Four-parameter logistic item response model

The lower asymptote absorbs guessing and the upper asymptote slipping; c = 0 and d = 1 recovers the two-parameter logistic exactly.

Usage

Irt4pl(y, theta, a, b, c = 0, d = 1)

Arguments

y: Observed 0/1 responses.
theta: Person abilities, same length as y.
a: Slope, positive.
b: Difficulty.
c: Lower asymptote.
d: Upper asymptote, greater than c.

Value

List with estimate, p, loglik, a, b, c, d, n, method.

Details

Formula: P = c + (d - c) / (1 + exp(-a(theta - b))).

References

Lord (1980), Applications of Item Response Theory to Practical Testing Problems, Lawrence Erlbaum, ch. 2; Barton and Lord (1981), ETS Research Report RR-81-20. doi:10.1002/j.2333-8504.1981.tb01255.x

Examples

Irt4pl(y = c(1, 0, 1), theta = c(0.5, -0.5, 1), a = 1, b = 0, c = 0.1, d = 0.95)
#> $estimate
#> [1] 0.5904666
#> 
#> $p
#> [1] 0.6290904 0.4209096 0.7213998
#> 
#> $loglik
#> [1] -1.336339
#> 
#> $a
#> [1] 1
#> 
#> $b
#> [1] 0
#> 
#> $c
#> [1] 0.1
#> 
#> $d
#> [1] 0.95
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "P = c + (d - c)/(1 + exp(-a(theta - b)))"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"