Variance models for estimating prediction intervals

A variance model estimates the variance of predicted values. It can be used to estimate prediction intervals. See the interval argument of

A variance model is built by earth if earth's varmod.method argument is specified. Results are stored in the $varmod field of the earth model. See the vignette “Variance models in earth” for details.

You probably won't need to directly call print.varmod or summary.varmod. They get called internally by

# S3 method for varmod
    object  = stop("no 'object' argument"),
    level   = .95,
    style   = "standard",
    digits  = 2,
    newdata = NULL,

A varmod object. This is the only required argument.


Same as's level argument.


Determines how the coefficients of the varmod are printed by summary.varmod: "standard" (default) "unit" for easy comparison normalize the coefficients by dividing by the first coefficient.


Number of digits to print. Default is 2.


Default NULL. Else print the interval coverage table for the new data.

Dots are passed on.


A "varmod" object has the following fields:

  • call The call used internally in the parent model to build the varmod object.

  • parent The parent earth model.

  • method Copy of the varmod.method argument to the parent model.

  • package NULL, unless method="gam", in which case either "gam" or "mgcv".

  • exponent Copy of the varmod.exponent argument to the parent model.

  • lambda Currently always 1, meaning use absolute residuals.

  • rmethod Currently always "hc2", meaning correct the residuals with 1/(1-h_ii).

  • converged Did the residual submodel IRLS converge?

  • iters Number of residual model IRLS iterations (1 to 50).

  • residmod The residual submodel. So for example, if varmod.method="lm", this will be an lm object.

  • The predicted residual standard deviation is clamped so it will always be at least this value. This prevents prediction of negative or absurdly small variances. See earth's varmod.clamp argument. Clamping takes place in predict.varmod, which is called by when estimating prediction intervals.

  • model.var An n x 1 matrix. The model.var for an observation is the estimated model variance for that observation over all datasets, and is estimated with repeated cross validation. It is the variance of the mean out-of-fold prediction for that observation over ncross repetitions.

  • abs.resids An n x 1 matrix. The absolute residuals used to build the residual model.

  • parent.x An n x p matrix. Parent earth model x.

  • parent.y An n x 1 matrix. Parent earth model y.

  • iter.rsq Weighted R-Squared of residual submodel residmod, after IRLS iteration.

  • iter.stderr Standard errors of the coefficients of the residual submodel residmod, after IRLS iteration.

See Also

plot.varmod, predict.varmod

  • varmod
  • summary.varmod

set.seed(1) # optional, for cross validation reproducibility

# note: should really use ncross=30 below but for a quick demo we don't

earth.mod <- earth(O3~temp, data=ozone1, nfold=10, ncross=3, varmod.method="lm")

print(summary(earth.mod)) # note additional info on the variance model

old.mfrow <- par(mfrow=c(2,2), mar=c(3, 3, 3, 1), mgp=c(1.5, 0.5, 0))

plotmo(earth.mod, do.par=FALSE, response.col=1, level=.90, main="earth model: O3~temp")

plot(earth.mod, which=3, level=.90) # residual plot: note 90% pred and darker conf intervals

# }
Documentation reproduced from package earth, version 4.5.1, License: GPL-3

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