PTBi {accuracy} | R Documentation

## functions to add random noise to a vector

### Description

These functions add noise to a vector. These are helper functions for `perturb` They are used to select the type and magnitude of noise applied to each vector in the data frame, when running the perturbation sensitivity analysis. Use them only if they are substantively justified – you can also supply custom functions for use with this perturbation framework.

### Usage

            #
            # identity function
            #

            PTBi(x,size=1)                          # identify function, returns original vector
                                                    # size is a dummy value, it is ignored
            #
            # minimal noise
            #

            PTBms(x, size=1)                                # adds minimal, scaled, noise
            PTBmsb(x, size=1, lbound=0, ubound=1)           # adds minimal, scaled, noise,
                                                    # resulting vector truncated to bounds
            PTBmsbr(x, size=1, lbound=0, ubound=1)          # adds minimal, scaled  noise, out of-bounds elements
                                                    # of vector resamples until within bounds

            #
            # Normally distributed noise
            #

            PTBn(x, size = 1)                       # adds normally distributed noise
            PTBnc(x, size = 1)                      # normally distributed noise,
                                                    # recentered to guarantee mean-zero disturbance
            PTBns(x, size = 1)                      # adds normally distributed, scaled, noise

            PTBnbr(x, size = 1, lbound=0, ubound=1)#
            PTBnsbr(x, size = 1, lbound=0, ubound=1)# adds normally (scaled)  distributed noise
                                                    # out of-bounds elements
                                                    # of vector resampled until within bounds

            PTBnbrr(x, size = 1, lbound=0, ubound=1)#
            PTBnsbrr(x, size = 1, lbound=0, ubound=1)       # adds normally distributed,scaled noise
                                                    # noise rescaled to bounds, and then
                                                    # out of bounds elements
                                                    # resampled until within bounds

            #
            # Uniformly distributed noise

            PTBu(x, size = 1)                       # adds uniformly distributed noise
            PTBuc(x, size = 1)                      # uniformly distributed noise,
                                                    # recentered to guarantee mean-zero disturbance
            PTBus(x, size = 1)                      # adds uniformly distributed, scaled, noise

            PTBubr(x, size = 1, lbound=0, ubound=1)#
            PTBusbr(x, size = 1, lbound=0, ubound=1)# adds uniformly, scaled,  distributed noise
                                                    # out of-bounds elements
                                                    # of vector resampled until within bounds

            PTBubrr(x, size = 1, lbound=0, ubound=1)#
            PTBusbrr(x, size = 1, lbound=0, ubound=1)       # adds unirformly distributed,scaled noise
                                                    # noise rescaled to bounds, and then
                                                    # out of bounds elements
                                                    # resampled until within bounds

### Arguments

`x` | vector to be perturbed
`size` | magnitude of noise
`ubound` | upper bound, can be a scalar or a vector of the same length as x
`lbound` | lower bound, can be a scalar or a vector of the same length as x

### Details

Noise is randomly adds to each observation in the vector according to the chosen distribution function: - 'minimal' adds .Machine$double.ep) or subtracts .Machine$double.neg.eps - 'uniform' adds uniformly distributed random [-size/2,+size/2] - 'normal' adds Normal(mean=0,stddev=size)

Noise is assymptotically mean zero. To guarantee mean-zero noise for a particular sample, use the "centered" helper functions, which adjust the noise vector to be approximately mean zero.

The 'scaled' functions, multiply each random deviate by $x_i$ for each observation in x. This is useful if measurement error is heteroscedastic.

Some helper functions can return a noisy vector guaranteed to be within given upper and lower bounds. This can be done through truncation, through resampling out-of-bounds observations, or by reducing the amount of noise added to entries close to the bounds.

### Value

Returns a new vector x', with the same length as x.

### Author(s)

Micah Altman Micah_Altman@harvard.edu http://www.hmdc.harvard.edu/micah_altman/

### References

Altman, M., J. Gill and M. P. McDonald. 2003. Numerical Issues in Statistical Computing for the Social Scientist. John Wiley & Sons. http://www.hmdc.harvard.edu/numerical_issues/

### See Also

`perturb`

### Examples

            x=1:1000
            x.i = PTBi(x)
            x.m = PTBms(x)
            x.u = PTBu(x,size=.01)
            x.us = PTBus(x,size=.01)
            x.uc = PTBuc(x,size=.01)

            sum(x-x.i)              # should be 0, identity transform
            sum(which(x!=x.i))      # also 0

            sum(x-x.m)              # should be quite small, very close to 0
            length(which(x!=x.m))   # should be near 1000

            sum(x-x.u)              # should be small
            length(which(x!=x.m))   # should be near 1000

            sum(x-x.us)             # should be small
            length(which(x!=x.m))   # should be near 1000

            sum(x-x.uc)             # should be near 0
            length(which(x!=x.m))   # should be near 1000

[Package accuracy version 1.35 Index]