Relationships between Linear Statistical Models
Vladimir G. Panov *
Institute of Industrial Ecology of Ural Branch of RAS, S. Kovalevskaya, 20, Ekaterinburg, 620990, Russian Federation.
Anatoly N. Varaksin
Institute of Industrial Ecology of Ural Branch of RAS, S. Kovalevskaya, 20, Ekaterinburg, 620990, Russian Federation.
*Author to whom correspondence should be addressed.
Abstract
To study the relationship between the linear statistical models we used methods of linear algebra, Hilbert spaces and statistics. It was found that there is a linear relationship between linear statistical models which is expressed by a matrix equality. Several corollaries are derived and discussed, and a new interpretation is proposed for the parameters of linear statistical model. The given relation between the linear statistical models may be useful for both theoretical analysis of statistical models and interpretation of applied statistical models, in particular, to analyze the impact of confounders.
Keywords: Linear statistical model, dependency, matrix equality, interpretation of linear model parameters, Cochran's multivariate formula.