The overarching objective of this study was to use the data science method of MCA to explore hidden associations among factors influencing student acceptance of MOOCs and heterogeneity sources. This has led to the development of an appropriate dataset based on a comprehensive review of related studies. The dataset was processed using the MultipleCar toolbox [91] and MCORRAN2 Matlab code [95], which are general software suitable for implementing correspondence analysis. The theory, sample and factor are the core variables of the dataset that were considered for the MCA to detect hidden associations. The number of observations in a study often refers to as sample size is an important research consideration. Sample size influences the precision, robustness and validity of the findings from research. The larger the sample size, the more robust is likely to be the study result, but it should not be either too small or too large. On one hand, very small samples can undermine the validity and prevent the generalization of findings. On the other hand, very large samples tend to amplify small differences into statistically significant differences and emphasize insignificant statistical differences [24]. Theoretical models in research offer the footing to establish credibility and application of a wrong theory can lead to erroneous interpretations, judgments and weedy conclusions. However, the selection of the right theory for research can enhance robustness, relevance and impactful findings [25].

This study has used MCA for the first time to investigate hidden associations among the variables of theory, sample and factor. The MCA enables the exploration of hidden associations among variable categories and observations not observed in the literature. It has helped in this study, to detect useful insights about hidden associations among the factors influencing student acceptance of MOOCs, theoretical models applied in the previous studies for factor exploration and sample sizes of students who participated in the different studies. The work reported in this paper is an important assignment that has been overlooked in the literature as evidence from the comprehensive review of the existing studies. Previous studies have improved the understanding of the application of MCA for factor exploration. Meta-regression analysis was used to show that “theoretical model” and “sample size” were statistically significant sources of heterogeneity in factors influencing student acceptance of MOOCs [23]. However, the investigation of associations among influencing factors and sources of heterogeneity that could have yielded significant insights was not previously found.

The MCA has helped this study address the literature chasm and further enrich the existing studies on MOOCs in the niche area of technology acceptance. There are some important findings from this study as elucidated as follows. Complex theories that combine two or more supplementary factors are rarely applied, but blended theories are commonly used for exploring factors influencing student acceptance of MOOCs. This study has found five previous studies in the literature that have used complex theories for exploring significant factors influencing student acceptance of MOOCs [21,53,81,82,84]. Very small samples usually between 101 and 411 are widely used, but very large samples are rarely used for exploring factors influencing student acceptance of MOOCs. The studies that have used very small samples constitute about 75.93% and the examples of such studies with less than 200 samples include [15,16,19,71,79,84]. Student satisfaction [7,19,52,53,60,74,75,82], student attitude [10,11,57,68,79,83], behavioral intention [5,21,51,59,72] and perceived usefulness [1,2,13,61,70] are the widely used factors for exploring student acceptance of MOOCs. The student satisfaction factor was shown in meta-analysis research to be the main significant factor influencing student acceptance of MOOCs [23]. A very small sample of students is the most unusual under the basic assumption that none of the variables are correlated. The single theory was best represented by the five dimensions, whilst student satisfaction has the poorest representation. The five dimensions found for dimension reduction were easily interpreted and labeled as single theory factors, blended theory factors, complex theory with small sample factors, large sample factors and complex theory with very large sample factors. The salient coordinates in the first and second dimensions suggest that these two dimensions are bipolar and the other three are unipolar. The bipolar dimensions contrast the influencing factors that are on the opposite sides of the dimensions [91]. The simplified principal coordinates of variables and observations were obtained using the widely known varimax rotation algorithm as recommended by the previous authors [91,99].

The first is formed by factors identified by single theories. It is associated with social competence and a combination cloud of factors of teacher knowledge, social influence, perceived functional value, intellectual capital, engagement on platform and perceived enjoyment. The second describes the factors identified by blended theories. It is more associated with computer self-efficacy, gamification perception, intrinsic motivation and a combination cloud of factors of utility value, perceived behavioral control, functional attachment and course quality. The third is composed of factors identified by extended theories. It is associated with facilitating conditions, self-regulation, knowledge outcome and a combination cloud of factors of task technology fit, subjective norm, perceived reputation, performance expectancy, perceived ease of use and flow experience. The last is formed by factors identified by complex theories. It is associated with very small sample, small sample, large sample, very large sample, factors of perceived usefulness, student attitude and a combination cloud of factors of student satisfaction, student habit and behavioral intention that explain student behaviors toward MOOC acceptance.