Factor analysis is a statistical tool for modeling observed variables and their correlations in terms of underlying independent, unobserved factors. This thesis focuses on sparse factor analysis models, which are characterized by factors that do not necessarily influence all observed variables. Recent results have shown that for such models, the dimension can always be upper-bounded. When a certain level of sparsity is present, a lower bound can also be determined. Clearly, in cases where both bounds coincide, a dimension formula is obtained. In this thesis, we seek to develop software in R to determine these bounds computationally, as this may already suffice to get the model’s dimension. As a practical application, we perform simulations to identify the smallest graph in terms of the number of nodes and edges for which the bounds vary, as well as to identify the graphs that have expected dimension despite differing bounds. For the latter case of graphs, we will make use of the computer algebra system MACAULAY2 to determine the dimension, as differing bounds do not provide definitive information. Moreover, we extend our dimension analysis to a particular case of sparse factor analysis models with dependent, unobserved factors.      «

Factor analysis is a statistical tool for modeling observed variables and their correlations in terms of underlying independent, unobserved factors. This thesis focuses on sparse factor analysis models, which are characterized by factors that do not necessarily influence all observed variables. Recent results have shown that for such models, the dimension can always be upper-bounded. When a certain level of sparsity is present, a lower bound can also be determined. Clearly, in cases where both b...     »