estimate_prod {psychmeta}

Estimation of statistics computed from products of random, normal variables

Description

This family of functions computes univariate descriptive statistics for the products of two variables denoted as "x" and "y" (e.g., mean(x * y) or var(x * y)) and the covariance between the products of "x" and "y" and of "u" and "v" (e.g., cov(x * y, u * v) or cor(x * y, u * v)). These functions presume all variables are random normal variables.

Available functions include:

• estimate_mean_prod: Estimate the mean of the product of two variables: x * y.

• estimate_var_prod: Estimate the variance of the product of two variables: x * y.

• estimate_cov_prods: Estimate the covariance between the products of two pairs of variables: x * y and u * v.

• estimate_cor_prods: Estimate the correlation between the products of two pairs of variables: x * y and u * v.

Usage

estimate_mean_prod(mu_x, mu_y, cov_xy)

estimate_var_prod(mu_x, mu_y, var_x, var_y, cov_xy)

estimate_cov_prods(mu_x, mu_y, mu_u, mu_v, cov_xu, cov_xv, cov_yu, cov_yv)

estimate_cor_prods(
  mu_x,
  mu_y,
  mu_u,
  mu_v,
  var_x,
  var_y,
  var_u,
  var_v,
  cov_xu,
  cov_xv,
  cov_yu,
  cov_yv,
  cov_xy,
  cov_uv
)

Arguments

mu_x

Expected value of variable x.

mu_y

Expected value of variable y.

cov_xy

Covariance between x and y.

var_x

Variance of variable x.

var_y

Variance of variable y.

mu_u

Expected value of variable u.

mu_v

Expected value of variable v.

cov_xu

Covariance between x and u.

cov_xv

Covariance between x and v.

cov_yu

Covariance between y and u.

cov_yv

Covariance between y and v.

var_u

Variance of variable u.

var_v

Variance of variable v.

cov_uv

Covariance between u and v.

Value

An estimated statistic computed from the products of random, normal variables.

References

Bohrnstedt, G. W., & Goldberger, A. S. (1969). On the exact covariance of products of random variables. Journal of the American Statistical Association, 64(328), 1439. doi:10.2307/2286081

Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55(292), 708. doi:10.2307/2281592