Item information function

For the two-parameter logistic the information peaks at theta = b with value a^2 / 4; test information is the sum over items and the asymptotic standard error of the ability estimate is its reciprocal square root.

Usage

Itinft(theta, a, b)

Arguments

theta

Ability values.

a

Item slopes, positive.

b

Item difficulties, same length as a.

Value

List with estimate (largest test information), information, test_information, se, n, method.

Details

Formula: I_j(theta) = a_j^2 P_j(theta) (1 - P_j(theta)).

References

Lord (1980), Applications of Item Response Theory to Practical Testing Problems, Lawrence Erlbaum, ch. 5.

Examples

Itinft(theta = 0.5, a = c(1, 2, 3, 4, 5, 6, 7, 8), b = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 0.4206959
#> 
#> $information
#>           [,1]      [,2]        [,3]         [,4]         [,5]         [,6]
#> [1,] 0.2350037 0.1807066 0.004972258 1.330444e-05 4.229745e-09 1.677199e-13
#>              [,7]         [,8]
#> [1,] 8.507406e-19 5.604167e-25
#> 
#> $test_information
#> [1] 0.4206959
#> 
#> $se
#> [1] 1.541757
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "I_j(theta) = a_j^2 P (1 - P), Lord (1980) ch. 5"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"