PMID- 24197708
OWN - NLM
STAT- MEDLINE
DCOM- 20140924
LR  - 20191210
IS  - 1554-3528 (Electronic)
IS  - 1554-351X (Linking)
VI  - 46
IP  - 2
DP  - 2014 Jun
TI  - Efficient Hessian computation using sparse matrix derivatives in RAM notation.
PG  - 385-95
LID - 10.3758/s13428-013-0384-4 [doi]
AB  - 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 (2) + P (2) K (2) + K (3)). The naive 
      implementation and numerical implementations are both O(P (2) K (3)), 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.
FAU - von Oertzen, Timo
AU  - von Oertzen T
AD  - Department of Psychology, University of Virginia, 1023 Millmont Street, 
      Charlottesville, VA, 22903, USA, timo@virginia.edu.
FAU - Brick, Timothy R
AU  - Brick TR
LA  - eng
PT  - Journal Article
PT  - Validation Study
PL  - United States
TA  - Behav Res Methods
JT  - Behavior research methods
JID - 101244316
SB  - IM
MH  - *Algorithms
MH  - Computer Simulation
MH  - Humans
MH  - *Likelihood Functions
MH  - Linear Models
MH  - *Models, Psychological
MH  - *Models, Statistical
MH  - Probability
EDAT- 2013/11/08 06:00
MHDA- 2014/09/25 06:00
CRDT- 2013/11/08 06:00
PHST- 2013/11/08 06:00 [entrez]
PHST- 2013/11/08 06:00 [pubmed]
PHST- 2014/09/25 06:00 [medline]
AID - 10.3758/s13428-013-0384-4 [doi]
PST - ppublish
SO  - Behav Res Methods. 2014 Jun;46(2):385-95. doi: 10.3758/s13428-013-0384-4.