dbfit {DBfit}

The main function for the double bootstrap method

Description

This function is used to implement the double bootstrap method. It is used to yield estimates of both regression coefficients and autoregressive parameters(rho), and also the inference of them.

Usage

## Default S3 method:
dbfit(x, y, arp, nbs = 500, nbscov = 500, 
conf = 0.95, correction = TRUE, method = "OLS", scores, ...)

Arguments

x

the design matrix, including intercept, i.e. the first column being ones.

y

the response variable.

arp

the order of autoregressive errors.

nbs

the bootstrap size for the first bootstrap procedure. Default is 500.

nbscov

the bootstrap size for the second bootstrap procedure. Default is 500.

conf

the confidence level of CI for rho, default is 0.95.

correction

logical. Currently, ONLY works for order 1, i.e. for order > 1, this correction will not get involved. If TRUE, uses the correction for cases that the estimate of rho is 0.99. Default is TRUE.

method

the method to be used for fitting. If "OLS", uses the ordinary least square lm; If "RANK", uses the rank-based fit rfit.

scores

Default is Wilcoxon scores

...

additional arguments to be passed to fitting routines

Details

Computes the double bootstrap as discussed in McKnight, McKean, and Huitema (2000). For details, see the references.

Value

coefficients

the estimates of regression coefficients based on the first bootstrap procedure

rho1

the Durbin two-stage estimate of the autoregressive parameter rho

adjar

the estimates of regression coefficients based on the first bootstrap procedure

mse

the mean square error

rho_CI_1

the first type of CI for rho, see the second reference for details.

rho_CI_2

the second type of CI for rho, see the second reference for details.

rho_CI_3

the third type of CI for rho, see the second reference for details.

betacov

the estimate of the variance-covariance matrix of betas

tabbeta

a table of point estimates, SE's, test statistics and p-values.

flag99

an indicator; if 1, it indicates the original fit yields an estimate of rho to be 0.99. When the correction is requested (default), the correction procedure kicks in, and the final estimates of rho is corrected. Only valid if order 1 is specified.

residuals

the residuals, that is response minus fitted values.

fitted.values

the fitted mean values.

Author(s)

Joseph W. McKean and Shaofeng Zhang

References

McKnight, S. D., McKean, J. W., and Huitema, B. E. (2000). A double bootstrap method to analyze linear models with autoregressive error terms. Psychological methods, 5 (1), 87.

Shaofeng Zhang (2017). Ph.D. Dissertation.

See Also

dbfit.formula

Examples

# make sure the dependent package Rfit is installed
# To save users time, we set both bootstrap sizes to be 100 in this example. 
# Defaults are both 500. 

# data(testdata)
# This data is generated by a two-phase design, with autoregressive order being one, 
# autoregressive coefficient being 0.6 and all regression coefficients being 0. 
# Both the first and second phase have 20 observations.

# y <- testdata[,5]
# x <- testdata[,1:4]
# fit1 <- dbfit(x,y,1, nbs = 100, nbscov = 100) # OLS fit, default
# summary(fit1) 
# Note that the CI's of autoregressive coef are not shown in the summary.
# Instead, they are attributes of model fit.
# fit1$rho_CI_1

# fit2 <- dbfit(x,y,1, nbs = 100, nbscov = 100 ,method="RANK") # rank-based fit

# When fitting with autoregressive order 2, 
# the estimate of the second order autoregressive coefficient should not be significant,
# since this data is generated with order 1.

# fit3 <- dbfit(x,y,2, nbs = 100, nbscov = 100)
# fit3$rho_CI_1 # The first row is lower bounds, and second row is upper bounds