parameter estimation
Definition
Parameter estimation refers to the process of quantifying model parameters from observed data, including both interaction effects between variables and main effects of individual variables. In the Ising model, applied in network psychometrics to binary psychological variables such as symptom presence, attitude endorsement, and test responses, estimation is complicated by an intractable normalizing constant whose computation grows exponentially with the number of variables in the network. Maximum likelihood estimation using the exact likelihood is therefore feasible only for small graphs, while pseudolikelihood approximations, specifically the joint pseudolikelihood and the disjoint pseudolikelihood, offer consistent alternatives for larger graphs. Simulation evidence comparing these approaches in terms of bias and variance shows that the joint pseudolikelihood closely approximates maximum likelihood estimates across network sizes, whereas the disjoint pseudolikelihood performs adequately only at large sample sizes.
Sources: Keetelaar et al. (2024)
Related Terms
- network psychometrics (1 shared article)
- maximum likelihood (1 shared article)
- pseudolikelihood (1 shared article)
- joint pseudolikelihood (1 shared article)
- Ising model (1 shared article)
- disjoint pseudolikelihood (1 shared article)
Applications
Parameter Estimation and Pseudolikelihood Approximation
When the exact likelihood is computationally intractable, pseudolikelihood functions replace it with products of conditional distributions, allowing parameter estimation to proceed for larger networks. The joint pseudolikelihood approximates the full joint distribution by conditioning each variable on all others, while the disjoint pseudolikelihood regresses each variable separately on the remaining variables using logistic regression. Both approaches yield consistent estimators, but their finite-sample bias and variance differ considerably, with the joint pseudolikelihood providing more stable estimates across varying network densities and sample sizes.
Sources: Keetelaar et al. (2024)
Parameter Estimation and Network Structure
The accuracy of parameter estimation in the Ising model depends on the structure of the network being modeled, particularly its density. Simulation results indicate that the disjoint pseudolikelihood performs better for sparse networks, whereas the joint pseudolikelihood is more accurate for dense networks.
Sources: Keetelaar et al. (2024)
