Old and New Ideas for Data Screening and Assumption Testing for Exploratory and Confirmatory Factor Analysis

Abstract

We provide a basic review of the data screening and assumption testing issues relevant to exploratory and confirmatory factor analysis along with practical advice for conducting analyses that are sensitive to these concerns. Historically, factor analysis was developed for explaining the relationships among many continuous test scores, which led to the expression of the common factor model as a multivariate linear regression model with observed, continuous variables serving as dependent variables, and unobserved factors as the independent, explanatory variables. Thus, we begin our paper with a review of the assumptions for the common factor model and data screening issues as they pertain to the factor analysis of continuous observed variables. In particular, we describe how principles from regression diagnostics also apply to factor analysis. Next, because modern applications of factor analysis frequently involve the analysis of the individual items from a single test or questionnaire, an important focus of this paper is the factor analysis of items. Although the traditional linear factor model is well-suited to the analysis of continuously distributed variables, commonly used item types, including Likert-type items, almost always produce dichotomous or ordered categorical variables. We describe how relationships among such items are often not well described by product-moment correlations, which has clear ramifications for the traditional linear factor analysis. An alternative, non-linear factor analysis using polychoric correlations has become more readily available to applied researchers and thus more popular. Consequently, we also review the assumptions and data-screening issues involved in this method. Throughout the paper, we demonstrate these procedures using an historic data set of nine cognitive ability variables.

El análisis factorial exploratorio de los ítems: una guía práctica, revisada y actualizada

“…En consecuencia, A) se recomienda usar el método MV, factorizando la matriz de correlaciones producto-momento de Pearson, si los ítems tienen un número suficiente de categorías de respuesta (5 o más), o son continuos (cosa bastante más improbable), y además se cumple razonablemente el supuesto de normalidad, para que pueda observarse la relación lineal asumida en las relaciones bivariadas entre los ítems (Flora, LaBrish y Chalmers, 2012). También se recomienda considerar otros indicadores de ajuste derivados del test ji-cuadrado que evalúen el error de aproximación y el grado de ajuste del modelo.…”

“…Cuando se analiza la matriz de correlaciones policóricas se recomienda usar MCO (e.g. Flora, et al, 2012;Forero et al, 2009;Lee, Zhang y Edwards, 2012) Mínimos Cuadrados Ordinarios: Aquí se agrupan una serie de métodos descriptivos que tienen como denominador común que determinan la solución factorial que hace que los residuales sean tan próximos a cero como sea posible. El uso de estos métodos ha mostrado buenos resultados en la factorización de ítems ordinales cuando se analiza la matriz de correlaciones policóricas (Forero et al, 2009;Lee et al, 2012).…”

“…Este método, en vez de usar la matriz reducida como input, con las comunalidades estimadas en la diagonal, minimiza la suma de los cuadrados de las diferencias entre las matrices de correlaciones observadas y reproducidas. Este método es el más recomendado actualmente (ver por ejemplo Flora et al, 2012), porque funciona bien cuando se trabaja con muestras pequeñas incluso cuando el número de variables es elevado, especialmente si el número de factores a retener es pequeño (Jung, 2013). Además evita la aparición de casos Heywood (saturaciones mayores que la unidad y varianzas de error negativas), más frecuentes con otros métodos de estimación.…”

El análisis factorial exploratorio de los ítems: análisis guiado según los datos empíricos y el software.

“…That article and the following one "Exploratory factor analysis of items: some additional considerations" (Ferrando & Lorenzo-Seva, 2014) present the currently recommended standards for the applied researcher in terms of factor analysis (FA). In this second part, first we will review and summarize the degree to which four different statistical packages, SPSS version 22.0, FACTOR version 10.3.01 (Lorenzo-Seva & Ferrando, 2006, 2013, PRELIS 12 version 9.10 (Jöreskog & Sörbom, 2007) and MPlus version 6.12 (Muthén & Muthén, 2007, 1998-2012, allow or limit the application of these standards. Second, we will analyze the results offered by each of these programs when factor analyzing empirical data from scales that inadequately, ambiguously, or optimally fit, depending on the case, the assumptions of the exploratory factor analysis (EFA) classic linear model.…”

Infant Clinical Pain Assessment: Core Behavioral Cues

“…Product-moment correlations between NFCS facial actions were examined. Because MBPS pain behaviour indicators are ordinal, matrices of polychoric correlations among indicators were calculated instead of productmoment correlations (see [13]). In order to continue our examination of scale structure with factor analysis, the items on each scale were expected to be moderately correlated (between .30…”