disjoint pseudolikelihood
Definition
Disjoint pseudolikelihood is an approximation method for the Ising model that completely bypasses the multivariate joint distribution by separately analyzing the conditional distribution of each variable given all remaining variables, effectively regressing each node on all others via logistic regression and reconstructing the network in a piecemeal fashion. Unlike the joint pseudolikelihood, which replaces the exact likelihood with a product of all conditional distributions estimated together, the disjoint pseudolikelihood treats each such regression as an independent estimation problem. Its normalizing constant requires only as many terms as there are response categories per variable, far fewer than the exponentially growing terms demanded by the exact likelihood. Although the estimator is consistent, simulation evidence shows it performs poorly at small to moderate sample sizes, with acceptable accuracy emerging only for large samples.
Sources: Keetelaar et al. (2024)
Related Terms
- network psychometrics (1 shared article)
- maximum likelihood (1 shared article)
- pseudolikelihood (1 shared article)
- parameter estimation (1 shared article)
- joint pseudolikelihood (1 shared article)
- Ising model (1 shared article)
Applications
Disjoint Pseudolikelihood and Joint Pseudolikelihood
Both the disjoint pseudolikelihood and the joint pseudolikelihood are approximations designed to circumvent the intractable normalizing constant of the Ising model, but they differ in how they handle the conditional distributions of the modeled variables. Simulation comparisons show that the joint pseudolikelihood produces estimates that more closely track maximum likelihood estimates across a wider range of sample sizes and network structures, whereas the disjoint pseudolikelihood performs better only in sparse networks and requires large samples to yield accurate parameter estimates.
Sources: Keetelaar et al. (2024)
Disjoint Pseudolikelihood and Lasso Estimation
The disjoint pseudolikelihood is frequently combined with Lasso regularization for edge selection in the Ising model, a pairing that underlies several applied psychometric tools including the IsingFit and MGM packages. Despite the practical popularity of this combination, edge selection based on the joint pseudolikelihood paired with regularization has been found to outperform the disjoint pseudolikelihood approach, though the specific contributions of bias and variance to that difference remain unclear.
Sources: Keetelaar et al. (2024)
Disjoint Pseudolikelihood and Network Structure
The relative performance of the disjoint pseudolikelihood depends on the topology of the network being estimated. Simulation results indicate that the disjoint pseudolikelihood is more efficient for sparse networks, while the joint pseudolikelihood yields better estimates for dense networks.
Sources: Keetelaar et al. (2024)
