Package 'vinereg'

Conditional log-likelihood

Description

Calculates the conditional log-likelihood of the response given the covariates.

Usage

cll(object, newdata, cores = 1)

Arguments

object	an object of class vinereg.
newdata	matrix of response and covariate values for which to compute the conditional distribution.
cores	integer; the number of cores to use for computations.

Examples

# simulate data
x <- matrix(rnorm(200), 100, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(100, 2, 0.5)))

# fit vine regression model
fit <- vinereg(y ~ ., dat)

cll(fit, dat)
fit$stats$cll

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Conditional PDF

Description

Calculates the conditional density of the response given the covariates.

Usage

cpdf(object, newdata, cores = 1)

Arguments

object	an object of class vinereg.
newdata	matrix of response and covariate values for which to compute the conditional density
cores	integer; the number of cores to use for computations.

Examples

# simulate data
x <- matrix(rnorm(200), 100, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(100, 2, 0.5)))

# fit vine regression model
fit <- vinereg(y ~ ., dat)

cpdf(fit, dat)

---

Conditional probability integral transform

Description

Calculates the conditional distribution of the response given the covariates.

Usage

cpit(object, newdata, cores = 1)

Arguments

object	an object of class vinereg.
newdata	matrix of response and covariate values for which to compute the conditional distribution.
cores	integer; the number of cores to use for computations.

Examples

# simulate data
x <- matrix(rnorm(200), 100, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(100, 2, 0.5)))

# fit vine regression model
fit <- vinereg(y ~ ., dat)

hist(cpit(fit, dat)) # should be approximately uniform

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Plot marginal effects of a D-vine regression model

Description

The marginal effects of a variable is the expected effect, where expectation is meant with respect to all other variables.

Usage

plot_effects(object, alpha = c(0.1, 0.5, 0.9), vars = object$order)

Arguments

object	a vinereg object
alpha	vector of quantile levels.
vars	vector of variable names.

Examples

# simulate data
x <- matrix(rnorm(200), 100, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(100, 2, 0.5)))

# fit vine regression model
fit <- vinereg(y ~ ., dat)
plot_effects(fit)

---

Predict conditional mean and quantiles from a D-vine regression model

Description

Predict conditional mean and quantiles from a D-vine regression model

Usage

## S3 method for class 'vinereg'
predict(object, newdata, alpha = 0.5, cores = 1, ...)

## S3 method for class 'vinereg'
fitted(object, alpha = 0.5, ...)

Arguments

object	an object of class vinereg.
newdata	matrix of covariate values for which to predict the quantile.
alpha	vector of quantile levels; NA predicts the mean based on an average of the 1:10 / 11-quantiles.
cores	integer; the number of cores to use for computations.
...	unused.

Value

A data.frame of quantiles where each column corresponds to one value of alpha.

See Also

vinereg

Examples

# simulate data
x <- matrix(rnorm(200), 100, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(100, 2, 0.5)))

# fit vine regression model
(fit <- vinereg(y ~ ., dat))

# inspect model
summary(fit)
plot_effects(fit)

# model predictions
mu_hat <- predict(fit, newdata = dat, alpha = NA) # mean
med_hat <- predict(fit, newdata = dat, alpha = 0.5) # median

# observed vs predicted
plot(cbind(y, mu_hat))

## fixed variable order (no selection)
(fit <- vinereg(y ~ ., dat, order = c("x.2", "x.1", "z.1")))

---

D-vine regression models

Description

Sequential estimation of a regression D-vine for the purpose of quantile prediction as described in Kraus and Czado (2017).

Usage

vinereg(
  formula,
  data,
  family_set = "parametric",
  selcrit = "aic",
  order = NA,
  par_1d = list(),
  weights = numeric(),
  cores = 1,
  ...,
  uscale = FALSE
)

Arguments

formula	an object of class "formula"; same as lm().
data	data frame (or object coercible by as.data.frame()) containing the variables in the model.
family_set	see family_set argument of rvinecopulib::bicop().
selcrit	selection criterion based on conditional log-likelihood. "loglik" (default) imposes no correction; other choices are "aic" and "bic".
order	the order of covariates in the D-vine, provided as vector of variable names (after calling vinereg:::expand_factors(model.frame(formula, data))); selected automatically if order = NA (default).
par_1d	list of options passed to kde1d::kde1d(), must be one value for each margin, e.g. list(xmin = c(0, 0, NaN)) if the response and first covariate have non-negative support.
weights	optional vector of weights for each observation.
cores	integer; the number of cores to use for computations.
...	further arguments passed to rvinecopulib::bicop().
uscale	if TRUE, vinereg assumes that marginal distributions have been taken care of in a preliminary step.

Details

If discrete variables are declared as ordered() or factor(), they are handled as described in Panagiotelis et al. (2012). This is different from previous version where the data was jittered before fitting.

Value

An object of class vinereg. It is a list containing the elements

formula

the formula used for the fit.

selcrit

criterion used for variable selection.

model_frame

the data used to fit the regression model.

margins

list of marginal models fitted by kde1d::kde1d().

vine

an rvinecopulib::vinecop_dist() object containing the fitted D-vine.

stats

fit statistics such as conditional log-likelihood/AIC/BIC and p-values for each variable's contribution.

order

order of the covariates chosen by the variable selection algorithm.

selected_vars

indices of selected variables.

Use predict.vinereg() to predict conditional quantiles. summary.vinereg() shows the contribution of each selected variable with the associated p-value derived from a likelihood ratio test.

References

Kraus and Czado (2017), D-vine copula based quantile regression, Computational Statistics and Data Analysis, 110, 1-18

Panagiotelis, A., Czado, C., & Joe, H. (2012). Pair copula constructions for multivariate discrete data. Journal of the American Statistical Association, 107(499), 1063-1072.

See Also

predict.vinereg

Examples

# simulate data
x <- matrix(rnorm(200), 100, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(100, 2, 0.5)))

# fit vine regression model
(fit <- vinereg(y ~ ., dat))

# inspect model
summary(fit)
plot_effects(fit)

# model predictions
mu_hat <- predict(fit, newdata = dat, alpha = NA) # mean
med_hat <- predict(fit, newdata = dat, alpha = 0.5) # median

# observed vs predicted
plot(cbind(y, mu_hat))

## fixed variable order (no selection)
(fit <- vinereg(y ~ ., dat, order = c("x.2", "x.1", "z.1")))

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