# tmt

The tmt Package provides conditional maximum likelihood (CML) estimation of item parameters in multistage designs (Zwitser & Maris, 2013, https://doi.org/10.1007/s11336-013-9369-6) and CML estimation for conventional designs. Additional features are the Likelihood Ratio test (Andersen, 1973, https://doi.org/10.1007/BF02291180) and simulation of multistage designs.

## Installation

To install the development version of the tmt package, please copy this commands in your R console:

``````# Install release version from CRAN
install.packages("tmt")
# Install development version from GitHub
devtools::install_github("jansteinfeld/tmt")``````

## Usage

You will find a detailed description of the package in the vignette:

``````library(tmt)

mstdesign <- "
B1 =~ paste0('i',1:5)
B2 =~ c(i6, i7, i8, i9, i10)
B3 =~ c(i11, i12, i13, i14, i15)
B4 =~ c(i16, i17, i18, i19, i20)
B5 =~ c(i21, i22, i23, i24, i25)
B6 =~ c(i26, i27, i28, i29, i30)

# define starting Block
Start == B4

# define branches
b1 := Start(0,2) + B2(0,2) + B1(0,5)
b2 := Start(0,2) + B2(3,5) + B3(0,5)
b3 := Start(3,5) + B5(0,2) + B3(0,5)
b4 := Start(3,5) + B5(3,5) + B6(0,5)
"
# simulate some data
items <- seq(-2,2,length.out=30)
names(items) <- c(paste0("i",1:30))
set.seed(1111)
dat_mst <- tmt_sim(mstdesign = mstdesign,
items = items,
persons = 500,
mean = 0,
sd = 1)
# estimate

mod1 <- tmt_rm(dat_mst,mstdesign = mstdesign)

summary(mod1)
#>
#> Call:
#>   tmt_rm(dat = dat_mst, mstdesign = mstdesign)
#>
#>
#> Results of Rasch model (mst) estimation:
#>
#> Difficulty parameters:
#>             est.b_i1   est.b_i2  est.b_i3   est.b_i4   est.b_i5   est.b_i6
#> Estimate   -1.715056 -1.6100686 -1.508108 -1.6100686 -1.3113453 -1.0468543
#> Std. Error  0.247141  0.2439233  0.241220  0.2439233  0.2371614  0.1520214
#>              est.b_i7   est.b_i8   est.b_i9  est.b_i10  est.b_i11
#> Estimate   -1.1508557 -0.9958313 -0.6997328 -0.4607495 -0.3807713
#> Std. Error  0.1535503  0.1513333  0.1480823  0.1464329  0.1326975
#>             est.b_i12 est.b_i13  est.b_i14   est.b_i15  est.b_i16
#> Estimate   -0.6500487 -0.222511 -0.2082786 -0.05286967 0.07542945
#> Std. Error  0.1359553  0.131522  0.1314425  0.13085158 0.11053665
#>            est.b_i17 est.b_i18 est.b_i19 est.b_i20 est.b_i21 est.b_i22
#> Estimate   0.2472522 0.3046942 0.5762328 0.5959613 0.7193856 0.5738666
#> Std. Error 0.1108281 0.1109871 0.1121476 0.1122602 0.1668250 0.1662375
#>            est.b_i23 est.b_i24 est.b_i25 est.b_i26 est.b_i27 est.b_i28
#> Estimate   0.8659746 1.0363980 1.1895060  1.401457  1.401457 1.2465019
#> Std. Error 0.1677771 0.1693014 0.1710693  0.245725  0.245725 0.2450162
#>            est.b_i29 est.b_i30
#> Estimate   1.5586564  1.830376
#> Std. Error 0.2475203  0.253225
#>
#> CLL: -3222.077
#> Number of iterations: 59
#> Number of parameters: 30``````

### Outlook

The following features are planned for future releases:

• the partial credit model for multistage designs
• missing values in multistage designs
• improving the speed of the package
• plots of the multistage design