An Integrative Variable- and Person-Centered Framework for Representing the Dimensionality of Math Interest

• In Event: Bifactor Models to Improve Theoretical and Analytical Precision and the Opportunity to Study Motivational Processes

Abstract

Background and Aims
Measures of motivational constructs, such as math interest, often yield data characterized by construct-relevant multidimensionality due to the presence of global and specific constructs (Morin et al., 2016; Perera et al., 2018, 2019). Wherever such psychometric multidimensionality is expected, it is critical to anchor person-centered examinations in bifactor representations of the construct under scrutiny to adequately disentangle generality and specificity (Morin et al., 2017). In person-centered investigation, the use of preliminary bifactor measurement structure may be critical to sufficiently disentangling distinct patterns of multidimensional math interest on which students may be differentially high, medium, or low (i.e., shape-differentiated profiles) from so-called “level-differentiated” profiles reflecting the tendency for individuals to be uniformly high, medium, or low across all interest constructs (Morin et al., 2016; Morin & Marsh, 2015). This is because generality in data renders the detection of shape-differentiated profiles more difficult as strong level effects, triggered by generality, induce strong level differences that dominate the profile configuration (Morin & Marsh, 2015). We illustrate this integrative framework with Renninger’s and Schofield’s (2014) measure of math interest, which possess both general and specific constructs.
Method
Our sample comprised 437 community college students. Of them, 48.7% of the sample was female, and 32.7% of the sample identified as of underrepresented minority status. Participation involved the completion of a battery of questionnaires, including the math interest measure from the STEM Tipping Points Survey (Renninger & Schofield, 2014), which was of particular focus in the current study. The math interest data were initially subjected to bifactor exploratory structural equation modeling (B-ESEM) to obtain factor scores to serve as mixture indicators. Based on the factor score mixture indicators latent profile analyses (LPA) were conducted to identify distinct profiles of math interest.
Results and Discussion
The math interest data were subjected to bifactor-ESEM with a CFA general factor and two specific ESEM with target (orthogonal) rotation. This model specification is especially useful where (a) generality and specificity are expected, (b) some items index only the general factor, and (c) there is psychometric multidimensionality due to item fallibility. The B-ESEM model provided a good fit to the data (χ⁠2 [62] = 176.808, p < .001, CFI = .967, TLI = .951, RMSEA = .065, and the general and specific factors were reasonably well-defined (Table 1). Based on the patterns of loadings, the general factor reflected general interest whereas the specific reflected competence and voluntary engagement. LPA, based on the B-ESEM mixture indicators, revealed support for a three-profile solution (see Table 2). Notably, the profiles were characterized by clear shape differentiation reflected subgroups indicative of (a) “Low general interest” (48.6%), (b) “general-interest-dominant” (32.8%), and (c) “high-interest-and-voluntary-engagement/lower competence” (18.6%) (Figure 1). Appropriate disaggregation of co-existing general and specific constructs should be a necessary precursor to person-centered examination where such psychometric multidimensionality is expected. We discuss the implications of this framework for motivation researchers as well as other possible solutions (e.g., factor mixture models) for accounting for generality and specificity in latent categorical variable models.

Authors

• Harsha Perera, University of Nevada - Las Vegas

• Matthew L. Bernacki, University of North Carolina Chapel Hill

• Candace Walkington, Southern Methodist University