Details:
Title  Algebraic factor analysis: tetrads, pentads and beyond.  Author(s)  Mathias Drton, Bernd Sturmfels, Seth Sullivant  Type  Article in Journal  Abstract  Factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables, known as factors, and all the random variables follow a multivariate normal distribution. The parameter space of a factor analysis model is a subset of the cone of positive definite matrices. This parameter space is studied from the perspective of computational algebraic geometry. Gröbner bases and resultants are applied to compute the ideal of all polynomial functions that vanish on the parameter space. These polynomials, known as model invariants, arise from rank conditions on a symmetric matrix under elimination of the diagonal entries of the matrix. Besides revealing the geometry of the factor analysis model, the model invariants also furnish useful statistics for testing goodnessoffit.  ISSN  01788051; 14322064/e 
URL 
http://link.springer.com/article/10.1007%2Fs0044000600332 
Language  English  Journal  Probab. Theory Relat. Fields  Volume  138  Number  34  Pages  463493  Publisher  Springer, Berlin/Heidelberg  Year  2007  Edition  0  Translation 
No  Refereed 
No 
