  The Ising model was originally developed to model magnetisation of solids in
statistical physics. As a network of binary variables with the probability of
becoming 'active' depending only on direct neighbours, the Ising model appears
appropriate for many other processes. For instance, it was recently applied in
psychology to model co-occurrences of mental disorders. It has been shown that
the connections between the variables (nodes) in the Ising network can be
estimated with a series of logistic regressions. This naturally leads to
questions of how well such a model predicts new observations and how well
parameters of the Ising model can be estimated using logistic regressions. Here
we focus on the high-dimensional setting with more parameters than observations
and consider violations of assumptions of the lasso. In particular, we
determine the consequences for both prediction and estimation when the sparsity
and restricted eigenvalue assumptions are not satisfied. We explain by using
the idea of connected copies (extreme multicollinearity) the fact that
prediction becomes better when either sparsity or multicollinearity is not
satisfied. We illustrate these results with simulations.
