An imputation method for categorical variables with application to nonlinear principal component analysis

Algorithmic-Type Imputation Techniques with Different Data Structures: Alternative Approaches in Comparison

“…Accordingly, we relied on the traditional linear PCA to build up the new version of the method, which will be termed Forward Imputation with the PCA (ForImpPCA). Although the logic behind ForImpPCA is very similar to the original ForImp (Ferrari et al 2011), it is characterized by several features. Since the dimensionality reduction problem is not the primary concern, the PCA method is merely involved as a tool functional to the imputation exercise.…”

“…The first is to re-formulate ForImp as an imputation technique for quantitative variables. Indeed, in its original version ForImp was not expressly developed as an imputation method, but rather as a method for missing data handling in NLPCA in alternative to commonly used standard options, such as passive treatment (Ferrari et al 2011). The second is to offer a critical comparison of the thus revised ForImp with missForest and IPCA based on various configurations of quantitative data as given by different patterns of skewness and correlation of variables.…”

“…In this work, attention is specifically drawn to three different logics of imputing, based on the use of random forest (Stekhoven and Bühlmann 2012), iterative PCA (Nora-Chouteau 1974) and the forward (Ferrari et al 2011) procedures respectively. In particular, Stekhoven and Bühlmann's method (missForest, Stekhoven and Bühlmann 2012) is an iterative technique for the imputation of continuous and/or categorical data based on a random forest, which is a random classifier introduced in the context of machine learning (Breiman 2001).…”

“…It has recently been subject to renewed interest as it is at the core of the multiple imputation technique with PCA, a component of a more general methodology (missMDA) introduced by Josse et al (2011) for imputing missing data with multivariate data analysis techniques. The Forward Imputation (ForImp) by Ferrari et al (2011) is a sequential procedure designed for extracting a latent dimension from ordinal variables in the presence of missing data. The nonlinear PCA (NLPCA) and the nearest-neighbour imputation (NNI) method are alternated in a step-by-step process that recovers the missing ordinal categories and then extracts the latent dimension.…”

Development of models for imputation of data from social networks on the basis of an extended matrix of attributes

“…Assessment of imputation by using the root mean squared error is widely made in various studies [14,24]. It is applicable only to numerical indicators and has a large number of modifications; however, the most popular variant is based on the normalized root mean squared error (NRMSE) [25], which is defined as follows: …”