On the Relevance of Assumptions Associated with Classical Factor Analytic Approaches†

Abstract

A personal trait, for example a person’s cognitive ability, represents a theoretical concept postulated to explain behavior. Interesting constructs are latent, that is, they cannot be observed. Latent variable modeling constitutes a methodology to deal with hypothetical constructs. Constructs are modeled as random variables and become components of a statistical model. As random variables, they possess a probability distribution in the population of reference. In applications, this distribution is typically assumed to be the normal distribution. The normality assumption may be reasonable in many cases, but there are situations where it cannot be justified. For example, this is true for criterion-referenced tests or for background characteristics of students in large scale assessment studies. Nevertheless, the normal procedures in combination with the classical factor analytic methods are frequently pursued, despite the effects of violating this “implicit” assumption are not clear in general. In a simulation study, we investigate whether classical factor analytic approaches can be instrumental in estimating the factorial structure and properties of the population distribution of a latent personal trait from educational test data, when violations of classical assumptions as the aforementioned are present. The results indicate that having a latent non-normal distribution clearly affects the estimation of the distribution of the factor scores and properties thereof. Thus, when the population distribution of a personal trait is assumed to be non-symmetric, we recommend avoiding those factor analytic approaches for estimation of a person’s factor score, even though the number of extracted factors and the estimated loading matrix may not be strongly affected. An application to the Progress in International Reading Literacy Study (PIRLS) is given. Comments on possible implications for the Programme for International Student Assessment (PISA) complete the presentation.

Perceptual correlates of successful body–prosthesis interaction in lower limb amputees: psychometric characterisation and development of the Prosthesis Embodiment Scale

“…PAF was selected in favour of principal component analysis, since this method is better suited for psychological models due to considering residual and error variance in the data 72 . Furthermore, PAF does not require multivariate normal distribution 73 which is often unlikely for psychological variables, and the effects of non-normal distribution on the number of extracted factors and the estimated loading matrix is negligible 74 . Although the PEmbS-LLA development based on previously reported psychometric findings 18 , for prostheses, the factor structure is yet unclear, so that initially exploratory factoring was applied; however, confirmatory factor analyses were performed post hoc (see below).…”

Perceptual correlates of successful body-prosthesis interaction in lower limb amputees: psychometric characterization and development of the Prosthesis Embodiment Scale

“…PAF was selected in favour of principal component analysis, since this method is better suited for psychological models because of considering residual and error variance in the data 71 . Furthermore, PAF does not require multivariate normal distribution 72 which is often unlikely for psychological variables, and the effects of non-normal distribution on the number of extracted factors and the estimated loading matrix is negligible 73 . Although the PEmbS development based on previously reported psychometric findings 16 , for prostheses, the factor structure is yet unclear, so that exploratory factoring was applied.…”

Desempeño de la escala de racismo basado en la genética en estudiantes de medicina

“…En condiciones ideales se espera que la escala sea unidimensional 'estrictamente'; en la vida real se acepta 'esencialmente' unidimensional 28 . Entre los criterios para una solución factorial aceptable se encuentra el porcentaje de la varianza que explica el factor(es) retenido(s).…”

“…No obstante, este desempeño puede mejorar con el ajuste del instrumento y la revisión teórica en el concepto 2,11 . Esto incluye la revisión de la redacción y el número de los incisos para lograr mejores indicadores, en particular, el aumento de la varianza que explica la escala, lograr más del 50 % de la varianza, más aun si la escala hipotéticamente mide una única dimensión 20,28,29,34 . Es importante tener presente que en Colombia, etniaraza es un concepto con distintos significados, y diferentes palabras se usan para denominar el mismo aspecto relacionado con el color de la piel.…”