The R-Package BCSMIRT (R Code and Packages) provides software for fitting a BCSM (two-parameter) IRT model for small sample sizes. The underlying idea is that the latent variable (person) is integrated out and a multivariate Probit model is fitted with an IRT implied dependence (error) structure. This avoids requiring a suitable frequency distribution of response patterns (to support Gauss-Hermite integration), and avoids simulating/estimating person parameters.

The number of model parameters is not increasing with more persons, and is limited to the number of item parameters and some prior parameters. The paper publication can be found here Publications Overview. It will make IRT models suitable for small samples (5-10 items, >50 persons). For small samples, the often problematic discrimination estimates will simply smooth towards a common mean value, when items do not provide sufficient information to estimate item-specific discriminations. This enables a robust error-free estimation of the two-parameter IRT model.

The software can handle missing data, unbalanced designs (planned missing data), but is restricted to binary observations. Future research will focus on ordinal data (more than two response categories), which should enable IRT for even smaller sample sizes.