This thesis considers three topics regarding LVM in educational measurement. The first is the estimation of LVM on data obtained from an adaptive test. For a particular class of LVM and a particular estimation procedure, it is explained that these models can be estimated on this kind of data. The second topic is the use of the sum score. For practical reason, many people prefer for reporting the use of a simple sum score instead of a latent variable estimate. It is explained under which conditions the latent variable approach and the sum score approach lead to the same ordering of candidates. The third topic is the lack of model fit in international surveys. Due to differences between countries, the same model does not fit in each country. It is explained how the use of different models in different countries can result in comparable scores between countries.
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