mst: Computerized Multistage Testing (MST)

In xluo11/xxIRT: Item Response Theory and Computer-Based Testing

Description

mst creates a multistage (MST) object for assembly

mst_route adds/removes a route to/from the MST

mst_get_indices maps the input indices to the actual indices

mst_obj adds objective functions to the MST

mst_constraint adds constraints to the MST

mst_stage_length sets length limits on stages

mst_rdp anchors the routing decision point (rdp) between adjacent modules

mst_module_mininfo sets the minimum information for modules

mst_assemble assembles the mst

mst_get_items extracts items from the assembly results

Usage

mst(pool, design, num_panel, method = c("topdown", "bottomup"),
  len = NULL, max_use = NULL, group = NULL, ...)

mst_route(x, route, op = c("+", "-"))

mst_get_indices(x, indices)

mst_obj(x, theta, indices = NULL, target = NULL, ...)

mst_constraint(x, coef, min = NA, max = NA, level = NULL,
  indices = NULL)

mst_stage_length(x, stages, min = NA, max = NA)

mst_rdp(x, theta, indices, tol = 0)

mst_module_info(x, thetas, min, max, indices)

mst_assemble(x, ...)

## S3 method for class 'mst'
print(x, ...)

## S3 method for class 'mst'
plot(x, ...)

mst_get_items(x, panel_ix = NULL, stage_ix = NULL, module_ix = NULL,
  route_ix = NULL)

Arguments

pool	the item pool (data.frame)
design	the MST design (string): e.g., "1-3", "1-2-2", "1-2-3"
num_panel	the number of panels (integer)
method	the design method (string): 'topdown' or 'bottomup'
len	the module/route length (integer)
max_use	the maximum selection of items (integer)
group	the grouping variable (string or vector)
...	further arguments
x	the MST object
route	a MST route represented by a vector of module indices
op	"+" to add a route and "-" to remove a route
indices	the indices of the route (topdown) or the module (bottomup) where objectives are added
theta	a theta point or interval over which the TIF is optimized
target	the target values of the TIF objectives. NULL for maximization
coef	the coefficients of the constraint
min	the lower bound of the constraint
max	the upper bound of the constraint
level	the constrained level, NA for quantitative variable
stages	the stage indices
tol	tolerance parameter (numeric)
thetas	theta points, a vector
panel_ix	the panel index, an int vector
stage_ix	the stage index, an int vector
module_ix	the module index, an int vector
route_ix	the route index, an integer

Details

There are two methods for designing a MST. The bottom-up approach adds objectives and constraints on individual modules, whereas the topdown approach adds objectives and constraints directly on routes.

plot.mst draws module information functions when byroute=FALSE and route information functions when byroute=TRUE

Examples

## Not run: 
## generate item pool
num_item <- 300
pool <- with(model_3pl_gendata(1, num_item), data.frame(a=a, b=b, c=c))
pool$id <- 1:num_item
pool$content <- sample(1:3, num_item, replace=TRUE)
pool$time <- round(rlnorm(num_item, 4, .3))
pool$group <- sort(sample(1:round(num_item/3), num_item, replace=TRUE))

## ex. 1: 1-2-2 MST, 2 panels, topdown
## 20 items in total and 10 items in content area 1 in each route
## maximize info. at -1 and 1 for easy and hard routes
x <- mst(pool, "1-2-2", 2, 'topdown', len=20, max_use=1)
x <- mst_obj(x, theta=-1, indices=1:2)
x <- mst_obj(x, theta=1, indices=3:4)
x <- mst_constraint(x, "content", 10, 10, level=1)
x <- mst_assemble(x, timeout=5)
plot(x, byroute=TRUE)
for(p in 1:x$num_panel)
  for(r in 1:x$num_route) {
     route <- paste(x$route[r, 1:x$num_stage], collapse='-')
     count <- sum(mst_get_items(x, panel_ix=p, route_ix=r)$content==1)
     cat('panel=', p, ', route=', route, ': ', count, ' items in content area #1\n', sep='')
  }

## ex. 2: 1-2-3 MST, 2 panels, bottomup,
## remove two routes with large theta change: 1-2-6, 1-3-4 
## 10 items in total and 4 items in content area 2 in each module
## maximize info. at -1, 0 and 1 for easy, medium, and hard modules
x <- mst(pool, "1-2-3", 2, 'bottomup', len=10, max_use=1)
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_obj(x, theta= 0, indices=c(1, 5))
x <- mst_obj(x, theta=-1, indices=c(2, 4))
x <- mst_obj(x, theta= 1, indices=c(3, 6))
x <- mst_constraint(x, "content", 4, 4, level=2)
x <- mst_assemble(x, timeout=10) 
plot(x, byroute=FALSE)
for(p in 1:x$num_panel)
  for(m in 1:x$num_module){
    count <- sum(mst_get_items(x, panel_ix=p, module_ix=m)$content==2)
    cat('panel=', p, ', module=', m, ': ', count, ' items in content area #2\n', sep='')
  }
 
## ex.3: same with ex.2 (w/o content constraints), but group-based  
x <- mst(pool, "1-2-3", 2, 'bottomup', len=12, max_use=1, group="group")
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_obj(x, theta= 0, indices=c(1, 5))
x <- mst_obj(x, theta=-1, indices=c(2, 4))
x <- mst_obj(x, theta= 1, indices=c(3, 6))
x <- mst_assemble(x, timeout=10)
plot(x, byroute=FALSE)
for(p in 1:x$num_panel)
  for(m in 1:x$num_module){
    items <- mst_get_items(x, panel_ix=p, module_ix=m)
    cat('panel=', p, ', module=', m, ': ', length(unique(items$id)), ' items from ', 
        length(unique(items$group)), ' groups\n', sep='')
  }
  
## ex.4: 2 panels of 1-2-3 top-down design
## 20 total items and 10 items in content area 3
## 6+ items in stage 1 & 2
x <- mst(pool, "1-2-3", 2, "topdown", len=20, max_use=1)
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_obj(x, theta=-1, indices=1)
x <- mst_obj(x, theta=0, indices=2:3)
x <- mst_obj(x, theta=1, indices=4)
x <- mst_constraint(x, "content", 10, 10, level=3)
x <- mst_stage_length(x, 1:2, min=6)
x <- mst_assemble(x, timeout=15)
head(x$items)
plot(x, byroute=FALSE)
for(p in 1:x$num_panel)
  for(s in 1:x$num_stage){
    items <- mst_get_items(x, panel_ix=p, stage_ix=s)
    cat('panel=', p, ', stage=', s, ': ', length(unique(items$id)), ' items\n', sep='')
  }

## ex.5: same with ex.4, but use RDP instead of stage length to control routing errors
x <- mst(pool, "1-2-3", 2, "topdown", len=20, max_use=1)
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_obj(x, theta=-1, indices=1)
x <- mst_obj(x, theta=0, indices=2:3)
x <- mst_obj(x, theta=1, indices=4)
x <- mst_constraint(x, "content", 10, 10, level=3)
x <- mst_rdp(x, 0, 2:3, .1)
x <- mst_module_mininfo(x, 0, 5, 2:3)
x <- mst_assemble(x, timeout=15)
plot(x, byroute=FALSE)

## End(Not run)

xluo11/xxIRT documentation built on May 4, 2019, 1:24 p.m.