Given the highly skewed distributions of responses, we conducted an EFA for ordered-categorical indicators based on a polychoric correlations coefficients matrix. For conducting the EFA, the principal axes factor analysis method and a maximum likelihood estimator were employed.
Subsequently, the indicated number of factors was extracted using an oblique Geomin-type rotation since different subdimensions of flow have been shown to intercorrelate Rheinberg et al. Based on the assumption derived from flow theory that RFSS flow scores should peak when participants report to perceive an optimal balance of skills and challenges, criterion validity was tested regressing RFSS flow scores on skills-challenge balance using polynomial regression models.
To investigate convergent validity, Spearman and point-biseral correlations between RFSS flow scores and theoretically flow-related reading and reader variables were calculated.
Discriminant validity was explored by calculating Spearman correlations between RFSS flow scores and presence, identification, suspense, and cognitive mastery scores. In order to confirm that RFSS items load on a distinct latent variable than items assessing presence, identification, suspense, or cognitive mastery, single-factor confirmatory factor analysis CFA models for ordered categorical indicators were contrasted with corresponding multi-factor models.
For all CFAs a robust weighted mean- and variance-adjusted least squares estimator WLSMV was used, which outperforms other estimators in case of skewed data distributions Flora and Curran, The 10 RFSS items were subjected to an EFA using the principal axes factor analysis method and a maximum likelihood estimator based on polychoric correlations coefficients. Indicating sufficiently strong relationships among items, the Kaiser-Meyer-Olkin measure of sampling adequacy was 0.
Solutions for both two and three factors were examined using oblique Geomin-type rotation. The Kaiser index of factorial simplicity Kaiser, for the two-factor solution was 0. Substantial cross-loadings of items 4 and 5 indicated ambiguous item-factor associations, which lead to the removal of these items, reducing the RFSS to eight items in total.
To test whether the calculation of a global flow score across subscales, as indicated by the theoretical assumption of flow being a higher-order concept for a multi-dimensional state, is psychometrically justified, a CFA model with Flow as a higher-order factor needs to be conducted. This model, however, is not identified with two first-order factors only Absorption and Smooth Processing , rendering it impossible to provide clear empirical evidence in favor or against the global flow score.
We therefore tested a first-order CFA model in which all items load on just one factor Flow , which is the closest possible approximation to testing the presumption of a global factor. In the following, we report results for both the empirically validated subscale scores and the theoretically indicated global flow score.
Individual RFSS flow scores were calculated by averaging item scores by participants. Table 3. Mean scores and SD for flow, presence, identification, suspense, cognitive mastery, and reading self-efficacy. Table 4 shows Spearman correlations of the RFSS flow score and both its Absorption and Smooth Processing subscale scores with reading and reader variables as well as with variables related to previous reading-related flow experiences.
As expected based on flow theory and results from general flow research, the RFSS scores showed positive associations to these variables. Table 4. Correlations of RFSS scale scores with reading and reader variables, previous reading-related flow experiences, and concepts of pleasure-related narrative engagement.
As can be seen in Table 4 , Spearman correlations of RFSS flow scores with presence, identification, and suspense scores revealed strong associations between these concepts, and a medium-level association between flow and cognitive mastery. If that was the case, a multi-factor CFA model with independent clusters and freely correlating latent variables, which includes both items from the RFSS and items assessing one of these other concepts, should show better data-fit than the corresponding unidimensional CFA model; thus, the former CFA model indicates two different latent variables underlying the two measures, whereas the latter indicates a single latent variable.
This assumption was tested for the RFSS paired with presence, identification, suspense, and cognitive mastery, respectively. In a first step, separate CFA models for each concept for flow see Figure 1 were conducted, based on which, in a second step, CFAs for all pairings followed.
Figure 1. As can be seen in Table 5 , the multi-factor model representing independent clusters for different measures showed better data-fit than the corresponding single-factor model for each construct pairing.
Table 5. Confirmatory factor analyses results and model comparisons for flow and other pleasure-related reading engagement concepts. Following the rationale of flow theory, we regressed the RFSS global flow and subscale scores on measures of perceived skills-challenge balance.
We combined RFSS scores into four categories to obtain sufficient data points per category and then conducted a second-order polynomial regression model for ordered categorical outcome variables.
Observations and regression lines are illustrated in Figure 2. Figure 2. Regression of the RFSS flow scores on balance of skills and challenges. For item A, observations right and, for item B, left of the vertical dashed line indicate perception of low challenge.
Individual observations are shown as jittered hollow circles. Against the background of psychometrically limited methods for flow measurement in fiction reading, we developed the RFSS, an 8-item reading-specific flow scale based on a well-established general flow scale, the FSS Rheinberg et al. Our study provides evidence that the RFSS is a useful instrument for assessing flow states in fiction reading. Thus, the scale shows 1 a conceptually adequate factorial structure and good reliability estimates, 2 the predicted relationship with perceived skills-challenge-balance, 3 associations with theoretically flow-related concepts, and 4 , on top of substantial convergence, also sufficient distinctness when compared to other concepts of pleasure-related narrative engagement.
However, two items which showed no clear loading pattern had to be discarded. Another three items did not load on the same factor as their FSS counterparts. Given that the FSS and RFSS differ both in the domain of application and in item wording, such minor alterations in the factorial structure were to be expected.
In any case, smooth processing and absorption flow components are theorized to add up to the specific state of flow Rheinberg et al. However, unlike larger multi-dimensional flow scales Jackson and Marsh, ; Jackson et al. Thus, the higher order model is not identified with two first-order factors only, rendering it impossible to provide evidence in favor or against calculating a global flow score.
The insufficient data-fit of a single-factor solution supports the multidimensional conceptualization of flow and the calculation of subscale scores, but cannot provide clarification regarding the global flow score.
In the absence of clear empirical evidence, the decision to report a global flow score when using the RFSS can only be based on considerations of feasibility and practical application, its widespread use in flow literature, also for the original FSS Rheinberg et al. To further validate the RFSS, the relationship between flow as measured by this scale and the flow-criterion of perceived optimally balanced challenges was examined.
These results indicate that while absorption and smooth processing independently of one another show different associations to perceived text challenge, the combination of both high absorption and smooth processing, which characterizes a flow state, can only be found for texts that pose a certain, optimal degree of challenge.
A closer examination of this association between skills-challenge balance and the global flow score, however, revealed that flow was also high for texts perceived as slightly less than optimally challenging. This finding could be a methodological artifact, since the corresponding self-reports might suffer from the difficulty to intuitively estimate skills-challenge balance in fiction reading and from potential biases toward a more flattering intellectual self-presentation.
On the other hand, flow might indeed not be limited to reading books perceived as optimally challenging only: A meta-analysis of 28 studies found flow to occur mostly, but by no means exclusively under optimally challenging conditions Fong et al. Following this rationale, books that pose a less than optimal challenge level on the reader can still be appealing to certain types of readers or become appealing under certain circumstances: For instance, a reader normally interested in challenging material, might pick up and enjoy a young-adult book when reading for relaxation purposes.
Whether fiction reading is an activity specifically associated with situations or individuals that facilitate flow experiences under less than optimally challenging conditions, remains an interesting open question for future research. Based on flow theory and research in other activities, we expected flow in fiction reading to be positively associated with intrinsic reading enjoyment i. The corresponding correlations obtained in our study were all in the expected direction, as were the correlations between RFSS flow scores and measures of previous reading-related flow experiences.
However, correlations were moderate in size. This might result from limited measurement reliability as most concepts were assessed with single-items. Correlations with measures of previous reading-related flow experiences could be particularly affected by methodological limitations, as these measures were based on a description of flow in fiction reading that had not been pre-tested or psychometrically analyzed itself.
For most constructs, correlations were higher with Absorption than with Smooth Processing scores. Therefore, it is also possible that global flow score correlations were artificially diminished as a consequence of the smooth processing part of flow being under-represented in the RFSS.
Conversely, correlations between RFSS flow scores and presence, identification, suspense, and cognitive mastery scores were overall high. This was to be expected, as all of the concepts share a strong relationship with reading pleasure. Importantly, CFA modeling empirically confirmed that there is still sufficient distinctness between these concepts within the global reading experience.
View 1 excerpt, references background. View 1 excerpt, references methods. This investigation a tested the ability of an a priori hierarchical structure of self-concept derivedfrom the Shavelson model to explain responses to the Self Description Questionnaire SDQ III, … Expand.
View 2 excerpts, references background. Goodness-of-fit indexes in confirmatory factor analysis : The effect of sample size. This investigation examined the influence of sample size on different goodness-of-fit indices used in confirmatory factor analysis CFA. The first two data sets were derived from large normative … Expand. Factors influencing the occurrence of flow state in elite athletes.
Abstract Understanding factors which may influence the occurrence of flow in elaite athletes was the goal of the present investigation.
Twenty-eight elite level athletes from seven sports were … Expand. View 3 excerpts, references background. Athletes in flow: A qualitative investigation of flow states in elite figure skaters. Abstract A qualitative investigation into the flow experiences of elite figure skaters was conducted in order to gain greater insight into the nature of flow in sport. Sixteen former US National … Expand.
Highly Influential. View 11 excerpts, references results, background and methods. Measurement and correlates of sport-specific cognitive and somatic trait anxiety: The sport anxiety scale. At the same time, this result presents a new contribution since other recent studies e.
Lee et al. This result can occur because, on the one hand, if a student does not identify the objectives of the system, they tend to leave the system and, consequently, decrease the number of attempts to view a particular page or mission in the system. At the same time, if the student manages to have a high concentration when using the system, they also tend to do more activities and consequently view the same page or section of the system more often.
Although we hypothesize the proposed justification, recent related studies e. The result obtained in our study corroborates the results of other recent studies conducted using other systems or in other domains Lee et al. Our results demonstrate that system usage time negatively affects the overall flow experience of students, which means that those students who quickly abandoned the use of the system were not able to achieve a high flow experience.
Predicting each of the flow experience dimensions see Table 5 and Fig. Similar to the correlation result, the analysis results demonstrate that, as proposed in other studies Lee et al. Thus, consequently, we believe that they perform fewer activities or exit the system faster. Based on the results presented in this article, it is possible to advance the currently existing literature and take another step towards the automatic identification of the flow experience in educational systems.
The study presented in this article has some kinds of limitations, which we seek to mitigate throughout the study. The experience measured in the study i. To mitigate this limitation, we use only previously validated methods i. At the same time, to ensure the quality of responses and to avoid external threats e.
Another limitation is related to our small sample size i. To mitigate this limitation, we used a robust statistical method capable of accurately analyzing data from small samples i. However, we highlight the importance of replicating the experiment with larger samples to provide a greater results generalization, and we are sure that this paper would serve as an excellent basis for such future research.
The p values also are affected by the sample size. This limitation also suggests the replication of the study with larger samples. At the same time, our results allow us to propose a research agenda that can be followed in the coming years.
Initially, our study was conducted with a relatively small sample i. Therefore, we recommend that future research replicate our study with a larger and more heterogeneous sample i. At the same time, our study was conducted based on a single session using the system. If, on the one hand, this study design allowed us to understand student behavior when using the system, on the other hand, it opened space for the need to understand whether student behavior remains a standard when the system is used more than once by the same group of students.
Thus, we recommend that future research replicate our study, however allowing students to use the system more than once over different days, performing multiple data collections over the days of use. Our study was conducted using a gamified educational system. Although these data are part of a specific context i. Therefore, we recommend that future research explore new data logs in addition to what we explored in this study, such as data logs related to student interaction with gamification elements.
In our study, we initially performed a correlational analysis and then, used advanced statistical techniques i. This choice is justified because it is an appropriate technique for this type of analysis, even with small populations.
However, the use of other techniques combined with a larger sample can help to deepen the results. Therefore, we suggest that future research can use other types of data analysis such as data mining and machine learning. Therefore, we recommend that future studies can propose practical approaches, such as developing algorithms that, based on student data logs, provide an automatic analysis identifying which students are or are not in a flow experience.
Predicting student flow experience in educational systems is a contemporary challenge. Original dataset available as Additional file 1. Cesari, V. Enhancing qualities of consciousness during online learning via multisensory interactions.
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Computers in Human Behavior, 54, — Henseler, J. The use of partial least squares path modeling in international marketing. In Sinkovics, R. To a certain extent, the results of this paper are of great significance for predicting the observable quantities of large-scale real systems and further suggest that the potential scale invariance of many real-world networks is often masked by finite-size effects. COVID has impacted many institutions and organizations around the world, disrupting the progress of research.
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To address this, we have been improving access via several different mechanisms. The RGN transformation process of a weighted S 1 geometric model. Furthermore, for each layer of the network, when the total number of nodes is not divisible by s , the number of nodes contained in the last coarse-graining block in the layer will be less than s , and it will still be mapped to the supernode in the next layer. Each solid curve represents the variation of the average degree of a particular network in the corresponding region along the RGN flow, and the dashed lines show the result predicted by Eq.
All results are averaged over 10 independent realizations.
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