MLboot {RXshrink}

Calculate Bootstrap distribution of Unrestricted Maximum Likelihood (ML) point-estimates for a Linear Model.

Description

Resample With-Replacement from a given data.frame and recompute MSE risk-optimal estimates of Beta-Coefficients and their Relative MSE risks using MLcalcs() to compute ML point-estimates.

Usage

  MLboot(form, data, reps=100, seed, rscale=1)

Arguments

form

Regression formula [y~x1+x2+...] suitable for use with lm().

data

data.frame containing observations on all variables in the formula.

reps

Number of Bootstrap replications: Minimum reps = 10, Default is reps = 100. While reps = 10000 is reasonable for bivariate (p=2) linear models, even that many reps could be excessive for models with p >> 2.

seed

Either an Integer between 1 and 999 or else missing to generate a random seed.

rscale

One of three possible choices (0, 1 or 2) for "rescaling" of variables (after being "centered") to remove all "non-essential" ill-conditioning: 0 implies no rescaling; 1 implies divide each variable by its standard error; 2 implies rescale as in option 1 but re-express answers as in option 0.

Details

Ill-conditioned and/or nearly multi-collinear linear regression models are unlikely to yield reasonable ML unbiased (OLS) point-estimates. But more reasonable ML "optimally-biased" point-estimates from generalized ridge regression (GRR) typically have questionable MSE risk characteristics because they are complicated non-linear functions of the observed y-outcome vector. Thus the distribution of bootstrap resamples is of considerable interest in both theory and practice.

Value

An output list object of class MLboot:

data

Name of the data.frame object specified as the second argument.

form

The regression formula specified as the first argument.

reps

Number of Bootstrap replications performed.

seed

Seed used to start random number generator.

n

Number of complete observations after removal of all missing values.

p

Number of beta, rmse or dmse estimates resampled.

ols.beta

OLS matrix (reps x p) of unbiased beta-coefficient estimates.

ols.rmse

OLS matrix (reps x p) of beta-coefficient relative variances.

opt.dmse

OPT matrix (reps x p) of delta shrinkage-factors with minimum MSE risk.

opt.beta

OPT matrix (reps x p) of biased beta-coefficient estimates.

opt.rmse

OPT matrix (reps x p) of beta-coefficient relative MSE risks.

Author(s)

Bob Obenchain <[e-mail]>

References

Thompson JR. (1968) Some shrinkage techniques for estimating the mean. Journal of the American Statistical Association 63, 113-122. (The "cubic" estimator.)

Obenchain RL. (2022) Efficient Generalized Ridge Regression. Open Statistics 3: 1-18. doi:10.1515/stat-2022-0108

Obenchain RL. (2022) RXshrink_in_R.PDF RXshrink package vignette-like document, Version 2.1. http://localcontrolstatistics.org

See Also

eff.ridge, correct.signs