Estimate Latent Parameters

Usage

estimate_params(data, n_levels, skew = 0)

Arguments

data

survey data with columns representing individual items. Apart from this, data can be of almost any class such as "data.frame" "matrix" or "array".

n_levels

number of response categories, a vector or a number.

skew

marginal skewness of latent variables, defaults to 0.

Value

A table of estimated parameters for each latent variable.

Details

The relationship between the continuous random variable $X$ and the discrete probability distribution $p_k$, for $k = 1, \dots, K$, can be described by a system of non-linear equations: $$p_{k} = F_{X}\left( \frac{x_{k - 1} - \xi}{\omega} \right) - F_{X}\left( \frac{x_{k} - \xi}{\omega} \right) \quad \text{for} \ k = 1, \dots, K$$ where:

$F_{X}$

is the cumulative distribution function of $X$,

$K$

is the number of possible response categories,

$x_{k}$

are the endpoints defining the boundaries of the response categories,

$p_{k}$

is the probability of the $k$-th response category,

$\xi$

is the location parameter of $X$,

$\omega$

is the scaling parameter of $X$.

The endpoints $x_{k}$ are calculated by discretizing a random variable $Z$ with mean 0 and standard deviation 1 that follows the same distribution as $X$. By solving the above system of non-linear equations iteratively, we can find the parameters that best fit the observed discrete probability distribution $p_{k}$.

The function estimate_params:

• Computes the proportion table of the responses for each item.

• Estimates the probabilities $p_{k}$ for each item.

• Computes the estimates of $\xi$ and $\omega$ for each item.

• Combines the estimated parameters for all items into a table.

See also

Examples

data(part_bfi)
vars <- c("A1", "A2", "A3", "A4", "A5")
estimate_params(data = part_bfi[, vars], n_levels = 6)
#>          items
#> estimates         A1         A2         A3         A4         A5
#>      mean -0.9759824  1.0830781  0.9776057  1.1723519  0.9006478
#>      sd    1.1798137  0.7968668  0.8432599  1.3825407  0.8648150