This paper discusses the development of a PCA-like method being able to capture the structure of incomplete multivariate data without any statistical assumption such as a multivariate normal distribution or a random missing process. This method, purely descriptive, is derived from a lower rank approximation of a data matrix with missing values. Parameters are estimated by the Newton-Raphson method in order to minimize the least squares criterion with respect to observed values. Two examples of educational measurement are added to demonstrate practial use of the method.