The Rasch Sampler

The Rasch sampler is an efficient algorithm to sample binary matrices with given marginal sums. It is a Markov chain Monte Carlo (MCMC) algorithm. The program can handle matrices of up to 1024 rows and 64 columns. A special option allows to sample square matrices with given marginals and fixed main diagonal, a problem prominent in social network analysis. In all cases the stationary distribution is uniform. The user has control on the serial dependency. (authors' abstract

The Rasch Sampler

The Rasch sampler is an efficient algorithm to sample binary matrices with given marginal sums. It is a Markov chain Monte Carlo (MCMC) algorithm. The program can handle matrices of up to 1024 rows and 64 columns. A special option allows to sample square matrices with given marginals and fixed main diagonal, a problem prominent in social network analysis. In all cases the stationary distribution is uniform. The user has control on the serial dependency

Item calibration in incomplete testing designs

This study discusses the justifiability of item parameter estimation in incomplete testing designs in item response theory. Marginal maximum likelihood (MML) as well as conditional maximum likelihood (CML) procedures are considered in three commonly used incomplete designs: random incomplete, multistage testing and targeted testing designs. Mislevy and Sheenan (1989) have shown that in incomplete designs the justifiability of MML can be deduced from Rubin's (1976) general theory on inference in the presence of missing data. Their results are recapitulated and extended for more situations. In this study it is shown that for CML estimation the justification must be established in an alternative way, by considering the neglected part of the complete likelihood. The problems with incomplete designs are not generally recognized in practical situations. This is due to the stochastic nature of the incomplete designs which is not taken into account in standard computer algorithms. For that reason, incorrect uses of standard MML- and CML-algorithms are discussed

DOI: 10.1007/S11336-008-9074-Z SOLUTION STRATEGIES AND ACHIEVEMENT IN DUTCH COMPLEX ARITHMETIC: LATENT VARIABLE MODELING OF CHANGE

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in solving the division problems in the two most recent assessments carried out in 1997 and in 2004. The students ’ strategies were classified into four categories. A data set resulted with two types of repeated observations within students: the nominal strategies and the dichotomous achievement scores (correct/incorrect) on the items administered. It is argued that latent variable modeling methodology is appropriate to analyze these data. First, latent class analyses with year of assessment as a covariate were carried out on the multivariate nominal strategy variables. Results showed a shift from application of the traditional long division algorithm in 1997, to the less accurate strategy of stating an answer without writing down any notes or calculations in 2004, especially for boys. Second, explanatory IRT analyses showed that the three main strategies were significantly less accurate in 2004 than they were in 1997

Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

covariate, predictor, explanatory IRT, latent class analysis, repeated categorical observations, incomplete design, mathematics education,

An item response model with internal restrictions on item difficulty

item response theory, componential models, linear restrictions,

An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals

MCMC, Rasch model, nonparametric tests, importance sampling, social networks,