| simulate_likert {latent2likert} | R Documentation |
Simulate Likert Scale Item Responses
Description
Simulates Likert scale item responses based on a specified number of response categories and the centered parameters of the latent variable.
Usage
simulate_likert(n_levels, cp)
Arguments
n_levels |
number of response categories for the Likert scale item. |
cp |
centered parameters of the latent variable.
Named vector including mean ( |
Details
The simulation process uses the following model detailed by
Boari and Nai-Ruscone. Let X be the continuous variable of interest,
measured using Likert scale questions with K response categories. The
observed discrete variable Y is defined as follows:
Y = k, \quad \text{ if } \ \ x_{k - 1} < X \leq x_{k}
\quad \text{ for } \ \ k = 1, \dots, K
where x_{k}, k = 0, \dots, K are endpoints defined in the domain
of X such that:
-\infty = x_{0} < x_{1} < \dots < x_{K - 1} < x_{K} = \infty.
The endpoints dictate the transformation of the density
f_{X} of X into a discrete probability distribution:
\text{Pr}(Y = k) = \int_{x_{k - 1}}^{x_{k}} f_{X}(x) \, dx
\quad \text{ for } \ \ k = 1, \dots, K.
The continuous latent variable is modeled using a skew normal distribution.
The function simulate_likert performs the following steps:
Ensures the centered parameters are within the acceptable range.
Converts the centered parameters to direct parameters.
Defines the density function for the skew normal distribution.
Computes the probabilities for each response category using optimal endpoints.
Value
A named vector of probabilities for each response category.
References
Boari, G. and Nai Ruscone, M. (2015). A procedure simulating Likert scale item responses. Electronic Journal of Applied Statistical Analysis 8(3), 288–297. doi:10.1285/i20705948v8n3p288
See Also
discretize_density for details on how to calculate
the optimal endpoints.
Examples
cp <- c(mu = 0, sd = 1, skew = 0.5)
simulate_likert(n_levels = 5, cp = cp)
cp2 <- c(mu = 1, sd = 2, skew = -0.3)
simulate_likert(n_levels = 7, cp = cp2)