Multiple Factor Analysis Based on NIPALS Algorithm to Solve Missing Data Problems

Abstract

Missing or unavailable data (NA) in multivariate data analysis is often treated with imputation methods and, in some cases, records containing NA are eliminated, leading to the loss of information. This paper addresses the problem of NA in multiple factor analysis (MFA) without resorting to eliminating records or using imputation techniques. For this purpose, the nonlinear iterative partial least squares (NIPALS) algorithm is proposed based on the principle of available data. NIPALS presents a good alternative when data imputation is not feasible. Our proposed method is called MFA-NIPALS and, based on simulation scenarios, we recommend its use until 15% of NAs of total observations. A case of groups of quantitative variables is studied and the proposed NIPALS algorithm is compared with the regularized iterative MFA algorithm for several percentages of NA.

Fast High-Resolution pKa Spectrotitrimetry for Quantification of Surface Functional Groups of Retisols

“…Prior to analysis, a Kaiser-Meyer-Olkin (KMO) test was used; the value was KMO = 0.6, which shows that the data are suited for factor analysis [52]. The decomposition was performed using NIPALS as the most standard algorithm providing the minimum numbers of ambiguous alarms and missed alarms [53,54], with the maximum number of iterations of 50 and a convergence criterion of 0.0001. The number of components describing the source set was selected using the cross-validation by the v-fold method; v was equal to 7, which provided the minimum error rate of the following PCA procedure and algorithm efficiency [55].…”