Package {vinereg}

vinereg: D-vine regression models

Description

Fit D-vine copula regression models for conditional mean and quantile prediction with continuous or discrete variables. The package provides automatic covariate selection, fixed-order models, conditional distribution diagnostics, and marginal fitted-quantile plots.

Author(s)

Maintainer: Thomas Nagler mail@tnagler.com

Authors:

• Thomas Nagler mail@tnagler.com

Other contributors:

• Dani Kraus [contributor]

References

Kraus, D. and Czado, C. (2017). D-vine copula based quantile regression. Computational Statistics & Data Analysis, 110, 1–18. doi:10.1016/j.csda.2016.12.009

Schallhorn, N., Kraus, D., Nagler, T., and Czado, C. (2017). D-vine quantile regression with discrete variables. doi:10.48550/arXiv.1705.08310

See Also

Useful links:

• https://tnagler.github.io/vinereg/

• Report bugs at https://github.com/tnagler/vinereg/issues

Conditional log-likelihood

Description

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

Usage

cll(object, newdata, cores = 1)

Arguments

Value

The scalar conditional log-likelihood evaluated on newdata.

Examples

# simulate data
x <- matrix(rnorm(100), 50, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(50, 2, 0.5)))

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

cll(fit, dat)
fit$stats$cll

Conditional density or probability mass

Description

Calculates the conditional density of a continuous response or conditional probability mass of a discrete response given the covariates.

Usage

cpdf(object, newdata, cores = 1)

Arguments

Value

A numeric vector containing one conditional density or probability mass per row of newdata.

Examples

# simulate data
x <- matrix(rnorm(100), 50, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(50, 2, 0.5)))

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

cpdf(fit, dat)

Conditional probability integral transform

Description

Evaluates the fitted conditional distribution of the response given the covariates. For a discrete response, this is the conditional CDF at the observed category, not a randomized probability integral transform.

Usage

cpit(object, newdata, cores = 1)

Arguments

Value

A numeric vector containing one conditional CDF value per row of newdata.

Examples

# simulate data
x <- matrix(rnorm(100), 50, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(50, 2, 0.5)))

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

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

Plot marginal effects of a D-vine regression model

Description

The points show fitted conditional quantiles against each requested variable. For variable X_k, the smooth curve estimates E[\hat Q_\alpha(Y \mid X) \mid X_k = x]. It therefore averages over the conditional distribution of the other variables. A curve for an unselected variable can vary when that variable is associated with selected predictors. The curve is descriptive and is not a partial-dependence or causal effect.

Usage

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

Arguments

Value

A ggplot2::ggplot() object.

Examples

# simulate data
x <- matrix(rnorm(100), 50, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(50, 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

Value

A data frame with one row per observation and one column per value of alpha. Columns are named by their quantile level; the conditional mean column is named mean.

See Also

vinereg

Examples

# simulate data
x <- matrix(rnorm(100), 50, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(50, 2, 0.5)))

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

# 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))

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

Details

If discrete variables are declared as ordered() or factor(), they are handled as described in Panagiotelis et al. (2012).

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.

factor_map

mapping from original variables to expanded 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(100), 50, 2)
y <- x %*% c(1, -2)
dat <- data.frame(y = y, x = x, z = as.factor(rbinom(50, 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")))

Standard methods for D-vine regression models

Description

These methods extract the fitted model's call information, data, effective degrees of freedom, conditional log-likelihood, and variable-wise summary.

Usage

## S3 method for class 'vinereg'
print(x, ...)

## S3 method for class 'vinereg'
summary(object, ...)

## S3 method for class 'vinereg'
logLik(object, ...)

## S3 method for class 'vinereg'
nobs(object, use.fallback = TRUE, ...)

## S3 method for class 'vinereg'
formula(x, ...)

## S3 method for class 'vinereg'
model.frame(formula, ...)

Arguments

Value

print() returns x invisibly. summary() returns a data frame with one row for the response and each selected predictor. logLik() returns an object of class logLik; its df attribute contains the effective degrees of freedom. nobs() returns the number of observations used for fitting. formula() and model.frame() return the model formula and frame.