Word Reading 15 vs 25 items. 10 000 students.

We use BM for ability estimation and compare 15 vs 25 items.

25 items

truethetas <- seq(-2.2,2.2, length.out=n)
est.df <- data.frame(truetheta=truethetas)

NMAX <- 25
SEMTHR <- .01 # UNATTAINABLE SO LENGTH WILL BE 25 FOR ALL STUDENTS
est.df$NMAX <- NMAX; est.df$SE <- SEMTHR;

stop <- list(rule = c("precision","length"), thr = c(SEMTHR, NMAX))
res <- simulateRespondents(thetas = truethetas,
                           itemBank = bank,
                           start=start,
                           test = list(method = "BM", itemSelect = "MFI"), 
                           stop = stop)

## Simulation process:  0 %
## Simulation process:  10 %
## Simulation process:  20 %
## Simulation process:  30 %
## Simulation process:  40 %
## Simulation process:  50 %
## Simulation process:  60 %
## Simulation process:  70 %
## Simulation process:  80 %
## Simulation process:  90 %
## Simulation process:  100 %

plot(res)

## The plot was not captured!

cond.df <- data.frame(condTheta=res$condTheta, 
                      condBias=res$condBias,
                      condRMSE=res$condRMSE,
                      condnItems=res$condnItems,
                      condSE=res$condSE)

15 items

truethetas <- seq(-2.2,2.2, length.out=n)
est.df <- data.frame(truetheta=truethetas)

NMAX <- 15
SEMTHR <- .01 # UNATTAINABLE SO LENGTH WILL BE 25 FOR ALL STUDENTS
est.df$NMAX <- NMAX; est.df$SE <- SEMTHR;

stop <- list(rule = c("precision","length"), thr = c(SEMTHR, NMAX))
res <- simulateRespondents(thetas = truethetas,
                           itemBank = bank,
                           start=start,
                           test = list(method = "BM", itemSelect = "MFI"), 
                           stop = stop)

## Simulation process:  0 %
## Simulation process:  10 %
## Simulation process:  20 %
## Simulation process:  30 %
## Simulation process:  40 %
## Simulation process:  50 %
## Simulation process:  60 %
## Simulation process:  70 %
## Simulation process:  80 %
## Simulation process:  90 %
## Simulation process:  100 %

plot(res)

## The plot was not captured!

Plots 15 vs 25

Conditional Bias

Conditional RMSE

Conditional SE