TY - JOUR
T1 - Singular value decomposition of probability matrices
T2 - Probabilistic aspects of latent dichotomous variables
AU - Gilula, Zvi
PY - 1979/8
Y1 - 1979/8
N2 - This paper gives a matrix approach to determine when a statistical dependence between two manifest categorical random variables can be viewed as generated by some unobserved latent variables, in the sense that the manifest variables are conditionally independent with respect to the latent variables. By the singular value decomposition of the matrix representing deviations from statistical independence of the two manifest variables, we give a necessary and sufficient condition for existence of dichotomous latent variables, which are 'responsible' for conditional independence. We give a technique for identifying the distributions of such latent variables and also the conditional distributions of the manifest variables given the latent variables. Finally, we discuss some probabilistic aspects.
AB - This paper gives a matrix approach to determine when a statistical dependence between two manifest categorical random variables can be viewed as generated by some unobserved latent variables, in the sense that the manifest variables are conditionally independent with respect to the latent variables. By the singular value decomposition of the matrix representing deviations from statistical independence of the two manifest variables, we give a necessary and sufficient condition for existence of dichotomous latent variables, which are 'responsible' for conditional independence. We give a technique for identifying the distributions of such latent variables and also the conditional distributions of the manifest variables given the latent variables. Finally, we discuss some probabilistic aspects.
KW - Identifiability
KW - Latent variable
KW - Manifest variable
KW - Singular value decomposition
UR - http://www.scopus.com/inward/record.url?scp=85042570356&partnerID=8YFLogxK
U2 - 10.1093/biomet/66.2.339
DO - 10.1093/biomet/66.2.339
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AN - SCOPUS:85042570356
SN - 0006-3444
VL - 66
SP - 339
EP - 344
JO - Biometrika
JF - Biometrika
IS - 2
ER -