Thetmt Package provides conditional maximum likelihood(CML) item parameter estimation of sequential as well as cumulativedeterministic multistage (MST) designs (Zwitser & Maris, 2015,<10.1007/s11336-013-9369-6>)as well as probabilistic sequential and cumulative multistage designs(Steinfeld & Robitzsch, 2021,<10.31234/osf.io/ew27f>).Supports CML item parameter estimation of conventional linear designsand additional functions for the likelihood ratio test (Andersen, 1973,<10.1007/BF02291180>)as well as functions for the simulation of several kinds of multistagedesigns.
To install the latest (development) version of thetmtpackage, please copy the following commands in your R console:
# Install release version from CRANinstall.packages("tmt")# Install development version from GitHubdevtools::install_github("jansteinfeld/tmt")The application of thetmt package is illustrated below.Further examples of different MST designs can be found in the associatedvignette of the package. To apply the package and the CML method, it isfirst necessary to specify the MST design. For this purpose, a modellanguage has been developed, which is illustrated in the first part ofthe example below. First, each module of the design needs to bespecified. The following deterministic sequential MST design consists ofsix modules, four paths and three stages. In the first part, the modulesof the MST design are defined (basically the allocation of items).Different methods are available, the user can either use the R functionpaste, but also address the elements manually as vectors. It isimportant that the names of the specified elements in the modules matchthose in the data. To illustrate the application, some data is thensimulated based on the specified MST design. In this example, a seed hasbeen set to make the results easier to compare and follow. Thetmt_rm function is available for the actual estimation of theitem parameters. If the data has been generated with thetmt_sim function, it would be sufficient to export the datagenerated with this function as part of the MST design. If the data hasnot been generated synthetically with this function, it is necessary tospecify the MST design.
A detailed description of the package (such as sequential cumulativeand probabilistic MST designs) can be found in the vignette.
library(tmt)# spezification of the mst designmstdesign<-" M1 =~ paste0('i',1:5) M2 =~ c(i6, i7, i8, i9, i10) M3 =~ c(i11, i12, i13, i14, i15) M4 =~ c(i16, i17, i18, i19, i20) M5 =~ c(i21, i22, i23, i24, i25) M6 =~ c(i26, i27, i28, i29, i30) # define branches p1 := M4(0,2) + M2(0,2) + M1(0,5) p2 := M4(0,2) + M2(3,5) + M3(0,5) p3 := M4(3,5) + M5(0,2) + M3(0,5) p4 := M4(3,5) + M5(3,5) + M6(0,5) "# application of the simulation function to generate som synthetic data items<-seq(-2,2,length.out=30)names(items)<-paste0("i",1:30) dat_mst<-tmt_sim(mstdesign = mstdesign,items = items,persons =500,seed =1111)# estimate the item parametersmod1<-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 est.b_i7 est.b_i8#> Estimate -2.3490510 -1.7664751 -2.1028057 -1.9872254 -1.4511516 -1.3097642 -1.2542426 -0.8697938#> Std. Error 0.2700265 0.2498593 0.2594456 0.2555346 0.2456593 0.1556009 0.1546331 0.1491392#> est.b_i9 est.b_i10 est.b_i11 est.b_i12 est.b_i13 est.b_i14 est.b_i15#> Estimate -0.7865043 -0.6227596 -0.6582138 -0.2153395 -0.2016450 -0.07909168 0.06922466#> Std. Error 0.1482092 0.1466760 0.1346944 0.1297456 0.1296568 0.12903128 0.12868102#> est.b_i16 est.b_i17 est.b_i18 est.b_i19 est.b_i20 est.b_i21 est.b_i22 est.b_i23#> Estimate 0.04382588 0.2171609 0.2750574 0.5483552 0.5681985 0.6245467 0.9624785 1.0910584#> Std. Error 0.11184169 0.1120871 0.1122291 0.1132990 0.1134044 0.1663841 0.1683083 0.1695429#> est.b_i24 est.b_i25 est.b_i26 est.b_i27 est.b_i28 est.b_i29 est.b_i30#> Estimate 1.2884075 1.5650529 1.4674082 1.5247222 1.5824928 2.0063785 1.819695#> Std. Error 0.1719177 0.1763681 0.2582108 0.2588762 0.2596804 0.2698234 0.264414#>#> CLL: -3179.989#> Number of iterations: 60#> Number of parameters: 30The following features are planned for future releases: