Covariance matrix, correlation matrix, variance and standard deviation for potential impact fractions

Computes the covariance (covariance) or correlation (correlation) for multiple potential impact fractions and the variance variance and standard deviation standard_deviationfor a potential impact fractions.

Usage

covariance(
  x,
  ...,
  var_p = NULL,
  var_beta = NULL,
  var_weights = NULL,
  var_pif_weights = NULL,
  var_pifs = NULL,
  warning = FALSE
)

variance(x, ...)

standard_deviation(x, ...)

correlation(x, ..., var_p = NULL, var_beta = NULL)

Arguments

x: A potential impact fraction
...: Multiple additional potential impact fraction objects separated by commas.
var_p: Estimate of the link_covariance matrix of p where the entry var_p[i,j] represents the link_covariance between p[i] and p[j].
var_beta: Estimate of the link_covariance matrix of beta where the entry var_beta[i,j] represents the link_covariance between beta[i] and beta[j].
var_weights: covariance matrix for the weights when calculating the total PIF (respectively PAF) in pif_total.
var_pif_weights: Covariance vector between the weights in pif_ensemble and the pif_atomic. This refers to the term \(\operatorname{Cov}\Big( \hat{q}_i,\widehat{\textrm{PIF}}_{B,j}\Big)\) in the equation below. If set to NULL its automatically calculated.
var_pifs: Covariance vector between the potential impact fractions in pif_ensemble and pif_atomic. This refers to the term \(\operatorname{Cov}\Big( \textrm{PIF}_{A,i}, \widehat{\textrm{PIF}}_{B,j}\Big)\) in the equation below. If set to NULL its automatically calculated.
warning: Boolean indicating whether to throw a warning if the labels on the fractions involved are not unique.

Value

A variance, covariance or correlation matrix.

Examples

# Get the approximate link_variance of a pif object
my_pif <- pif(p = 0.5, p_cft = 0.25, beta = 1.3,
              var_p = 0.1, var_beta = 0.2)
variance(my_pif)
#> [1] 0.07233754

# This is the same as link_covariance with just 1 pIF
covariance(my_pif)
#>            [,1]
#> [1,] 0.07233754

# Calculate the link_covariance between 3 fractions with shared relative risk
beta <- 0.3
var_beta <- 0.1
pif1 <- pif(0.5, 0.2, beta, var_p = 0.5 * (1 - 0.5) / 100, var_beta = var_beta)
pif2 <- pif(0.3, 0.1, beta, var_p = 0.3 * (1 - 0.3) / 100, var_beta = var_beta)
pif3 <- pif(0.7, 0.3, beta, var_p = 0.7 * (1 - 0.7) / 100, var_beta = var_beta)
covariance(pif1, pif2, pif3)
#>             [,1]        [,2]        [,3]
#> [1,] 0.008789254 0.006486541 0.010220324
#> [2,] 0.006486541 0.005074095 0.007703812
#> [3,] 0.010220324 0.007703812 0.012268945

# The link_covariance between a pif and itself only has the link_variance as entries
covariance(pif1, pif1)
#>             [,1]        [,2]
#> [1,] 0.008789254 0.008789254
#> [2,] 0.008789254 0.008789254

# Or if there is a link_covariance structure between different betas you can specify with
# var_beta in the link_covariance
betas <- c(1.3, 1.2, 1.27)

# link_covariance among all betas
var_beta <- matrix(c(
  1.0000000, -0.12123053, 0.35429369,
  -0.1212305, 1.00000000, -0.04266409,
  0.3542937, -0.04266409, 1.00000000
), byrow = TRUE, ncol = 3)
pif1 <- pif(0.5, 0.2, betas[1], var_p = 0.5 * (1 - 0.5) / 100, var_beta = var_beta[1, 1])
pif2 <- pif(0.3, 0.1, betas[2], var_p = 0.3 * (1 - 0.3) / 100, var_beta = var_beta[2, 2])
pif3 <- pif(0.3, 0.1, betas[3], var_p = 0.3 * (1 - 0.3) / 100, var_beta = var_beta[3, 3])
covariance(pif1, pif2, pif3, var_beta = var_beta)
#>              [,1]          [,2]          [,3]
#> [1,]  0.042197697 -5.651801e-03  1.629740e-02
#> [2,] -0.005651801  5.536138e-02 -9.642887e-05
#> [3,]  0.016297402 -9.642887e-05  5.410105e-02

# Compute the correlation
correlation(pif1, pif2, pif3, var_beta = var_beta)
#>            [,1]         [,2]         [,3]
#> [1,]  1.0000000 -0.116933525  0.341091700
#> [2,] -0.1169335  1.000000000 -0.001761979
#> [3,]  0.3410917 -0.001761979  1.000000000