Multiple Imputation of missing values in exploratory factor analysis of multidimensional scales: estimating latent trait scores

Abstract

Título: Imputación múltiple de valores perdidos en el análisis factorial exploratorio de escalas multidimensionales: estimación de las puntuaciones de rasgos latentes. Resumen: Los investigadores con frecuencia se enfrentan a la difícil tarea de analizar las escalas en las que algunos de los participantes no han respondido a todos los ítems. En este artículo nos centramos en el análisis factorial exploratorio de escalas multidimensionales (es decir, escalas que constan de varias de subescalas), donde cada subescala se compone de una serie de ítems de tipo Likert, y el objetivo del análisis es estimar las puntuaciones de los participantes en los rasgos latentes correspondientes. En este contexto, se propone un nuevo enfoque para hacer frente a las respuestas faltantes que se basa en (1) la imputación múltiple de las respuestas faltantes y (2) la rotación simultánea de las muestras de datos imputados. Se ha aplicado el método en una muestra de datos reales en que las respuestas que faltantes fueron introducidas artificialmente siguiendo un patrón real de respuestas faltantes, y un estudio de simulación basado en conjuntos de datos artificiales. Los resultados muestran que nuestro enfoque (en concreto, Hot-Deck de imputación múltiple seguido de rotación Consensus Promin) es capaz de calcular correctamente la puntuación factorial estimada incluso para los participantes que tienen valores perdidos. Palabras clave: Valores perdidos; Imputación Hot-Deck; Imputación Predictive mean matching; Imputación múltiple; Consensus Rotation; Puntuaciones factoriales; Análisis factorial exploratorio. Abstract:Researchers frequently have to analyze scales in which some participants have failed to respond to some items. In this paper we focus on the exploratory factor analysis of multidimensional scales (i.e., scales that consist of a number of subscales) where each subscale is made up of a number of Likert-type items, and the aim of the analysis is to estimate participants' scores on the corresponding latent traits. We propose a new approach to deal with missing responses in such a situation that is based on (1) multiple imputation of non-responses and (2) simultaneous rotation of the imputed datasets. We applied the approach in a real dataset where missing responses were artificially introduced following a real pattern of non-responses, and a simulation study based on artificial datasets. The results show that our approach (specifically, Hot-Deck multiple imputation followed of Consensus Promin rotation) was able to successfully compute factor score estimates even for participants that have missing data.

Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution

“…So, in principle, two basic recommendations need to be made. The first one is to use listwise computation and, if this is not possible, schemas other than pairwise deletion should be used to deal with missing data (see Arbuckle, 1996;Lorenzo-Seva & Van Ginkel, 2016;Wothke, 1993). The second one is to 'clean' the data set and remove the offending items described above, which, in addition, do not provide any relevant information.…”

On using multiple imputation for exploratory factor analysis of incomplete data

“…Recently, authors like Josse, Husson, and Pagés (2011), Dray and Josse (2015), Van Ginkel (2016), andMcNeish (2016) have considered multiple imputation (MI) in the sense of Rubin (Rubin, 2004;Schafer, 1997;Carpenter & Kenward, 2012) to deal with the missing data problem in PCA and EFA. Rubin's multiple imputation first imputes the data using, for example, a joint (Schafer, 1997) or conditional (Van Buuren, 2007) model, then in the second step performs the usual analysis on each completed (imputed) data set.…”

Investigating Primary School Teachers’ Knowledge Towards Meanings of Fractions

“…One of the assumptions of the exploratory factor analysis is that the data are obtained at equal intervals and continuously. Since the scoring of the data in the prepared success test is "1" for the correct answers and "0" for the wrong answers, the correlation matrix that we should base on when we want to do an exploratory factor analysis should be the Polychoric (tetrachoric) correlation matrix (Lorenzo-Seva & Van Ginkel, 2016). When it is desired to perform exploratory factor analysis for success tests, it is stated that a factor analysis based on tetrachoric correlation matrix should be performed (Lorenzo-Seva & Ferrando, 2013).…”