = 0.05), family = cox, data = GBSG) shrink(fit1, type = "global", method = "dfbeta") dfbeta.pw <- shrink(fit1, type = "parameterwise", method = "dfbeta") dfbeta.pw dfbeta.pw$postfit # correlations between shrinkage factors and standard errors of shrinkage factors cov2cor(dfbeta.pw$ShrinkageFactorsVCOV) sqrt(diag(dfbeta.pw$ShrinkageFactorsVCOV)) shrink(fit1, type = "parameterwise", method = "dfbeta", join = list(c("age.1", "age.2"))) #shrink(fit1, type = "global", method = "jackknife") #shrink(fit1, type = "parameterwise", method = "jackknife") #shrink(fit1, type = "parameterwise", method = "jackknife", # join = list(c("age.1", "age.2"))) # obtain global, parameterwise and joint shrinkage with one call to 'shrink' shrink(fit1, type = "all", method = "dfbeta", join = list(c("age.1", "age.2"))) ## Example with rcs library("rms") fit2 <- coxph(Surv(rfst, cens) ~ rcs(age) + log(prm + 1), data = GBSG, x = TRUE) shrink(fit2, type = "global", method = "dfbeta") shrink(fit2, type = "parameterwise", method = "dfbeta") shrink(fit2, type = "parameterwise", method = "dfbeta", join = list(c("rcs(age)"))) shrink(fit2, type = "parameterwise", method = "dfbeta", join = list(c("rcs(age)"), c("log(prm + 1)"))) ## Examples with glm & mfp (family = binomial) set.seed(888) intercept <- 1 beta <- c(0.5, 1.2) n <- 1000 x1 <- rnorm(n, mean = 1, sd = 1) x2 <- rbinom(n, size = 1, prob = 0.3) linpred <- intercept + x1 * beta[1] + x2 * beta[2] prob <- exp(linpred) / (1 + exp(linpred)) runis <- runif(n, 0, 1) ytest <- ifelse(test = runis < prob, yes = 1, no = 0) simdat <- data.frame(cbind(y = ifelse(runis < prob, 1, 0), x1, x2)) fit3 <- glm(y ~ x1 + x2, family = binomial, data = simdat, x = TRUE) summary(fit3) shrink(fit3, type = "global", method = "dfbeta") shrink(fit3, type = "parameterwise", method = "dfbeta") shrink(fit3, type = "parameterwise", method = "dfbeta", join = list(c("x1", "x2"))) utils::data("Pima.te", package="MASS") utils::data("Pima.tr", package="MASS") Pima <- rbind(Pima.te, Pima.tr) fit4 <- mfp(type ~ npreg + glu + bmi + ped + fp(age, select = 0.05), family = binomial, data = Pima) summary(fit4) shrink(fit4, type = "global", method = "dfbeta") shrink(fit4, type = "parameterwise", method = "dfbeta") # fit objects of class mfp: for 'join' use variable names as given in 'names(coef(fit4))' shrink(fit4, type = "parameterwise", method = "dfbeta", join = list(c("age.1"))) ## Examples with glm & mfp (family = gaussian) and lm utils::data("anorexia", package = "MASS") contrasts(anorexia$Treat) <- contr.treatment(n = 3, base = 2) fit5 <- glm(Postwt ~ Prewt + Treat, family = gaussian, data = anorexia, x = TRUE) fit5 shrink(fit5, type = "global", method = "dfbeta") # which is identical to the more time-consuming jackknife approach: # shrink(fit5, type = "global", method = "jackknife") shrink(fit5, type = "parameterwise", method = "dfbeta") shrink(fit5, type = "parameterwise", method = "dfbeta", join = list(c("Treat1", "Treat3"))) fit6 <- lm(Postwt ~ Prewt + Treat, data = anorexia, x = TRUE, y = TRUE) fit6 shrink(fit6, type = "global", method = "dfbeta") shrink(fit6, type = "parameterwise", method = "dfbeta") shrink(fit6, type = "parameterwise", method = "dfbeta", join=list(c("Treat1", "Treat3"))) utils::data("GAGurine", package = "MASS") fit7 <- mfp(Age ~ fp(GAG, select = 0.05), family = gaussian, data = GAGurine) summary(fit7) shrink(fit7, type = "global", method = "dfbeta") shrink(fit7, type = "parameterwise", method = "dfbeta") # fit objects of class mfp: for 'join' use variable names as given in 'names(coef(fit7))' shrink(fit7, type = "parameterwise", method = "dfbeta", join = list(c("GAG.1", "GAG.2")))
shrink
This class of objects is returned by the shrink function. Objects of this
class have methods for the functions coef, predict, print,
summary, and vcov.
## S3 method for class 'shrink' summary(object, digits = 6, ...)## S3 method for class 'shrink' summary(object, digits = 6, ...)
object |
an object of class |
digits |
integer, used for number formatting with |
... |
further arguments. |
A matrix with regression coefficients of the orginial fit, corresponding shrinkage factors and shrunken regression coefficients.
shrink, coef.shrink, print.shrink,
predict.shrink, vcov.shrink
shrink
This class of objects is returned by the shrink function. Objects of this
class have methods for the functions coef, predict, print,
summary, and vcov.
## S3 method for class 'shrink' vcov(object, digits = 6, ...)## S3 method for class 'shrink' vcov(object, digits = 6, ...)
object |
object of class |
digits |
integer, used for number formatting with |
... |
further arguments. |
A matrix of the estimated covariances between the obtained shrinkage factors.
shrink,coef.shrink, predict.shrink,
print.shrink, summary.shrink