4-Parameter Logistic Curve.

4-parameter logistic curve for item response theory.

Usage

fourPL(a = 1, b, c = 0, d = 1, theta)

Arguments

a

Discrimination parameter (slope).

b

Difficulty (severity) parameter (inflection point).

c

Guessing parameter (lower asymptote).

d

Careless errors parameter (upper asymptote).

theta

Person's level on the construct.

Value

Probability of item endorsement (or expected value on the item).

Details

Estimates the probability of item endorsement as function of the four-parameter logistic (4PL) curve and the person's level on the construct (theta).

See also

doi:10.1177/0146621613475471

Other IRT: deriv_d_negBinom(), discriminationToFactorLoading(), itemInformation(), reliabilityIRT(), standardErrorIRT(), test_info_4PL()

Examples

fourPL(b = 2, theta = -4:4) #1PL
#> [1] 0.002472623 0.006692851 0.017986210 0.047425873 0.119202922 0.268941421
#> [7] 0.500000000 0.731058579 0.880797078
fourPL(b = 2, a = 1.5, theta = -4:4) #2PL
#> [1] 0.0001233946 0.0005527786 0.0024726232 0.0109869426 0.0474258732
#> [6] 0.1824255238 0.5000000000 0.8175744762 0.9525741268
fourPL(b = 2, a = 1.5, c = 0.10, theta = -4:4) #3PL
#> [1] 0.1001111 0.1004975 0.1022254 0.1098882 0.1426833 0.2641830 0.5500000
#> [8] 0.8358170 0.9573167
fourPL(b = 2, a = 1.5, c = 0.10, d = 0.95, theta = -4:4) #4PL
#> [1] 0.1001049 0.1004699 0.1021017 0.1093389 0.1403120 0.2550617 0.5250000
#> [8] 0.7949383 0.9096880