Investigating the Dimensionality of Early Numeracy Using the Bifactor Exploratory Structural Equation Modeling Framework

Abstract

The few studies that have analyzed the factorial structure of early number skills have mainly used confirmatory factor analysis (CFA) and have yielded inconsistent results, since early numeracy is considered to be unidimensional, multidimensional or even underpinned by a general factor. Recently, the bifactor exploratory structural equation modeling (bifactor-ESEM)—which has been proposed as a way to overcome the shortcomings of both the CFA and the exploratory structural equation modeling (ESEM)—proved to be valuable to account for the multidimensionality and the hierarchical nature of several psychological constructs. The present study is the first to investigate the dimensionality of early number skills measurement through the application of the bifactor-ESEM framework. Using data from 644 prekindergarten and kindergarten children (4 to 6 years old), several competing models were contrasted: the one-factor CFA model; the independent cluster model (ICM-CFA); the exploratory structural equation modeling (ESEM); and their bifactor counterpart (bifactor-CFA and bifactor-ESEM, respectively). Results indicated acceptable fit indexes for the one-factor CFA and the ICM-CFA models and excellent fit for the others. Among these, the bifactor-ESEM with one general factor and three specific factors (Counting, Relations, Arithmetic) not only showed the best model fit, but also the best coherent factor loadings structure and full measurement invariance across gender. The bifactor-ESEM appears relevant to help disentangle and account for general and specific factors of early numerical ability. While early numerical ability appears to be mainly underpinned by a general factor whose exact nature still has to be determined, this study highlights that specific latent dimensions with substantive value also exist. Identifying these specific facets is important in order to increase quality of early numerical ability measurement, predictive validity, and for practical implications.

The structure of early numeracy: Evidence from multi-factorial models

“…This would be consistent with both the broad number sense factor proposed by Braeuning et al [18], and the multifactorial model proposed by Milburn et al [19] that includes a combined numeracy factor alongside distinct curriculum-aligned factors. This conceptualisation would also be consistent with suggestions that early numeracy is likely composed of both general and domain specific numerical factors [9,47]. Further research is needed both to more directly assess these hypotheses, and to assess whether or not the proposed core skills are more relevant to early numerical development than curriculum-aligned skills.…”

“…In addition to study aims and methods impacting the number of factors identified, different analysis techniques may suggest alternative ways of interpreting the structure of early numeracy. For instance, Dierendonck et al [47] investigated early numeracy using various modelling techniques, including CFA, bifactor-CFA, and bifactor exploratory structural equation modelling. A key distinction between these techniques is that bifactor models account for any shared communality of items through assuming the construct (e.g., early numeracy) is independently influenced by both a single general factor plus several domain specific factors.…”

Empirical development and verification of career well-being scale for teachers in Taiwan: Implications for workplace counseling

“…The bootstrapping method was employed (Bootstrap = 5000), and the preliminary CFA results revealed that the four-factored model established in Study 2 was mildly supported (χ 2 = 666.36, df = 98, χ 2 /df = 6.80, CFI = 0.87, RMSEA = 0.10, SRMR = 0.09). The information obtained through the goodness-of-fit test indicated that ESEM was required to broaden our understanding of the organization of CWB ( Marsh et al, 2013 ; Fresno et al, 2020 ; Dierendonck et al, 2021 ; Gegenfurtner and Quesada-Pallarès, 2022 ).…”

“…Doing so can provide useful information for determining the latent optimal structure of CWB established in the literature ( Asparouhov and Muthén, 2009 ). CFA has been criticized for its overly simplistic, restrictive, and idealistic independent cluster model assumption ( Xiao et al, 2019 ; Dierendonck et al, 2021 ), which has led to CFA frequently failing to meet several standards of good measurement (e.g., goodness-of-fit, measurement invariance, and well-differentiated factors; Marsh et al, 2020 ). Because of this, ESEM has been proposed as a potential alternative.…”

HBMIRT: A SAS macro for estimating uni- and multidimensional 1- and 2-parameter item response models in small (and large!) samples

“…Suppose we have assessed early numeracy (Dierendonck et al, 2021) with a standardized test in a sample consisting of 140 kindergarten children (the SAS listing to generate the data set and the listing for the analyses as well as the respective output are provided in Appendix B). The test encompasses three theoretical facets, each assessed by 10 items, namely counting, relations, and arithmetic.…”