estimate_params {latent2likert}

Estimate Latent Parameters

Description

Estimates the location and scaling parameters of the latent variables from existing survey data.

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.

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.

Value

A table of estimated parameters for each latent variable.

See Also

discretize_density for details on calculating the endpoints, and part_bfi for example of the survey data.

Examples

data(part_bfi)
vars <- c("A1", "A2", "A3", "A4", "A5")
estimate_params(data = part_bfi[, vars], n_levels = 6)