tweights: Function `tweights`

Description

Returns a vector p of resampling probabilities such that the column means of tboot(dataset = dataset, p = p) equals target on average.

Usage

tweights(dataset, target = apply(dataset, 2, mean), distance = "klqp",
  maxit = 1000, tol = 1e-08, warningcut = 0.05, silent = FALSE,
  Nindependent = 0)

Arguments

dataset

Data frame or matrix to use to find row weights.

target

Numeric vector of target column means. If the 'target' is named, then all elements of names(target) should be in the dataset.

distance

The distance to minimize. Must be either 'euchlidean,' 'klqp' or 'klpq' (i.e. Kullback-Leibler). 'klqp' which is exponential tilting is recommended.

maxit

Defines the maximum number of iterations for optimizing 'kl' distance.

tol

Tolerance. If the achieved mean is to0 far from the target (i.e. as defined by tol) an error will be thrown.

warningcut

Sets the cutoff for determining when a large weight will trigger a warning.

silent

Allows silencing of some messages.

Nindependent

Assumes the input also includes 'Nindependent' samples with independent columns. See details.

Value

An object of type tweights. This object contains the following components:

weights: Tilted weights for resampling
originalTarget: Will be null if target was not changed.
target: Actual target that was attempted.
achievedMean: Achieved mean from tilting.
dataset: Inputed dataset.
X: Reformated dataset.
Nindependent: Inputed 'Nindependent' option.

Details

Let $p_i = 1/n$ be the probability of sampling subject $i$ from a dataset with $n$ individuals (i.e. rows of the dataset) in the classic resampling with replacement scheme. Also, let $q_i$ be the probability of sampling subject $i$ from a dataset with $n$ individuals in our new resampling scheme. Let $d(q,p)$ represent a distance between the two resampling schemes. The tweights function seeks to solve the problem: $$q = argmin_p d(q,p)$$ Subject to the constraint that: $$ sum_i q_i = 1$$ and $$ dataset' q = target$$ where dataset is a n x K matrix of variables input to the function.

$$d_{euclidian}(q,p) = sqrt( \sum_i (p_i-q_i)^2 )$$ $$d_{kl}(q,p) = \sum_i (log(p_i) - log(q_i))$$

Optimization for Euclidean distance is a quadratic program and utilizes the ipop function in kernLab. Optimization for the others utilize a Newton-Raphson type iterative algorithm.

If the original target cannot be achieved. Something close to the original target will be selected. A warning will be produced and the new target displayed.

The 'Nindependent' option augments the dataset by assuming some additional specified number of patients. These patients are assumed to made up of a random bootstrapped sample from the dataset for each variable marginally leading to independent variables.

Examples

Run this code

# NOT RUN {
 target=c(Sepal.Length=5.5, Sepal.Width=2.9, Petal.Length=3.4)
 w = tweights(dataset = iris, target = target, silent = TRUE)
 simulated_data = tboot(nrow = 1000, weights = w)
# }