We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Efficient Hessian computation using sparse matrix derivatives in RAM notation.
- Authors
Oertzen, Timo; Brick, Timothy
- Abstract
This article proposes a new, more efficient method to compute the minus two log likelihood, its gradient, and the Hessian for structural equation models (SEMs) in reticular action model (RAM) notation. The method exploits the beneficial aspect of RAM notation that the matrix derivatives used in RAM are sparse. For an SEM with K variables, P parameters, and P′ entries in the symmetrical or asymmetrical matrix of the RAM notation filled with parameters, the asymptotical run time of the algorithm is O( P ′ K + P K + K). The naive implementation and numerical implementations are both O( P K), so that for typical applications of SEM, the proposed algorithm is asymptotically K times faster than the best previously known algorithm. A simulation comparison with a numerical algorithm shows that the asymptotical efficiency is transferred to an applied computational advantage that is crucial for the application of maximum likelihood estimation, even in small, but especially in moderate or large, SEMs.
- Subjects
HESSIAN matrices; MATRIX derivatives; RETICULAR formation; STRUCTURAL equation modeling; PSYCHOLOGICAL research
- Publication
Behavior Research Methods, 2014, Vol 46, Issue 2, p385
- ISSN
1554-351X
- Publication type
Article
- DOI
10.3758/s13428-013-0384-4