D-vine regression models

Source: R/vinereg.R

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

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.

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.

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.

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))
#> D-vine regression model: y | x.2, x.1 
#> nobs = 100, edf = 2, cll = 17.47, caic = -30.94, cbic = -25.73 

# inspect model
summary(fit)
#>   var edf        cll      caic      cbic      p_value
#> 1   y   0 -218.94275  437.8855  437.8855           NA
#> 2 x.2   1   73.02642 -144.0528 -141.4477 1.264121e-33
#> 3 x.1   1  163.38599 -324.7720 -322.1668 4.851392e-73
plot_effects(fit)
#> `geom_smooth()` using method = 'loess' and formula = 'y ~ x'


# 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 model: y | x.2, x.1, z.1 
#> nobs = 100, edf = 2, cll = 17.47, caic = -30.94, cbic = -25.73