Hare: hazard regression

Description

This function summarizes both the stepwise selection process of the model fitting by hare, as well as the final model that was selected using AIC/BIC.

Usage

## S3 method for class 'hare'
summary(object, ...) 
## S3 method for class 'hare'
print(x, ...) 

Arguments

Details

These function produce identical printed output. The main body consists of two tables.

The first table has six columns: the first column is a possible number of dimensions for the fitted model;

the second column indicates whether this model was fitted during the addition or deletion stage;

the third column is the log-likelihood for the fit;

the fourth column is -2 * loglikelihood + penalty * (dimension), which is the AIC criterion - hare selected the model with the minimum value of AIC;

the last two columns give the endpoints of the interval of values of penalty that would yield the model with the indicated number of dimensions (NAs imply that the model is not optimal for any choice of penalty).

At the bottom of the first table the dimension of the selected model is reported, as is the value of penalty that was used.

Each row of the second table summarizes the information about a basis function in the final model. It shows the variables involved, the knot locations, the estimated coefficient and its standard error and Wald statistic (estimate/SE).

Note

Since the basis functions are selected in an adaptive fashion, typically most Wald statistics are larger than (the magical) 2. These statistics should be taken with a grain of salt though, as they are inflated because of the adaptivity of the model selection.

Author(s)

Charles Kooperberg clk@fredhutch.org.

References

Charles Kooperberg, Charles J. Stone and Young K. Truong (1995). Hazard regression. Journal of the American Statistical Association, 90, 78-94.

Charles J. Stone, Mark Hansen, Charles Kooperberg, and Young K. Truong. The use of polynomial splines and their tensor products in extended linear modeling (with discussion) (1997). Annals of Statistics, 25, 1371–1470.

See Also

hare, plot.hare, dhare, hhare, phare, qhare, rhare.

Examples

fit <- hare(testhare[,1], testhare[,2], testhare[,3:8]) 
summary(fit) 

Results