Package {CanonicalFamilyExtra}

SuperLearner wrapper for cv.glmnet that works with the extra families

Description

A wrapper of glmnet::cv.glmnet() similar to SuperLearner::SL.glmnet(), except that family can be binomial_extra. SuperLearner::SL.glmnet() only passes the name of family and thus cannot pass the full customized families like binomial_extra().

Usage

SL.glmnet.extra(
  Y,
  X,
  newX,
  family,
  obsWeights,
  id,
  alpha = 1,
  nfolds = 10,
  nlambda = 100,
  useMin = TRUE,
  loss = "deviance",
  ...
)

Arguments

Value

A list with two elements:

pred

The predicted values for the rows in newX.

fit

A list. Contains all objects necessary to get predictions for new observations from specific algorithm.

Similar to the value of SuperLearner::SL.glmnet().

Examples

    set.seed(321)
    expit <- binomial()$linkinv
    X <- matrix(rnorm(100 * 5), nrow = 100)
    y <- expit(1 + X[,1] + X[,2]) + rnorm(100)
    require(SuperLearner)
    SL.library<-list(c("SL.glmnet.extra","All"),
                     c("SL.glmnet.extra","screen.glmnet.extra"))
    SuperLearner(y, data.frame(X), family=binomial_extra(),
                 SL.library = SL.library, cvControl = list(V = 2))

Family object for fitting binomial (e.g., logistic, probit) regression model with potentially unbounded continuous outcome

Description

A family object for fitting binomial models (i.e., generalized linear models with range contained in the open unit interval (0,1)) with continuous outcomes that may fall outside the unit interval [0,1]. Also works with glmnet::glmnet() as well as SL.glmnet.extra() and screen.glmnet.extra(). Generally, the object aims to fit a model ranged in [0,1].

Usage

binomial_extra(
  link = "logit",
  variance = "mu(1-mu)",
  family = c("gaussian", "binomial")
)

Arguments

Details

This family is useful, for example, when the estimand is a conditional probability function while the outcome is a transformed pseudo-outcome so that the estimator is multiply robust, or estimating a regression function with known bounds while the outcome might not respect the known bounds. Naive approaches such as glm(family=binomial()), glm(family=quasibinomial()), glm(family=gaussian(link="logit")), glm(family=quasi(link="logit",variance="constant")) etc. might not work appropriately in such cases.

Particularly for logistic model, because of using the binomial working likelihood and its canonical link, the model fitting is a convex problem and does not depend on starting value.

The output has family="gaussian" by default to be compatible with other learners in SuperLearner::SuperLearner(), because when the outcome is continuous, other learners might not perform correctly with family="binomial".

When running geepack::geeglm() or gee::gee() with binomial_extra, the working mean-variance relationship is determined by the family of binomial_extra. Need to specify family="binomial" to use binomial working mean-variance relationship. The default "gaussian" will lead to Gaussian working mean-variance relationship.

Value

a family object

Examples

set.seed(123)
expit <- binomial()$linkinv

# glm
x <- rnorm(100)
y <- expit(1 + x) + rnorm(100)
glm(y~x, family = binomial_extra()) # or family=binomial_extra, or family="binomial_extra"

# Counterexamples: These naive approaches yield errors or are not reliable
try(glm(y~x, family = binomial()))
try(glm(y~x, family = quasibinomial()))
try(glm(y~x, family = gaussian(link = "logit")))
# setting starting value might fix this approach,
# but the problem is non-convex and requires valid starting value
try(glm(y~x, family = gaussian(link = "logit"), start = c(-1,0)))
try(glm(y~x, family = quasi(link = "logit", variance = "constant")))

#glmnet
X <- matrix(rnorm(100 * 5), nrow = 100)
y <- expit(1 + X[,1]) + rnorm(100)
require(glmnet)
glmnet(X, y, family = binomial_extra())
# or family=binomial_extra; cannot use family="binomial_extra"

# Counterexamples: These naive approaches yield errors
try(glmnet(X, y, family = binomial()))
try(glmnet(X, y, family = gaussian(link = "logit")))
try(glmnet(X, y, family = quasi(link = "logit", variance = "constant")))

# other links/variance for glm
x <- rnorm(100)
y <- expit(1 + x) + rnorm(100)
glm(y~x, family = binomial_extra("probit")) # probit regression
glm(y~x, family = binomial_extra(variance = "constant")) # least squares

# within SuperLearner
X <- matrix(rnorm(100 * 3), nrow = 100)
y <- expit(1 + X[,1]) + rnorm(10)
require(SuperLearner)
SuperLearner(y, data.frame(X), family=binomial_extra(),
             SL.library = c("SL.glm", "SL.ipredbagg"), cvControl = list(V = 2))

#GEE
x <- rnorm(100)
y <- expit(1 + x) + rnorm(100)
id <- rep(1:20, each=5)
geepack::geeglm(y ~ x, family = binomial_extra(family = "binomial"), id = id)
gee::gee(y ~ x, family = binomial_extra(family = "binomial"), id = id)

Family object for fitting log-linear model with potentially unbounded continuous outcome, particularly with Poisson working likelihood

Description

A family object for fitting Poisson models (i.e., generalized linear models with range contained in the open unit interval (0,\infty)) with continuous outcomes that may not be non-negative integers. Also works with glmnet::glmnet() as well as SL.glmnet.extra() and screen.glmnet.extra(). Generally, the object aims to fit a model ranged in (0,\infty).

Usage

poisson_extra(link = "log", variance = "mu", family = c("gaussian", "poisson"))

Arguments

Details

This family is useful, for example, when the estimand is a conditional probability function while the outcome is a transformed pseudo-outcome so that the estimator is multiply robust, or estimating a positive regression function while the outcome might be negative or non-integers. Naive approaches such as glm(family=poisson()), glm(family=quasipoisson()), glm(family=gaussian(link="log")), glm(family=quasi(link="log",variance="constant")) etc. might not work appropriately or reliably in such cases.

Particularly for log-linear model, because of using the Poisson working likelihood and its canonical link, the model fitting is a convex problem and does not depend on starting value.

The output has family="gaussian" by default to be compatible with other learners in SuperLearner::SuperLearner(), because when the outcome is continuous, other learners might not perform correctly with family="poisson".

When running geepack::geeglm() or gee::gee() with poisson_extra, the working mean-variance relationship is determined by the family of poisson_extra. Need to specify family="poisson" to use Poisson working mean-variance relationship. The default "gaussian" will lead to Gaussian working mean-variance relationship.

Value

a family object

Examples

set.seed(123)

# glm
x <- rnorm(100)
y <- exp(-1 + x) + rnorm(100)
glm(y~x, family = poisson_extra()) # or family=poisson_extra, or family="poisson_extra"

# Counterexamples: These naive approaches yield errors or are not reliable
try(glm(y~x, family = poisson()))
try(glm(y~x, family = quasipoisson()))
try(glm(y~x, family = gaussian(link = "log")))
# setting starting value might fix this approach,
# but the problem is non-convex and requires valid starting value
try(glm(y~x, family = gaussian(link = "log"), start = c(-1,0)))
try(glm(y~x, family = quasi(link = "log", variance = "constant")))
# setting starting value might fix this approach,
# but the problem is non-convex and requires valid starting value
try(glm(y~x, family = quasi(link = "log", variance = "constant"), start = c(-1,0)))

#glmnet
X <- matrix(rnorm(100 * 5), nrow = 100)
y <- exp(1 + X[,1]) + rnorm(100)
require(glmnet)
glmnet(X, y, family = poisson_extra())
# or family=poisson_extra; cannot use family="poisson_extra"

# Counterexamples: These naive approaches yield errors or are not reliable
try(glmnet(X, y, family = poisson()))
try(glmnet(X, y, family = gaussian(link = "log")))
try(glmnet(X, y, family = quasi(link = "log", variance = "constant")))

# within SuperLearner
X <- matrix(rnorm(100 * 3), nrow = 100)
y <- exp(1 + X[,1]) + rnorm(10)
require(SuperLearner)
SuperLearner(y, data.frame(X), family=poisson_extra(),
             SL.library = c("SL.glm", "SL.ipredbagg"), cvControl = list(V = 2))

#GEE
x <- rnorm(100)
y <- exp(-1 + x) + rnorm(100)
id <- rep(1:20, each=5)
geepack::geeglm(y ~ x, family = poisson_extra(family = "poisson"), id = id)
gee::gee(y ~ x, family = poisson_extra(family = "poisson"), id = id)

SuperLearner screener using cv.glmnet that works with the extra families

Description

A wrapper of glmnet::cv.glmnet() similar to SuperLearner::screen.glmnet(), except that family can be binomial_extra. SuperLearner::screen.glmnet() only passes the name of family (e.g., "gaussian", "binomial") and thus cannot pass the full customized families like binomial_extra().

Usage

screen.glmnet.extra(
  Y,
  X,
  family,
  alpha = 1,
  minscreen = 2,
  nfolds = 10,
  nlambda = 100,
  ...
)

Arguments

Value

A logical vector with the length equal to the number of columns in X. TRUE indicates the variable (column of X) should be included. Similar to the value of SuperLearner::screen.glmnet().

Examples

    set.seed(321)
    expit <- binomial()$linkinv
    X <- matrix(rnorm(100 * 5), nrow = 100)
    y <- expit(1 + X[,1] + X[,2]) + rnorm(100)
    require(SuperLearner)
    SL.library<-list(c("SL.glmnet.extra","All"),
                     c("SL.glmnet.extra","screen.glmnet.extra"))
    SuperLearner(y, data.frame(X), family=binomial_extra(),
                 SL.library = SL.library, cvControl = list(V = 2))