2018/07/28 by Lourens Waldorp, Maarten Marsman, Waldorp, Lourens +3 · 1 citation
Mathematics · Psychology · #Advanced Statistical Methods and Models #FOS: Mathematics #Mental Health Research Topics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1807.10902
openalex publication_date 2018/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Ising model was originally developed to model magnetisation of solids in\nstatistical physics. As a network of binary variables with the probability of\nbecoming 'active' depending only on direct neighbours, the Ising model appears\nappropriate for many other processes. For instance, it was recently applied in\npsychology to model co-occurrences of mental disorders. It has been shown that\nthe connections between the variables (nodes) in the Ising network can be\nestimated with a series of logistic regressions. This naturally leads to\nquestions of how well such a model predicts new observations and how well\nparameters of the Ising model can be estimated using logistic regressions. Here\nwe focus on the high-dimensional setting with more parameters than observations\nand consider violations of assumptions of the lasso. In particular, we\ndetermine the consequences for both prediction and estimation when the sparsity\nand restricted eigenvalue assumptions are not satisfied. We explain by using\nthe idea of connected copies (extreme multicollinearity) the fact that\nprediction becomes better when either sparsity or multicollinearity is not\nsatisfied. We illustrate these results with simulations.\n