linearization: Use Taylor linearization to get variance-covariance estimate

In bschneidr/schneidr: Utilities for data visualization, data wrangling, and mathematical statistics.

Description

Use Taylor linearization (i.e. the Delta Method) to obtain the variance of a function or the variance-covariance matrix of a vector-valued function

Usage

get_tsl_variance(f, values, vcov_matrix)

Arguments

f	An expression or list of expressions created using the 'expression()' function, e.g. 'expression(x/y)' or 'list(expression(sin(x + y)), expression(cos(x + y)))'.
values	A named list of values where first derivatives are to be evaluated, e.g. 'list(y = 10, x = 5)'. The names must match variables in the expression(s).
vcov_matrix	A variance-covariance matrix for the variables in the expression must be provided.

Value

A variance-covariance matrix for the expressions evaluated at the specified points. If only one expression is provided, the result is a single numeric value.

Examples

# Sample values of y and x
var_cov_pop <- matrix(c(5,4,4,5), byrow = TRUE, nrow = 2)
sampled_obs <- MASS::mvrnorm(n = 100, mu = c(120, 100), Sigma = var_cov_pop)

y <- sampled_obs[,1]
x <- sampled_obs[,2]

# Estimate ratio of y to x
ratio <- mean(y)/mean(x)

# Estimate sampling covariance of X and Y
x_y_vcov_estimate <- cov(sampled_obs) / (nrow(sampled_obs) - 1)

# Estimate sampling covariance of ratio
get_tsl_variance(list('ratio' = expression(y/x),
                      'product' = expression(x/y)),
                 values = list('y' = mean(y),
                               'x' = mean(x)),
                 vcov_matrix = x_y_vcov_estimate)

bschneidr/schneidr documentation built on Dec. 25, 2021, 4:55 p.m.