mpt2irt is an R package that accompanies the paper A new model for acquiescence at the interface of psychometrics and cognitive psychology (Plieninger & Heck, 2018). Therein, we extend the response style model of Böckenholt (2012) to acquiescence. The model is essentially a hierarchical multinomial processing tree (MPT) model with an item response theory (IRT) structure of its parameters. To estimate the model parameters, we build on Bayesian hierarchical modeling and fit the model in either Stan or JAGS.

In order to use the package, you will need either JAGS or RStan.

To install JAGS, visit https://sourceforge.net/projects/mcmc-jags/.

To install RStan, visit https://github.com/stan-dev and carefully follow the instructions. This may also involve the following steps:

• Installing Rtools
• Configuration of the C++ Toolchain
• Creating or editing a Makevars file on Windows

Actually, the Stan part of mpt2irt was split off for easier maintenance and is provided in the package mpt2irtStan. User have to install both packages even though they will interface only with mpt2irt.

The package mpt2irt can be installed directly from GitHub, and this should automatically also install mpt2irtStan:

# install.packages("remotes")
remotes::install_github("hplieninger/mpt2irt")

However, because compiling the code in mpt2irtStan takes a while and may need a special setup (see above), users are encouraged to first install mpt2irtStan via remotes::install_github("hplieninger/mpt2irtStan"). During installation, users may be asked to update or install the rstantools package (version >= 2.0.0) and should agree. If this was successful, the main package mpt2irt can be installed afterwards.

# This is a minimal working example, where data are generated and subsequently fit.
library("mpt2irt")
N <- 20
J <- 10
betas <- cbind(rnorm(J, .5), rnorm(J, .5), rnorm(J, 1.5), rnorm(J, 0))
dat   <- generate_irtree_ext(N = N, J = J, betas = betas, beta_ARS_extreme = .5)

# fit model
res1 <- fit_irtree(dat$X, revItem = dat$revItem, M = 200)
res2 <- summarize_irtree_fit(res1)
res3 <- tidyup_irtree_fit(res2)
res3$plot

The proposed Acquiescence Model is a mixture model. Existing approaches to ARS (e.g., Billiet & McClendon, 2000; Ferrando et al., 2016; Maydeu-Olivares & Coffman, 2006) view acquiescence as a shift process. A graphical comparison of the two approaches in terms of the predicted category probabilities may be found at https://hplieninger.shinyapps.io/shift-vs-mixture-ARS.