PMID- 35102490
OWN - NLM
STAT- MEDLINE
DCOM- 20220908
LR  - 20221004
IS  - 1860-0980 (Electronic)
IS  - 0033-3123 (Print)
IS  - 0033-3123 (Linking)
VI  - 87
IP  - 3
DP  - 2022 Sep
TI  - Factor Analysis Procedures Revisited from the Comprehensive Model with Unique 
      Factors Decomposed into Specific Factors and Errors.
PG  - 967-991
LID - 10.1007/s11336-021-09824-8 [doi]
AB  - Factor analysis (FA) procedures can be classified into three types (Adachi in 
      WIREs Comput Stat https://onlinelibrary.wiley.com/doi/abs/10.1002/wics.1458 , 
      2019): latent variable FA (LVFA), matrix decomposition FA (MDFA), and its variant 
      (Stegeman in Comput Stat Data Anal 99: 189-203, 2016) named completely decomposed 
      FA (CDFA) through the theorems proved in this paper. We revisit those procedures 
      from the Comprehensive FA (CompFA) model, in which a multivariate observation is 
      decomposed into common factor, specific factor, and error parts. These three 
      parts are separated in MDFA and CDFA, while the specific factor and error parts 
      are not separated, but their sum, called a unique factor, is considered in LVFA. 
      We show that the assumptions in the CompFA model are satisfied by the CDFA 
      solution, but not completely by the MDFA one. Then, how the CompFA model 
      parameters are estimated in the FA procedures is examined. The study shows that 
      all parameters can be recovered well in CDFA, while the sum of the parameters for 
      the specific factor and error parts is approximated by the LVFA estimate of the 
      unique factor parameter and by the MDFA estimate of the specific factor 
      parameter. More detailed results are given through our subdivision of the CompFA 
      model according to whether the error part is uncorrelated among variables or not.
CI  - (c) 2022. The Author(s).
FAU - Adachi, Kohei
AU  - Adachi K
AUID- ORCID: 0000-0001-5349-046X
AD  - Osaka University, 1-2 Yamadaoka, Suita, Osaka , 565-0871, Japan. 
      adachi@hus.osaka-u.ac.jp.
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
DEP - 20220201
PL  - United States
TA  - Psychometrika
JT  - Psychometrika
JID - 0376503
SB  - IM
MH  - Factor Analysis, Statistical
MH  - *Psychometrics
PMC - PMC9433369
OTO - NOTNLM
OT  - Inter-variable error correlations
OT  - completely decomposed factor analysis
OT  - comprehensive factor analysis model
OT  - latent variable factor analysis
OT  - matrix decomposition factor analysis
EDAT- 2022/02/02 06:00
MHDA- 2022/09/09 06:00
PMCR- 2022/02/01
CRDT- 2022/02/01 06:10
PHST- 2021/01/26 00:00 [received]
PHST- 2021/10/26 00:00 [revised]
PHST- 2022/02/02 06:00 [pubmed]
PHST- 2022/09/09 06:00 [medline]
PHST- 2022/02/01 06:10 [entrez]
PHST- 2022/02/01 00:00 [pmc-release]
AID - 10.1007/s11336-021-09824-8 [pii]
AID - 9824 [pii]
AID - 10.1007/s11336-021-09824-8 [doi]
PST - ppublish
SO  - Psychometrika. 2022 Sep;87(3):967-991. doi: 10.1007/s11336-021-09824-8. Epub 2022 
      Feb 1.