select the next item by maximum Fisher information

Usage

compute_next_item_grm(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,model="GRM",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
under the graded response model there is no nearest neighbour shortcut because
the information curves differ in height and shape so the information of every
available item has to be computed at theta
an item with a large alpha_j whose thresholds cover the current theta wins most
of the comparisons and is used far more often than the rest of the bank which
is why randomesque matters more here than under the rating scale model

Examples

bank<-matrix(c(1.227,0.845,1.694,1.012,2.103,
               -2.183,-1.542,-1.021,-2.460,-0.812,
               -0.874,-0.415,-0.231,-1.105,0.094,
               0.316,0.783,0.652,0.047,0.881,
               1.592,2.064,1.438,1.271,1.736),
             nrow=5,
             dimnames=list(c(1,2,3,4,5),
                           c("alphaj","betaj1","betaj2","betaj3","betaj4")))
catR::nextItem(bank,model="GRM",theta=0,criterion="MFI") # with catR installed
#> $item
#> [1] 5
#> 
#> $par
#> alphaj betaj1 betaj2 betaj3 betaj4 
#>  2.103 -0.812  0.094  0.881  1.736 
#> 
#> $info
#> [1] 1.329314
#> 
#> $criterion
#> [1] "MFI"
#> 
#> $randomesque
#> [1] 1
#> 
#> $name
#> [1] "5"
#> 
#> $prior.prop
#> [1] NA
#> 
#> $post.prop
#> [1] NA
#> 
#> $cb.prop
#> [1] NA
#> 
compute_next_item_grm(theta=0,bank)
#> $item
#> [1] 5
#> 
#> $info
#> [1] 1.329314
#> 
#> $available
#> [1] 1 2 3 4 5
#>