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 expontential tilting is recomneded.

maxit

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

tol

Tolerance. If the achieved mean is to 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 warnint.

silent

Allows silencing some messages.

Nindependent

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

Value

An object of type tweights. This object conains 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 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. The euclidean based solution helps form a starting value which is used along with the constOptim function and lagrange multipliers to solve the Kullback-Leibler distance optimization. Output is the optimal porbability (p)

The 'Nindependent' option augments the dataset by assuming some additional specified number of patients. These pateints are assumed to made up of a random bootstrapped sample from the dataset for each variable marginaly leading to indepenent 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)
# }