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International large-scale assessment (LSA) studies which assess students’ knowledge in different content domains use item response theory (IRT) models. An important feature of IRT models is that trait level estimates with invariant meaning may be obtained from any set of items or persons when a model fits the data. Since a model never perfectly fits and country participation in international LSA studies differs from cycle to cycle the question about stability of proficiency scores arises. The main purpose of the paper is to determine the effect of the composition of the calibration sample in PIRLS 2006 in the item and person parameter estimates. This contributes to better understanding of the property of “invariance” of IRT models in real data.