The last decades have seen an unprecedented growth in the availability and accessibility of data, highly influenced by the ubiquity of digital media and the internet. As society contends with data's increasing impact on the nature of knowledge, communication, and privacy, it faces a pressing need for citizens who are intelligent producers and…

This dissertation comprises three papers that propose, discuss, and illustrate models to make improved inferences about research questions regarding student achievement in education. Addressing the types of questions common in educational research today requires three different "extensions" to traditional educational assessment: (1)…