select the next item by maximum Fisher information

Usage

compute_next_item_dichotomous(theta, bank, out = NULL, D = 1, randomesque = 1)

Arguments

theta: current ability estimate
bank: matrix of item parameters
out: vector of the indices of the items already administered
D: metric constant can be 1 or 1.702
randomesque: number of most informative items to draw at random from
1 is pure maximum information and 3 to 5 spreads item exposure

Value

item index of the selected item in the bank
info information of the selected item at theta
available indices of the items still available

Note

this function should return the same result as
catR::nextItem(itemBank,theta,out,criterion="MFI") when randomesque is 1 and
the most informative item is unique
when several items tie exactly catR draws one of them at random while this
function takes the first
with randomesque above 1 catR also keeps every item tied with the last one kept
so it can draw from more than randomesque items
when every item has the same a with c=0 and d=1 the information curves are
copies of one another shifted by b and symmetric around it so the most
informative item is the one whose b is closest to theta
with different a c or d the curves differ in height and shape so the
information of every available item has to be computed at theta

Examples

bank<-matrix(c(1.75,1.80,1.85,1.90,1.95,
              -3,-2,0,2,3,
               0.1,0.1,0.1,0.1,0.1,
               0.9,0.9,0.9,0.9,0.9),
             nrow=5,
             dimnames=list(c(1,2,3,4,5),
                           c("a","b","c","d")))
catR::nextItem(bank,theta=0,criterion="MFI")
#> $item
#> [1] 3
#> 
#> $par
#>    a    b    c    d 
#> 1.85 0.00 0.10 0.90 
#> 
#> $info
#>      3 
#> 0.5476 
#> 
#> $criterion
#> [1] "MFI"
#> 
#> $randomesque
#> [1] 1
#> 
#> $name
#> [1] "3"
#> 
#> $prior.prop
#> [1] NA
#> 
#> $post.prop
#> [1] NA
#> 
#> $cb.prop
#> [1] NA
#> 
compute_next_item_dichotomous(theta=0,bank)
#> $item
#> [1] 3
#> 
#> $info
#>      3 
#> 0.5476 
#> 
#> $available
#> [1] 1 2 3 4 5
#>