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Jurgen Rost passed away on July 1st, 2017, after a long and serious illness. For those who do not know him well, he was a professor of psychology at the Christian Albrechts University of Kiel, and research director at the institute for science education before his early retirement.Jurgen was a brilliant and passionate psychometrician. He is known internationally as a leading scholar in this area for his groundbreaking contributions to item response theory and latent class modeling. His work on the development of mixture distribution Rasch models had a lasting impact on the field. Jurgen was not only interested in developing the sophisticated theory of his models but he was also passionate about making his work, and more general, advanced psychometric modeling, accessible to applied researchers. He wrote a textbook on test theory that became the essential German language reference on item response theory. This textbook was published in a first edition in 1996, and then republished in 2004 in extended and revised form. It became the go-to reference for applied researchers and has been used by academic teachers for entry-level and advanced classes on modern test theory.In collaboration with his doctoral students he also developed user friendly computer programs, among these WINMIRA and MULTIRA, that allowed researchers to apply complex psychometric models through easy to use graphical interfaces. These software packages are central tools accompanying the textbook, and were included first on CDROM and later as a download, together with exercises and example data sets that were part of the chapters. That way readers could practice what they learned immediately using free versions of these programs, which can be used to estimate a vast majority of the models discussed in Jurgen's textbook.Aside from writing textbooks and developing teaching tools, Jurgen was also a very active book editor, often in conjunction with colleagues, and often based on groundbreaking conferences that brought together scholars from across the world who followed different lines of thought, and who would consider their own approaches different from those of others. A (mis-)conception that was often either softened or resolved after either attending one of these conferences, or after reading the proceedings that came out of these meetings. Among many of the impactful edited volumes, two are of particular and of continued interest to the world of psychometrics: "Latent Trait and Latent Class Models" edited by Rolf Langeheine and Jurgen Rost, published in 1988, and named by Neil Henry one of the most important references on latent class analysis in his 50-year review of research in this domain. This volume is recognized as a classic, and was followed by another emerging classic entitled "Applications of Latent Trait and Latent Class Models in the Social Sciences", published in 1997, and edited by Jurgen Rost, and his long-term friend and colleague Rolf Langeheine as co-editor. These two volumes brought together researchers and results that stirred developments of integrated and general families of psychometric models. …

The aim of the research presented here is the use of extensions of longitudinal item response theory (IRT) models in the analysis and comparison of group-specific growth in large-scale assessments of educational outcomes. A general discrete latent variable model was used to specify and compare two types of multidimensional item-response-theory (MIRT) models for longitudinal data: (a) a model that handles repeated measurements as multiple, correlated variables over time and (b) a model that assumes one common variable over time and additional variables that quantify the change. Using extensions of these MIRT models, we approach the issue of modeling and comparing group-specific growth in observed and unobserved subpopulations. The analyses presented in this paper aim at answering the question whether academic growth is homogeneous across types of schools defined by academic demands and curricular differences. In order to facilitate answering this research question, (a) a model with a single two-dimensional ability distribution was compared to (b) a model assuming multiple populations with potentially different two-dimensional ability distributions based on type of school and to (c) a model that assumes that the observations are sampled from a discrete mixture of (unobserved) populations, allowing for differences across schools with respect to mixing proportions. For this purpose, we specified a hierarchical-mixture distribution variant of the two MIRT models. The latter model, (c), is a growth-mixture MIRT model that allows for variation of the mixing proportions across clusters in a hierarchically organized sample. We applied the proposed models to the PISA-I-Plus data for assessing learning and change across multiple subpopulations. The results of this study support the hypothesis of differential growth.