International large-scale assessments (ILSAs) play an important role in
educational research and policy making. They collect valuable data on education
quality and performance development across many education systems, giving
countries the opportunity to share techniques, organizational structures, and
policies that have proven efficient and successful. To gain insights from ILSA
data, we identify non-cognitive variables associated with students' academic
performance. This problem has three analytical challenges: 1) academic
performance is measured by cognitive items under a matrix sampling design; 2)
there are many missing values in the non-cognitive variables; and 3) multiple
comparisons due to a large number of non-cognitive variables. We consider an
application to the Programme for International Student Assessment (PISA),
aiming to identify non-cognitive variables associated with students'
performance in science. We formulate it as a variable selection problem under a
general latent variable model framework and further propose a knockoff method
that conducts variable selection with a controlled error rate for false
selections