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Item Information Function for 4PLM

Source: R/ICCtoTIC.R
ItemInformationFunc.Rd

Computes the Item Information Function (IIF) for the four-parameter logistic model in Item Response Theory. The information function indicates how precisely an item measures ability at different theta levels.

Usage

ItemInformationFunc(x, a = 1, b, c = 0, d = 1)

Arguments

x

Numeric. The ability parameter (theta).

a

Numeric. The slope (discrimination) parameter. Default is 1.

b

Numeric. The location (difficulty) parameter.

c

Numeric. The lower asymptote (guessing) parameter. Default is 0.

d

Numeric. The upper asymptote (carelessness) parameter. Default is 1.

Value

A numeric value representing the item information at the given ability level.

Details

Higher discrimination (a) parameters result in higher information. Items provide maximum information near their difficulty (b) parameter. The guessing (c) and upper asymptote (d) parameters reduce the maximum information an item can provide.

See also

LogisticModel

Examples

# Information at ability = 0 for an item with b = 0
ItemInformationFunc(x = 0, a = 1.5, b = 0, c = 0, d = 1)
#> [1] 0.5625

# Compare information at different ability levels
sapply(seq(-3, 3, 0.5), function(x) ItemInformationFunc(x, a = 1, b = 0))
#>  [1] 0.04517666 0.07010372 0.10499359 0.14914645 0.19661193 0.23500371
#>  [7] 0.25000000 0.23500371 0.19661193 0.14914645 0.10499359 0.07010372
#> [13] 0.04517666