estimate_mean_and_sd: Estimate mean and standard deviation

In markolalovic/responsesR: Converting Latent Variables into Likert Scale Responses

Estimate mean and standard deviation

Description

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.

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.

Value

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

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)

markolalovic/responsesR documentation built on Oct. 15, 2024, 11:14 a.m.