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You have repeated measures within subjects so (1|subjectID2) is appropriate. curriculum and classMode are your fixed effects and the focus of your research question, so these should not be grouping variabls for random itercepts. The first model is the better one. Questions about how to do things in specific software are off-topic here, and I don't know ...

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LDA is a simplification of QDA in which you compare two quantities given some data $\mathbf{x}$: the likelihood of $\mathbf{x}$ given it comes from class $1$ denoted $p(\mathbf{x}\mid c=1)$ is compared to the likelihood for another class (which we denote $0$) denoted $p(\mathbf{x}\mid c=0)$. LDA and QDA both ask the following question: Is the likelihood of \$...

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You might want to look into the quadrat count method. It simply imposes a regular grid on top of your set of points and counts the number if points in each square. This pdf contains some background and a few examples to get you started. The method is part of the larger field point pattern analysis.

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