R: TDboost Tweedie Regression Modeling

TDboost {TDboost} | R Documentation

## TDboost Tweedie Regression Modeling

### Description

Fits TDboost Tweedie Regression models.

### Usage

    TDboost(formula = formula(data),
        distribution = list(name="EDM",alpha=1.5),
        data = list(),
        weights,
        var.monotone = NULL,
        n.trees = 100,
        interaction.depth = 1,
        n.minobsinnode = 10,
        shrinkage = 0.001,
        bag.fraction = 0.5,
        train.fraction = 1.0,
        cv.folds=0,
        keep.data = TRUE,
        verbose = TRUE)

    TDboost.fit(x,y,
            offset = NULL,
            misc = NULL,
            distribution = list(name="EDM",alpha=1.5),
            w = NULL,
            var.monotone = NULL,
            n.trees = 100,
            interaction.depth = 1,
            n.minobsinnode = 10,
            shrinkage = 0.001,
            bag.fraction = 0.5,
            train.fraction = 1.0,
            keep.data = TRUE,
            verbose = TRUE,
            var.names = NULL,
            response.name = NULL)

    TDboost.more(object,
             n.new.trees = 100,
             data = NULL,
             weights = NULL,
             offset = NULL,
             verbose = NULL)

### Arguments

`formula` | a symbolic description of the model to be fit. The formula may include an offset term (e.g. y~offset(n)+x). If `keep.data=FALSE` in the initial call to `TDboost` then it is the user's responsibility to resupply the offset to `TDboost.more`.
`distribution` | a list with a component `name` specifying the distribution and any additional parameters needed. Tweedie regression is available and `distribution` must a list of the form `list(name="EDM",alpha=1.5)` where `alpha` is the index parameter that must be in (1,2]. When `alpha=2`, the distribution reduces to gamma. The current version's Tweedie regression methods do not handle non-constant weights and will stop.
`data` | an optional data frame containing the variables in the model. By default the variables are taken from `environment(formula)`, typically the environment from which `TDboost` is called. If `keep.data=TRUE` in the initial call to `TDboost` then `TDboost` stores a copy with the object. If `keep.data=FALSE` then subsequent calls to `TDboost.more` must resupply the same dataset. It becomes the user's responsibility to resupply the same data at this point.
`weights` | an optional vector of weights to be used in the fitting process. Must be positive but do not need to be normalized. If `keep.data=FALSE` in the initial call to `TDboost` then it is the user's responsibility to resupply the weights to `TDboost.more`.
`var.monotone` | an optional vector, the same length as the number of predictors, indicating which variables have a monotone increasing (+1), decreasing (-1), or arbitrary (0) relationship with the outcome.
`n.trees` | the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion.
`cv.folds` | Number of cross-validation folds to perform. If `cv.folds`>1 then `TDboost`, in addition to the usual fit, will perform a cross-validation, calculate an estimate of generalization error returned in `cv.error`.
`interaction.depth` | The maximum depth of variable interactions. 1 implies an additive model, 2 implies a model with up to 2-way interactions, etc.
`n.minobsinnode` | minimum number of observations in the trees terminal nodes. Note that this is the actual number of observations not the total weight.
`shrinkage` | a shrinkage parameter applied to each tree in the expansion. Also known as the learning rate or step-size reduction.
`bag.fraction` | the fraction of the training set observations randomly selected to propose the next tree in the expansion. This introduces randomnesses into the model fit. If `bag.fraction`<1 then running the same model twice will result in similar but different fits. `TDboost` uses the R random number generator so `set.seed` can ensure that the model can be reconstructed. Preferably, the user can save the returned `TDboost.object` using `save`.
`train.fraction` | The first `train.fraction * nrows(data)` observations are used to fit the `TDboost` and the remainder are used for computing out-of-sample estimates of the loss function.
`keep.data` | a logical variable indicating whether to keep the data and an index of the data stored with the object. Keeping the data and index makes subsequent calls to `TDboost.more` faster at the cost of storing an extra copy of the dataset.
`object` | a `TDboost` object created from an initial call to `TDboost`.
`n.new.trees` | the number of additional trees to add to `object`.
`verbose` | If TRUE, TDboost will print out progress and performance indicators. If this option is left unspecified for TDboost.more then it uses `verbose` from `object`.
`x, y` | For `TDboost.fit`: `x` is a data frame or data matrix containing the predictor variables and `y` is the vector of outcomes. The number of rows in `x` must be the same as the length of `y`.
`offset` | a vector of values for the offset
`misc` | For `TDboost.fit`: `misc` is an R object that is simply passed on to the TDboost engine.
`w` | For `TDboost.fit`: `w` is a vector of weights of the same length as the `y`.
`var.names` | For `TDboost.fit`: A vector of strings of length equal to the number of columns of `x` containing the names of the predictor variables.
`response.name` | For `TDboost.fit`: A character string label for the response variable.

### Details

This package implements a regression tree based gradient boosting estimator for nonparametric multiple Tweedie regression. The code is a modified version of `gbm` library originally written by Greg Ridgeway.

Boosting is the process of iteratively adding basis functions in a greedy fashion so that each additional basis function further reduces the selected loss function. This implementation closely follows Friedman's Gradient Boosting Machine (Friedman, 2001).

In addition to many of the features documented in the Gradient Boosting Machine, `TDboost` offers additional features including the out-of-bag estimator for the optimal number of iterations, the ability to store and manipulate the resulting `TDboost` object.

`TDboost.fit` provides the link between R and the C++ TDboost engine. `TDboost` is a front-end to `TDboost.fit` that uses the familiar R modeling formulas. However, `model.frame` is very slow if there are many predictor variables. For power-users with many variables use `TDboost.fit`. For general practice `TDboost` is preferable.

### Value

`TDboost`, `TDboost.fit`, and `TDboost.more` return a `TDboost.object`.

### Author(s)

Yi Yang yi.yang6@mcgill.ca, Wei Qian wxqsma@rit.edu and Hui Zou hzou@stat.umn.edu

### References

Yang, Y., Qian, W. and Zou, H. (2013), “A Boosted Tweedie Compound Poisson Model for Insurance Premium” Preprint.

G. Ridgeway (1999). “The state of boosting,” Computing Science and Statistics 31:172-181.

J.H. Friedman (2001). “Greedy Function Approximation: A Gradient Boosting Machine,” Annals of Statistics 29(5):1189-1232.

J.H. Friedman (2002). “Stochastic Gradient Boosting,” Computational Statistics and Data Analysis 38(4):367-378.

### See Also

`TDboost.object`, `TDboost.perf`, `plot.TDboost`, `predict.TDboost`, `summary.TDboost`,

### Examples

    data(FHT)
    # training on data1
    TDboost1 <- TDboost(Y~X1+X2+X3+X4+X5+X6,         # formula
        data=data1,                   # dataset
        var.monotone=c(0,0,0,0,0,0), # -1: monotone decrease,
                                     # +1: monotone increase,
                                     #  0: no monotone restrictions
        distribution=list(name="EDM",alpha=1.5),
                                     # specify Tweedie index parameter
        n.trees=3000,                # number of trees
        shrinkage=0.005,             # shrinkage or learning rate,
                                     # 0.001 to 0.1 usually work
        interaction.depth=3,         # 1: additive model, 2: two-way interactions, etc.
        bag.fraction = 0.5,          # subsampling fraction, 0.5 is probably best
        train.fraction = 0.5,        # fraction of data for training,
                                     # first train.fraction*N used for training
        n.minobsinnode = 10,         # minimum total weight needed in each node
        cv.folds = 5,                # do 5-fold cross-validation
        keep.data=TRUE,              # keep a copy of the dataset with the object
        verbose=TRUE)                # print out progress

    # print out the optimal iteration number M
    best.iter <- TDboost.perf(TDboost1,method="test")
    print(best.iter)

    # check performance using 5-fold cross-validation
    best.iter <- TDboost.perf(TDboost1,method="cv")
    print(best.iter)

    # plot the performance
    # plot variable influence
    summary(TDboost1,n.trees=1)         # based on the first tree
    summary(TDboost1,n.trees=best.iter) # based on the estimated best number of trees

    # making prediction on data2
    f.predict <- predict.TDboost(TDboost1,data2,best.iter)

    # least squares error
    print(sum((data2$Y-f.predict)^2))

    # create marginal plots
    # plot variable X1 after "best" iterations
    plot.TDboost(TDboost1,1,best.iter)
    # contour plot of variables 1 and 3 after "best" iterations
    plot.TDboost(TDboost1,c(1,3),best.iter)

    # do another 20 iterations
    TDboost2 <- TDboost.more(TDboost1,20,
                     verbose=FALSE) # stop printing detailed progress

    # fit a gamma model (when alpha = 2.0)
    data2 <- data1[data1$Y!=0,]
    TDboost3 <- TDboost(Y~X1+X2+X3+X4+X5+X6,         # formula
        data=data2,                   # dataset
        distribution=list(name="EDM",alpha=2.0),
        n.trees=3000, 				 # number of trees
        train.fraction = 0.5,        # fraction of data for training,
        verbose=TRUE)                # print out progress
    best.iter2 <- TDboost.perf(TDboost3,method="test")

[Package TDboost version 1.2 Index]