This lecture was presented at the 6th psychometric summer school held at the Moscow Higher School of Economics in August 2019.
The lecture describes the kinds of problems in CFA that lead to inadmissible solutions and then provides multiple approaches that can overcome this result. Solutions include fixing negative error variances to a small positive value, deleting highly correlated factors, subordinating one of a pair of highly correlated factors, using MI and EPC values to remove items that do not correspond wtih simple structure.