oREV: An item response theory-based open receptive vocabulary task for 3- to 8-year-old children.

Individual differences in early language abilities are an important predictor of later life outcomes. High-quality, easy-access measures of language abilities are rare, especially in the preschool and primary school years. The present study describes the construction of a new receptive vocabulary task for children between 3 and 8 years of age. The task was implemented as a browser-based web application, allowing for both in-person and remote data collection via the internet. Based on data from N = 581 German-speaking children, we estimated the psychometric properties of each item in a larger initial item pool via item response modeling. We then applied an automated item selection procedure to select an optimal subset of items based on item difficulty and discrimination. The so-constructed task has 22 items and shows excellent psychometric properties with respect to reliability, stability, and convergent and discriminant validity. The construction, implementation, and item selection process described here makes it easy to extend the task or adapt it to different languages. All materials and code are freely accessible to interested researchers. The task can be used via the following website: https://ccp-odc.eva.mpg.de/orev-demo .

A General Theorem and Proof for the Identification of Composed CFA Models.

In this article, we present a general theorem and proof for the global identification of composed CFA models. They consist of identified submodels that are related only through covariances between their respective latent factors. Composed CFA models are frequently used in the analysis of multimethod data, longitudinal data, or multidimensional psychometric data. Firstly, our theorem enables researchers to reduce the problem of identifying the composed model to the problem of identifying the submodels and verifying the conditions given by our theorem. Secondly, we show that composed CFA models are globally identified if the primary models are reduced models such as the CT-C[Formula: see text] model or similar types of models. In contrast, composed CFA models that include non-reduced primary models can be globally underidentified for certain types of cross-model covariance assumptions. We discuss necessary and sufficient conditions for the global identification of arbitrary composed CFA models and provide a Python code to check the identification status for an illustrative example. The code we provide can be easily adapted to more complex models.