Estimate mean and standard deviation — estimate_mean_and

Estimates the mean and standard deviation of a latent variable given the discrete probabilities of its observed Likert scale responses.

Usage

estimate_mean_and_sd(prob, n_levels, skew = 0, eps = 1e-06, maxit = 100)

Arguments

prob: named vector of probabilities for each response category.
n_levels: number of response categories for the Likert scale item.
skew: marginal skewness of the latent variable, defaults to 0.
eps: tolerance for convergence, defaults to 1e-6.
maxit: maximum number of iterations, defaults to 100.

Value

A numeric vector with two elements: the estimated mean and standard deviation.

Details

This function uses an iterative algorithm to solve the system of non-linear equations that describe the relationship between the continuous latent variable and the observed discrete probability distribution of Likert scale responses. The algorithm ensures stability by reparameterizing the system and applying constraints to prevent stepping into invalid regions.

Examples

prob <- c("1" = 0.313, "2" = 0.579, "3" = 0.105, "4" = 0.003)
# returns estimates that are close to the actual mean and sd: c(-1, 0.5)
estimate_mean_and_sd(prob, 5)
#> [1] -1.0025695  0.5004155