The R-package Bayesrel allows to estimate some of the most common reliability coefficients in the Bayesian and frequentist framework. The package is available on CRAN, and the latest version can be obtained via github.

A tutorial can be found here (appendix):

Pfadt, J. M., van den Bergh, D., Sijtsma, K., Moshagen, M., & Wagenmakers, E.-J. (2021). Bayesian estimation of single-test reliability coefficients. Multivariate Behavioral Research.


multiTree is a java-based computer program for the analysis of multinomial processing tree models. Among other things, multiTree provides parameter estimation, hypothesis testing, checks for identifiability, bootstrapping, and power analysis. For download and additional information, see

For details, see:

Moshagen, M. (2010). multiTree: A computer program for the analysis of multinomial processing tree models. Behavior Research Methods, 42, 42-54.

If you prefer to use multiTree in the R environment, you may use the corresponding R interface. The multiTreeR package is available at github.

Lower bound N for FIA 

The Fisher information approximation (FIA) of the normalized maximum likelihood is a model selection criterion based on the minimum description length principle. FIA should only be used if the total number of observations exceeds a lower bound. This Excel sheet computes this lower-bound N in contexts with multiple candidate models, to be used in conjunction with a suitable MPT modeling software such as multiTree. Get the Excel-Sheet here.

For details, see

Heck, D. W., & Moshagen, M., & Erdfelder, E. (2014). Model selection by minimum description length: Lower-bound sample sizes for the Fisher information approximation. Journal of Mathematical Psychology, 60, 29-34.


semPower allows for performing compromise, a priori, and post hoc power analyses for structural equation models. The R-package is available from CRAN, the latest version from github. A subset of the analyses are provided as a Shiny app online at

For more details see the github page and the manual. For a in-depth tutorial, see:

Jobst, L. J., Bader, M., & Moshagen, M. (in press). A Tutorial on Assessing Statistical Power and Determining Sample Size for Structural Equation Models. Psychological Methods.

For details on using compromise power analyses in model testing, see:

Moshagen, M., & Erdfelder, E. (2016). A new strategy for testing structural equation models. Structural Equation Modeling, 23, 54-60.


RRreg implements univariate and multivariate analyses of various randomized response (RR) designs. RRreg is a package for the R statistics environment and can be downloaded from CRAN. The source code is available at github. For further details, see the manual and

Heck, D. W., & Moshagen, M. (2018). RRreg: An R Package for Correlation and Regression Analyses of Randomized Response Data. Journal of Statistical Software, 85, 1-29.

For details on using RRreg to analyze cheating paradigms, see 

Moshagen, M., & Hilbig, B. E. (2017). The statistical analysis of cheating paradigms. Behavior Research Methods, 49, 724 - 732.


NOTAMO is an R package that estimates the parameters of a quantile mixture cumulative distribution function to comply with prespecified central moments. The quantile mixture can be used with the NORTA algorithm to generate multivariate non-normally distruted samples with given covariance matrix and central moments. NOTAMO can be downloaded from github. For details, see

Auerswald, M., & Moshagen, M. (2017). Sampling from arbitrary non-normal distributions with given covariance and central moments.


NNNLSEM generates non-normal data with given moments using a structural model with non-linear linking functions. Get the MATLAB script here. For details, see

Auerswald, M., & Moshagen, M. (2015). Generating correlated, non-normally distributed data using a non-linear structural model. Psychometrika, 80, 920-937.