gen.weight: Generate Weights

In irtQ: Unidimensional Item Response Theory Modeling

Generate Weights

Description

This function generates a set of normalized weights based on theta (ability) values to be used in functions such as est_score(), sx2_fit(), and covirt().

Usage

gen.weight(n = 41, dist = "norm", mu = 0, sigma = 1, l = -4, u = 4, theta)

Arguments

n	An integer specifying the number of theta (node) values for which weights are to be generated. Default is 41.
dist	A character string indicating the distribution type used to generate weights. Available options are "norm" for a normal distribution, "unif" for a uniform distribution, and "emp" for an empirical distribution. If dist = "norm", either n or theta must be provided. If dist = "unif", only n is applicable. If dist = "emp", only theta must be specified.
mu, sigma	Mean and standard deviation of the normal distribution (used when dist = "norm").
l, u	Lower and upper bounds of the uniform distribution (used when dist = "unif").
theta	A numeric vector of empirical theta (node) values for which weights are generated.

Details

If theta is not specified, n equally spaced quadrature points and corresponding weights are generated from either the normal or uniform distribution:

• When dist = "norm", Gaussian quadrature points and weights are computed using gauss.quad.prob() from the statmod package.

• When dist = "unif", equally spaced points are drawn from the specified interval [l, u], and weights are proportional to the uniform density.

If theta is specified:

• When dist = "norm", the weights are proportional to the normal density evaluated at each theta value and normalized to sum to 1.

• When dist = "emp", equal weights are assigned to each provided theta value.

Value

A data frame with two columns:

• theta: The theta (node) values.

• weight: The corresponding normalized weights.

Author(s)

Hwanggyu Lim [e-mail]

See Also

est_score(), sx2_fit(), covirt()

Examples

## Example 1:
## Generate 41 Gaussian quadrature points and weights from the normal distribution
gen.weight(n = 41, dist = "norm", mu = 0, sigma = 1)

## Example 2:
## Generate 41 theta values and weights from the uniform distribution,
## given a minimum value of -4 and a maximum value of 4
gen.weight(n = 41, dist = "unif", l = -4, u = 4)

## Example 3:
## Generate normalized weights from the standard normal distribution,
## given a user-defined set of theta values
theta <- seq(-4, 4, by = 0.1)
gen.weight(dist = "norm", mu = 0, sigma = 1, theta = theta)

## Example 4:
## Generate equal normalized weights for theta values
## randomly sampled from the standard normal distribution
theta <- rnorm(100)
gen.weight(dist = "emp", theta = theta)

irtQ documentation built on July 27, 2026, 9:08 a.m.