Development and Validation of a Circumplex-Based Affective-State Scale for First-Year Engineering Students

Abstract

Despite growing awareness of the emotional challenges faced by engineering students and their impact on academic performance and retention, the field lacks validated tools to systematically assess affective states in theoretically grounded ways. First-year students are particularly vulnerable during the transition to university-level engineering education, experiencing stress, anxiety, and disengagement that contribute to attrition. This study aimed to develop and validate a psychometrically sound scale based on Russell’s Circumplex Model of Affect to assess first-year engineering students’ emotional experiences and provide educators with a theoretically grounded assessment instrument. A 12-item circumplex-based affective-state scale was administered to 176 first-year engineering students. Validation combined exploratory factor analysis on raw and ipsatized data, Procrustes alignment to check how closely the items formed a circle, and structural summary modeling to test circumplex geometry. Internal consistency was assessed using Cronbach’s α and McDonald’s ω. Exploratory factor analysis confirmed a robust two-dimensional Valence × Arousal structure explaining 51% of total variance. Procrustes rotation yielded excellent item-level congruence coefficients (0.929–1.000), while Structural Summary Modeling revealed strong sinusoidal patterns (R² = 0.94), indicating a near-circular configuration consistent with circumplex theory. Internal consistency was high across both dimensions (Cronbach’s α ≥ 0.76; McDonald’s ω ≥ 0.84). The validated scale provides a reliable, theoretically coherent instrument for assessing engineering student emotions along pleasant–unpleasant and activation–deactivation dimensions, enabling systematic emotional assessment and targeted interventions while addressing critical gaps in affective assessment tools.

1. Introduction

Emotion plays a pivotal yet often underappreciated role in academic settings, influencing student performance, engagement, and overall well-being. In engineering education, traditionally characterized by a focus on technical proficiency and rational problem-solving—the emotional dimensions of learning have been largely overlooked. However, growing evidence underscores that those emotional factors are deeply intertwined with students’ academic success and persistence in engineering programs (Ajjawi et al., 2019; Lönngren et al., 2020). Recent research reveals the significant scope of mental health challenges in engineering education, with 66% of engineering students exhibiting symptoms of at least one mental health condition, with only 24% receiving an official diagnosis compared to 37% in the general university population (Costabile, 2024; Wright et al., 2023). This striking disparity highlights the “culture of stress” that pervades engineering education (Jensen & Cross, 2021), where faculty and staff recognize this culture as a barrier to supporting student mental health and well-being, with students expressing beliefs that poor mental health is an expectation in engineering (Hammer et al., 2024).

Contrary to the perception of engineering as a purely logical discipline, emotional experiences significantly shape how students approach complex problem-solving tasks, interact with peers and faculty, and envision their future in the field (Asghar et al., 2024; Kellam et al., 2018; Husman et al., 2015). Recognizing and responding to students’ emotional landscapes is therefore essential for cultivating inclusive and supportive learning environments (Josiam et al., 2025; Kostolansky et al., 2023). This is particularly critical in engineering, where the intensity and rigor of the curriculum can trigger stress, anxiety, and disillusionment factors that can contribute to attrition. The competitive culture of many engineering programs perpetuates a “meritocracy of difficulty” where student success is interpreted as “being able to take it” (Jensen & Cross, 2021), intensifying emotional pressures and leading to feelings of inadequacy and isolation.

Embracing emotional awareness in pedagogy is not an ancillary consideration but a core element of effective engineering educational professional transformation (Asghar et al., 2024; Josiam et al., 2025). First-year engineering students are especially vulnerable to emotional distress as they navigate the transition from secondary school to the highly structured and demanding context of university-level engineering education (Mirabelli et al., 2025; Rivers et al., 2024). This period involves significant cognitive, social, and personal adjustments, including managing increased academic workload, adapting to autonomous learning, and finding a sense of belonging in a new social environment (Atiq & Batra, 2024; Elliott & Lakin, 2020; Willems et al., 2019). The phenomenon known as “learning shock”, the transition from knowledge-based learning to independent assessment and evaluation, represents a primary reason why many promising students do not pursue engineering careers (Elliott & Lakin, 2020; Power et al., 2025).

Recent longitudinal research tracking week-to-week changes in first-year engineering student well-being demonstrates that first-year students report significantly more stress and anxiety than final-year students (Ramteke & Ansari, 2016). Many students report heightened levels of stress, uncertainty, and self-doubt during this time, often forming critical decisions about their academic trajectory within the first semester (Danowitz & Beddoes, 2022; Wang et al., 2023). Stressors affect students differently throughout the academic year, with particular vulnerability during competitive program placement periods. If unaddressed, such challenges can erode motivation and hinder retention. If unaddressed, such challenges can erode motivation and hinder retention (Asghar et al., 2024; Mukherjee & Kittur, 2025). As such, engineering educators must prioritize emotional competence and psychological support to foster resilience, persistence, and success among first-year students. To support this pedagogical shift, reliable and theoretically grounded tools for assessing student emotions are essential (Josiam et al., 2025; Kostolansky et al., 2023). This study addresses that need by developing and validating an effective-state scale tailored to the emotional dynamics experienced by engineering students.

2. Literature Review and Theoretical Background

2.1. Assessment of First-Year Engineering Students’ Emotions

Understanding how first-year engineering students experience emotion is essential for improving retention and academic performance. Assessing the emotional experiences of first-year engineering students is crucial, as emotions play a significant role in learning, persistence, and identity development within the discipline. Positive emotions such as curiosity, interest, and pride have been linked to deeper engagement and improved academic performance, while negative emotions such as frustration, anxiety, and alienation can hinder learning and contribute to attrition (Pekrun et al., 2002). In engineering education, early exposure to challenging coursework, team dynamics, and unclear expectations may evoke a wide range of emotional responses. Researchers have advocated for the integration of emotion-focused assessment tools, such as the Achievement Emotions Questionnaire (AEQ) and reflective journaling, to better understand these experiences (Pekrun, 2006; Dogham et al., 2025). Additionally, Gesun et al. (2021) highlight that emotions are not just by-products of learning but are entangled with students’ sense of belonging, self-efficacy, and perceived fit within the engineering culture. By systematically assessing emotions in the first year, educators can design interventions that promote resilience, inclusion, and a more supportive learning environment.

The transition to university-level engineering can be an especially stressful period, intensifying the impact of emotional factors on students. Emotion plays a foundational role in shaping student experiences, especially during the transition into university-level programs (Elliott & Lakin, 2020; Ramteke & Ansari, 2016; Wilson et al., 2022). First-year students often encounter a confluence of academic, social, and psychological challenges that test their emotional resilience (Power et al., 2025). These include adapting to increased academic rigor, managing time independently, and navigating new peer dynamics in environments where class sizes tend to be much larger than students are accustomed to, with greater emphasis on self-responsibility and new social settings lacking established networks of friends. Research consistently demonstrates that emotional well-being is closely linked to academic outcomes such as persistence, motivation, and performance (Asghar et al., 2024; Ramteke & Ansari, 2016; Wilson et al., 2022). Recent studies indicate that 12 percent of first-year engineering students report moderate or higher depression, and 14 percent report moderate or higher anxiety (Wilson et al., 2022). Students experiencing chronic stress or a lack of belonging may struggle to concentrate, experience decreased self-efficacy or consider leaving the program altogether (Asghar et al., 2024; Nguyen & Kittur, 2024). The expectation to persevere through rigor, stress, and suffering of the engineering environment contributes to engineering students’ reluctance to seek help, with research documenting cultures of stress and shame that normalize mental health issues and harm overall student mental health (Hammer et al., 2024).

Positive emotions serve as important protective factors amidst the challenges faced by engineering students in their year. Conversely, positive emotions like curiosity and pride can enhance creativity, deepen engagement, and improve learning retention (Kellam et al., 2018). The first year is particularly critical, as emotional experiences during this time often set the tone for students’ long-term commitment to the field (Kostolansky et al., 2023; Power et al., 2025). Recent research has identified five distinct categories of emotional configurations that students experience: disciplinarity ability, disciplinary identity, disciplinary engagement, disciplinary community, and disciplinary self-consciousness (Kostolansky et al., 2023). These configurations demonstrate that emotional experiences are not isolated phenomena but common experiences for many students in engineering education, with 50% or more participants describing 91% of the emotional configurations. Recent findings about emotionally responsive student support reveal that engineering course load and marginalization both create emotional discomfort, while peers and instructors can cause both comfortable and uncomfortable emotions (Josiam et al., 2025). Despite this, engineering education has historically sidelined emotional dimensions, prioritizing technical mastery over holistic student development (Josiam et al., 2025; Kellam et al., 2018). To support this shift, educators need validated tools that can reliably capture students’ emotional experiences and help tailor interventions that build emotional resilience and support retention especially in the vulnerable first-year period (Asghar et al., 2024; Nguyen & Kittur, 2024).

2.2. The Circumplex of Emotion and Its Applications

The Circumplex Model of Affect provides a useful theoretical framework for understanding emotions in educational contexts. The Circumplex Model of Affect, developed by J. A. Russell (1980), offers a compelling theoretical framework for assessing and interpreting emotions (Posner et al., 2009). It conceptualizes emotions along two continuous dimensions: valence (pleasure-displeasure) and arousal (activation-deactivation) (Kuppens et al., 2013). Emotions are thus mapped in a circular space where states like excitement (high arousal, positive valence) and boredom (low arousal, negative valence) occupy distinct yet related positions (Pattisapu et al., 2024). This model provides a parsimonious yet nuanced way to represent the emotional experiences of students in educational settings (Kuppens et al., 2013). The circumplex has been widely used in psychology and educational research due to its empirical robustness and adaptability. Recent applications demonstrate how Russell’s two-dimensional model (valence and arousal) successfully categorizes academic emotions into four types: negative low arousal, negative high arousal, positive low arousal, and positive high arousal academic emotions (Kuppens et al., 2013). This specific academic application strengthens the theoretical justification for circumplex-based assessment tools in educational contexts.

Although its use in engineering education is still emerging, the circumplex model is showing promise for both research and pedagogy. In the context of engineering education, empirical application of the circumplex model’s application is scarce, with only a handful of published studies in the last decade directly using it to map engineering students’ emotional states. For example, recent work has applied the model to discourse analysis in specific courses or to classify emotional trajectories in project-based and multi-modal course contexts, but comprehensive or large-scale quantitative studies remain uncommon (Josiam et al., 2025; Kostolansky et al., 2023). Much of the existing research demonstrates proof-of-concept or pilot uses rather than fully embedded curricular interventions. Nevertheless, it can help instructors and researchers identify emotional states that correlate with specific academic behaviors such as how anxiety impacts test performance or how boredom correlates with disengagement in lectures (Kellam et al., 2018). Importantly, the circumplex accommodates the complex, mixed emotional states that students often experience during learning, making it ideal for capturing the affective nuances of first-year engineering students (Posner et al., 2005). Recent studies have begun exploring how the circumplex can inform pedagogical strategies in STEM (Kuppens et al., 2013; Pattisapu et al., 2024). Research on affect-adaptive systems demonstrates the practical utility of valence and arousal dimensions for real-time emotional state detection (Schmitz-Hübsch et al., 2022). These systems show that the majority of subjects demonstrate correlations between valence and performance and would therefore benefit from an affect-adaptive system. Interventions that aim to shift students from low-arousal negative states (e.g., apathy) to high-arousal states (e.g., enthusiasm) can improve engagement and persistence (Josiam et al., 2025). However, interindividual differences pose a major challenge for the development of affect-adaptive systems, as research suggests different directions in the emotions-performance relationship require individualized interpretation of emotional states (Schmitz-Hübsch et al., 2022).

This study seeks to address gaps in existing assessment tools by providing a domain-specific approach in the circumplex model. Yet there remains a lack of domain-specific tools tailored to the unique emotional and cognitive demands of engineering education (Asghar et al., 2024; Nguyen & Kittur, 2024). Research shows that existing affective assessment instruments focus primarily on cognitive and psychomotor aspects, with limited attention to affective dimensions. This study addresses that gap by developing a circumplex-based affective-state scale designed specifically for engineering contexts. By doing so, it not only contributes to theoretical understanding but also provides practical tools to enhance emotional insight and instructional responsiveness in engineering classrooms, supporting recent institutional initiatives like specialized mental health support hubs for engineering students such as Purdue’s CARE (Community, Assistance, and Resources for Engineering Students) Hub and successful blended counseling programs combining positive psychology and cognitive therapy approaches that have shown effectiveness in reducing depression and stress among undergraduate engineering students (Kalamatianos et al., 2025).

2.3. Circumplex Model and Discrete Emotion Inventories

The circumplex model of affect offers distinct advantages over traditional discrete emotion inventories in education research. The circumplex model of affect offers some advantages over discrete emotion inventories because it offers a more flexible and nuanced framework for capturing the dynamic and multidimensional nature of students’ emotional experiences in engineering education. Discrete emotion inventories typically ask students to select from a fixed list of named emotions (e.g., anger, fear, joy), which may not capture the range or subtlety of affective states experienced during academic tasks. In contrast, the circumplex model organized along the dimensions of valence (pleasant–unpleasant) and arousal (high–low activation) allows us to map affective responses in a continuous space, enabling finer-grained analysis of how emotions shift across learning contexts and time (J. A. Russell, 1980; Posner et al., 2005). This model also accommodates mixed or ambivalent emotional states that are common in high-stakes environments like first-year engineering, such as simultaneous anxiety and excitement. Moreover, the circumplex approach facilitates visual and statistical interpretation, making it particularly useful for identifying emotional patterns across populations and informing affect-sensitive interventions. Ultimately, the circumplex model aligns with our goal of understanding affect not as a set of isolated labels, but as an integrated, fluctuating component of students’ academic and social development.

3. Research Design

3.1. Methods

This study employed a quantitative research design to validate a circumplex-based affective-state scale for assessing the emotional experiences of first-year engineering students. The scale was grounded in Russell’s Circumplex Model of Affect, which conceptualizes emotions along the dimensions of valence and arousal. Instrument validation development and validation incorporated both exploratory and confirmatory factor analytic procedures to evaluate the structure, reliability, and validity of the scale.

3.2. Participants and Data Collection

This study was conducted at a Midwestern R1 university and involved students enrolled in three sections of a first-year engineering introductory course, totaling 72 students per section. Across three course sections (≈72 students each; ≈216 enrolled), a total of 176 students completed the scale (estimated response rate ≈81%). The course is designed to foster students’ integration and socialization in the engineering profession and support their academic and social integration on campus. The curriculum (see Table 1) is designed to promote students’ holistic development and can be organized into five types groups (Bowman et al., 2003; Reid et al., 2018; Chen, 2014): (1) general engineering courses; (2) professional skills development; (3) orientation-type and academic advising activities; (4) activities designed to foster integration (learning communities, social opportunities); and (5) general education courses, such as mathematics and natural sciences.

Table 1. Sample FYE components at the institution, and referred to in this paper.

FYE Topics as Defined in (Bowman et al., 2003; Reid et al., 2018; Chen, 2014)	Illustration of the Engineering Topic at the Institution
General engineering course	Engineering design Thinking
Professional skills development	Team design project, cross-cultural communication diversity assignment (CCCD)
Orientation-type and academic advising activities	Engineering your major (exploration of all engineering majors offered in the college)
Activities designed to foster integration	Peer mentoring, Students-faculty interaction
General education courses	Mathematics, Physics, Chemistry

At the end of the first semester, students were invited to complete a Qualtrics survey. The survey was conducted at this time to ensure responses reflected students’ emotional experiences after they had encountered the full spectrum of first-year academic and social challenges. This timing provides a comprehensive assessment of the affective states shaped by university-level transitions, coursework, and peer interactions. Emotion measurement was operationalized through a self-report instrument mapped onto Russell’s Circumplex Model of Affect, spanning 12 emotion categories positioned at 30° intervals around the circumplex (i.e., full 360° coverage). The use of 12 items at 30° spacing is grounded in recent work showing that this arrangement offers higher precision and validity when mapping the full circular model of affect, compared to more sparsely spaced octant designs (Yik et al., 2011). This approach ensures each item maps clearly to unique sector of valence-arousal space and captures nuanced emotional states.

This study received approval from the university’s Institutional Review Board (IRB), and all participants provided informed consent in accordance with ethical research guidelines. Sample size was determined to ensure sufficient power for factor analytic procedures. Based on standard recommendations of 10–15 participants per item (MacCallum et al., 1999), a minimum of 120 respondents was required. Our sample size exceeds this benchmark with a total of N = 176 adults (Male = 104 (59%)) completing the 12-item affective-state scale, responding on a 6-point Likert format (1 = Not at all to 6 = Extremely). The Kaiser–Meyer–Olkin statistic of 0.83 further supports sampling adequacy for reliable factor extraction.

3.3. Data Analysis

All participants completed a 12-item self-report measure of emotional states (see Table 2 for item angles in a Valence × Arousal circumplex) using a 6-point Likert scale ranging from 1 (“Not at all”) to 6 (“Extremely”). All analyses were conducted using R (Version 4.4.2), utilizing the psych, lavaan, GPArotation, circumplex, mvn, and ggplot2 packages. Analyses proceeded in five sequential phases: data screening, exploratory factor analysis, circumplex diagnostics, confirmatory model testing, and reliability estimation. Data were screened by computing descriptive statistics (means, standard deviations, skewness, kurtosis) for each item, followed by checks for sampling adequacy via the Kaiser–Meyer–Olkin (KMO) statistic and Bartlett’s test of sphericity. The determinant of the correlation matrix was examined to rule out multicollinearity, and the Henze–Zirkler test (using the BHEP variant in the mvn package) assessed multivariate normality. Potential multivariate outliers were identified through Mahalanobis distance at p < 0.001, with key analyses replicated both with and without flagged cases to confirm robustness of findings.

Table 2. Theoretical placement of the 12 affect items on the Valence × Arousal circumplex.

Affective State	Circumplex Category	Angle (°)	Notes
Happy Satisfied	Pleasure	0°	High valence, moderate arousal
Enthusiastic Inspired	Activated pleasure	30°	High valence, high arousal
Energetic Excited	Pleasant activation	60°	High arousal, still pleasurable
Active Alert	Activation	90°	High arousal, neutral valence
Jittery Nervous	Unpleasant activation	120°	High arousal, low valence
Tense Bothered	Activated displeasure	150°	High arousal, strong displeasure
Unhappy Dissatisfied	Displeasure	180°	Low valence, medium arousal
Blue Uninspired	Deactivated displeasure	210°	Low valence, low arousal
Dull Bored	Unpleasant deactivation	240°	Very low arousal, unpleasant
Passive Quiet	Deactivation	270°	Low arousal, neutral valence
Relaxed Calm	Pleasant deactivation	300°	Low arousal, pleasant
Secure At Ease	Deactivated pleasure	330°	Very low arousal, positive valence

Two complementary exploratory factor analyses (EFAs) were conducted. First, raw Likert responses were examined via a polychoric correlation matrix and principal-axis factoring with oblimin rotation to account for the ordinal nature of the data. Factor retention was guided by scree plot inspection and Horn’s parallel analysis. Second, to minimize between-person response styles and better capture within-person emotional structure (Acton & Revelle, 2004; Gurtman & Pincus, 2003), each participant’s item scores were ipsatized (row-centered)—that is, we subtracted each individual’s average score from their response, so the analysis focused on how each student rated one emotion relative to their own average, rather than comparing absolute scores across students; and reanalyzed using Pearson correlations with principal-axis extraction. To facilitate interpretability, two anchor items (Happy-Satisfied and Active-Alert) positioned at 0°and 90° (Active Alert) were used to define the Valence and Arousal axes. Target rotation and oblimin re-rotation were then applied. The resulting two-factor loading matrix from the ipsatized data was rotated onto a 12-point unit circle via Procrustes analysis (a technique for aligning two spatial configurations). Tucker’s congruence coefficients (φ) were computed at both item and model levels, using 1000 random rotations to assess significance and adopting φ ≥ 0.90 as the threshold for acceptable alignment (van de Vijver & Leung, 1997). Uniform angular spacing was assessed via the standard deviation of deviations from the ideal 30° increments. To further evaluate the circumplex structure, the Structural Summary Method (SSM) (Zimmermann & Wright, 2017) was applied to ipsatized item means (bootstrapped with 2000 replications) to model cosine patterns of affective distribution. This included bootstrap-based estimates of amplitude, displacement, and R². Additional geometric diagnostics (Gaps, Rotation, Fisher, Variance) from Orthosim tested for equal spacing and communality symmetry.

Finally, four nested confirmatory factor models were tested on raw data using diagonally weighted least squares (DWLS) in the lavaan package. These models represented increasingly flexible assumptions about circularity (circular vs. elliptical structure): (a) a fully constrained circle (fixed angles and communalities), (b) a quasi-circumplex with equal angles but free communalities, (c) a quasi-circumplex with free angles but equal communalities, and (d) a fully flexible orthogonal two-factor solution with both angles and communalities freed. Identification followed conventional practices (one loading per factor set to 1.0, latent variances estimated), and model fit was evaluated using χ², the Comparative Fit Index (CFI), the Tucker–Lewis Index (TLI), and the Root Mean Square Error of Approximation (RMSEA). Fit criteria followed Hu and Bentler’s (1999) guidelines: CFI ≥ 0.90 and RMSEA ≤ 0.08 for acceptable fit. Internal consistency for the Valence and Arousal dimensions was examined using both McDonald’s ω and Cronbach’s α, acknowledging that ω provides a more robust estimate when factor loadings vary. All thresholds and analytic decisions (e.g., KMO ≥ 0.80, factor retention criteria, φ ≥ 0.90, amplitude ≥ 0.40, R² ≥ 0.70, and CFA fit criteria) were specified a priori, and no items required further revision based on these benchmarks.

4. Results

This section presents analyses supporting a strong two-dimensional (Valence × Arousal) structure for the 12-item affective-state scale. The analyses include data screening, exploratory factor analysis (EFA) on raw and ipsatized data, circumplex diagnostics, confirmatory factor analysis (CFA), and reliability testing. Results across all approaches converge to confirm the theoretical model’s validity and instrument’s internal consistency.

4.1. Data Screening

Prior to conducting the exploratory factor analysis (EFA), several assumption checks were performed to assess the suitability of the data. A total of 176 participants completed 12 items measuring affective states on a 6-point Likert scale (1 = Not at all, 6 = Extremely). There were no missing values in the dataset. The Kaiser–Meyer–Olkin (KMO) measure of sampling adequacy was 0.83, indicating that the data were well-suited for factor analysis (Kaiser, 1974). All individual items had KMO values above the recommended threshold of 0.70, ranging from 0.72 to 0.89. Bartlett’s test of sphericity was significant, χ²(66) = 871.01, p < 0.001, indicating that the correlation matrix was not an identity matrix and thus appropriate for factor analysis. The determinant of the correlation matrix was 0.00598, which is above the critical value of 0.00001, suggesting no issues with multicollinearity. These check supports the factorability of the correlation matrix.

Multivariate normality was assessed using the Henze–Zirkler test, which indicated a violation of the normality assumption, HZ = 1.08, p < 0.001. While univariate skewness and kurtosis values for most variables were within acceptable ranges (skewness < ±1.07, kurtosis < ±0.68), the violation of multivariate normality confirmed the need for a robust extraction method; accordingly, principal-axis factoring was employed for subsequent EFAs rather than maximum likelihood.

Lastly, Mahalanobis distance identified three multivariate outliers (observations 101, 160, and 176). These were retained for analysis but flagged for sensitivity checks. To evaluate their influence, the EFA was re-run after removing the outliers; the same two-factor solution emerged and accounted for a comparable amount of total variance (46.0% without outliers vs. 48.0% with outliers). Factor loadings remained substantively similar, with only minor shifts in secondary loadings (e.g., for HappySatisfied and ActiveAlerte). This indicates that the outliers did not distort the factor structure, supporting the robustness of the model. Given the stability of the factor structure, the outliers were retained in the final analysis, and a two-factor model was formally adopted for subsequent procedures.

4.2. Exploratory Factor Analysis (EFA)

Two exploratory factor analyses (EFAs) were conducted to examine the underlying structure of the 12-item affect measure, corresponding to the hypothesized Valence × Arousal circumplex model.

4.2.1. Raw Data

An initial EFA was performed on raw Likert-type responses using a polychoric correlation matrix and principal-axis extraction with oblimin rotation. Factor retention was guided by scree plot inspection and Horn’s parallel analysis, both of which indicated a possible three-factor solution (see Figure 1). Nevertheless, given the theoretical expectation of a two-dimensional circumplex and the preference for parsimony, both two- and three-factor solutions were estimated and compared. Fit statistics for these models are summarized in Table 3. Although the three-factor solution exhibited superior numerical fit (χ² = 0.53, df = 33, p = 1.00; RMSR = 0.03; adjusted RMSR = 0.05; cumulative variance explained = 59.0%), the two-factor model also showed acceptable fit (χ² = 1.27, df = 43, p = 1.00; RMSR = 0.09; adjusted RMSR = 0.11; cumulative variance explained = 48.1%). The diagonal-weighted least squares (DWLS) χ² values for both models were near zero, common with polychoric analyses, so absolute fit indices were not heavily interpreted (Muthén, 1993). Because the three-factor solution may reflect empirical wording clusters rather than distinct conceptual dimensions, the two-factor solution was retained for subsequent circumplex validation. This confirms the appropriateness of a two-factor (Valence and Arousal) structure underlying the data.

Figure 1. Parallel analysis scree plots for (a) raw polychoric correlations and (b) ipsatized Pearson correlations.

Table 3. Descriptive statistics and normality indices for the 12 affective-state items (n = 176).

	n	Mean	sd	Range	Skew	Kurtosis
Passive Quiet	176	3.01	1.14	5	0.21	−0.36
Relaxed Calm	176	3.48	1.20	5	0.16	−0.39
Secure At Ease	176	3.86	1.16	5	−0.17	−0.52
Happy Satisfied	176	4.14	1.23	5	−0.34	−0.39
Enthusiastic Inspired	176	4.00	1.06	5	−0.28	−0.20
Energetic Excited	176	4.01	1.16	5	−0.44	−0.10
Active Alert	176	3.97	1.27	5	−0.32	−0.40
Jittery Nervous	176	2.81	1.37	5	0.50	−0.54
Tense Bothered	176	2.75	1.22	5	0.65	−0.24
Unhappy Dissatisfied	176	2.45	1.20	5	0.87	0.38
Blue Uninspired	176	2.37	1.14	5	0.68	0.11
Dull Bored	176	2.32	1.21	5	1.07	0.68

Note: Skewness < ±1.07, kurtosis < ±0.68, and HZ > 0.99 indicated a non-normal distribution at the multivariate level, justifying principal-axis factoring for EFA.

In the retained two-factor raw-data solution, Factor 1 (Valence) is characterized by positive loadings for pleasant states (e.g., HappySatisfied, EnthusiasticInspired) and negative loadings for unpleasant states (e.g., UnhappyDissatisfied, TenseBothered). Factor 2 (Arousal) captures higher-activation states (e.g., EnergeticExcited at a strong positive loading), although some calmer states (e.g., RelaxedCalm) also load positively but more moderately (see Table 4). The two factors demonstrate a moderate negative correlation (r = −0.57), suggesting a mildly elliptical circumplex in the raw responses. Communalities range from 0.10 to 0.81, and the mean item complexity is 1.1.

Table 4. Model fit indices comparing the 2-factor vs. 3-factor raw solutions and the final 2-factor ipsatized EFA.

Fit Statistic	2-Factor Raw	3-Factor Raw	2-Factor Ipsatized
χ2 (df), p-value	1.27 (43), p = 1.00	0.53 (33), p = 1.00	21.73 (43), p = 0.97
RMSR	0.09	0.03	0.06
Adjusted RMSR (df-corrected)	0.11	0.05	0.08
Cumulative Variance Explained (%)	48.1%	59.0%	51.0%
Proportion Variance MR1/MR2/…	25%/23%	25%/23%/10%	33%/18%
Mean Item Complexity	1.1	1.5	1.2
Factor Correlation (Max)	−0.57	−0.45	0.44

4.2.2. Ipsatized Data (Centered Scores)

To better reflect within-person affective structure and reduce between-person response style bias (Acton & Revelle, 2004; Gurtman & Pincus, 2003), a second EFA was conducted on ipsatized (row-centered) data. Here, Pearson correlations were used with principal-axis extraction and oblimin rotation. Parallel analysis again supported a two-factor solution. The final two-factor ipsatized model showed good fit (χ² = 21.73, df = 43, p = 0.97; RMSR = 0.06; adjusted RMSR = 0.08), explaining 51.0% of total variance (33% for Factor 1, 18% for Factor 2). The mean item complexity was 1.2. Ipsatized data analysis confirmed the two-factor model and slightly improved model fit, indicating the scale’s robustness when controlling for individual response biases.

In the ipsatized solution, Factor 1 similarly reflects Valence by loading positively on pleasant states (e.g., HappySatisfied, EnergeticExcited, EnthusiasticInspired) and negatively on unpleasant states (e.g., UnhappyDissatisfied, TenseBothered). Factor 2 (Arousal) more clearly differentiates high-arousal items (e.g., JitteryNervous, ActiveAlerte) from calm, low-arousal items (e.g., RelaxedCalm, SecureAtEase). In contrast to the raw data, the two factors showed a moderate positive correlation (r = 0.44), indicating a slightly elliptical but theoretically coherent circumplex structure.

As noted in Table 4, factor polarity was reversed where necessary for interpretability, aligning Factor 1 with pleasant (positive loadings) versus unpleasant (negative loadings) valence, and Factor 2 with high (positive loadings) versus low (negative loadings) arousal. This flipping of signs does not alter the model fit or loadings but improves alignment with circumplex theory.

4.3. Convergent Findings

Factor loadings for both the raw-data and ipsatized models are listed in Table 4 and Table 5. Notably, the raw-data solution shows a moderate negative correlation between Valence and Arousal (r = −0.57), while the ipsatized structure indicates a moderate positive correlation (r = 0.44). Such differences are expected when shifting from between-person to within-person variance. In both solutions, however, the same two latent factors emerge—Valence and Arousal consistently, thus providing strong support for the hypothesized circumplex framework. These findings strengthen evidence for the validity and reliability of the two-dimensional emotional structure measured by the scale.

Table 5. Factor loadings (Oblimin rotation) for the raw-data (Valence, Arousal) solution and the ipsatized (Valence, Arousal) solution.

	Raw Data		Ipsatized Data
Item	Valence	Arousal	Valence	Arousal
PassiveQuiet	−0.36	0.11	−0.42	−0.28
RelaxedCalm	−0.08	0.46	−0.11	−0.73
SecureAtEase	0.14	0.51	0.22	−0.57
HappySatisfied	0.19	0.73	0.70	−0.22
EnthusiasticInspired	0.04	0.75	0.72	−0.04
EnergeticExcited	0.00	0.87	0.82	−0.01
ActiveAlert	−0.28	0.62	0.58	0.33
JitteryNervous	−0.69	0.10	−0.11	0.66
TenseBothered	−0.73	−0.01	−0.26	0.61
UnhappyDissatisfied	−0.87	−0.06	−0.68	0.26
BlueUninspired	−0.74	−0.08	−0.71	0.08
DullBored	−0.61	−0.05	−0.72	0.15

Note: Factor polarity was reversed where necessary so that Valence has positive loadings for pleasant states (e.g., HappySatisfied) and negative loadings for unpleasant states (e.g., UnhappyDissatisfied), whereas Arousal has positive loadings for high-activation states (e.g., EnergeticExcited) and negative loadings for low-activation states (e.g., RelaxedCalm). This sign flip does not affect the underlying model or fit indices but serves to facilitate interpretability with the circumplex framework. Bolded loadings indicate the primary (largest absolute) loading for each item in each solution.

4.4. Circumplex Diagnostics

Because circumplex geometry is conceptually grounded in within-person affective dynamics, all circular diagnostics were conducted on the ipsatized (row-centered) factor loadings rather than the raw scores. After extracting a two-factor solution (Valence and Arousal) using principal-axis factoring with oblimin rotation, the ipsatized loading matrix was rotated onto a 12-point unit circle via Procrustes analysis. Item-level Tucker’s congruence coefficients (φ) ranged from 0.929 to 1.000 (M = 0.969), well above the 0.90 threshold for circumplex fit. A permutation test with 1000 random rotations confirmed this alignment was highly unlikely due to chance (p < 0.001). The standard deviation of item angles from their ideal 30° spacing was 19.8°, implying a mild elliptical distortion yet remaining under the ≤30° guideline for near-uniform circularity (van de Vijver & Leung, 1997).

Structural Summary Modeling (SSM) (Zimmermann & Wright, 2017) applied to the ipsatized item means yielded a strong cosine curve with amplitude = 0.94 (95% CI [0.79, 1.09]), angular displacement = 112° (95% CI [106.5°, 117.7°]), and R² = 0.94, indicating a strong sinusoidal pattern centered in the pleasant activation quadrant. Orthosim indices (Gaps = 0.087; Rotation = 0.77; Fisher = 0.30; Variance = 0.59, all p > 0.05) were non-significant, providing further evidence of even angular spacing and only minor variation in communalities. Collectively, these results exceeded all preregistered thresholds (φ ≥ 0.90; amplitude ≥ 0.40; R² ≥ 0.70), confirming that the 12 items form a robust, two-dimensional circumplex with only minor elliptical distortion. These diagnostics provide strong empirical support for the circumplex structure underpinning the scale items.

As illustrated in Figure 2, items theorized to reflect high valence (e.g., HappySatisfied, EnthusiasticInspired) clustered on one side, while those capturing unpleasant affects (e.g., UnhappyDissatisfied, TenseBothered, BlueUninspired) occupy the opposite side. Likewise, high-arousal states (e.g., JitteryNervous, ActiveAlerte) appear near the top, whereas lower-arousal states (e.g., RelaxedCalm, PassiveQuiet) load closer to the bottom. Consequently, the Procrustes-rotated solution offers clear Valence × Arousal distinctions at the within-person level, bolstering evidence for a near-circular configuration consistent with the hypothesized circumplex model.

Figure 2. Circumplex structure of the 12 affective items following Procrustes rotation.

Factor scores were derived from ipsatized data using principal axis factoring with oblimin rotation and rotated onto a theoretical 12-point unit circle. Items approximate a circular configuration consistent with the Valence × Arousal model.

4.5. Confirmatory Models

Four nested confirmatory factor analysis (CFA) models were fit to raw scores using diagonally weighted least squares (DWLS) estimation to test progressively relaxed assumptions of circumplex structure. Model A represented a fully constrained circular structure (equal angles and communalities), whereas Model D allowed both angles and communalities to vary freely (see Table 6).

Table 6. Fit statistics for nested circumplex CFA models (DWLS, N = 176).

Model	χ2	df	p	CFI	TLI	RMSEA	SRMR
A. Equal angles + Equal communalities	3755.70	66	<0.001	0.18	0.18	0.57	0.43
B. Equal angles, free communalities	17,208.04	66	<0.001	0.00	−2.80	1.22	0.92
C. Free angles, equal communalities	2899.38	55	<0.001	0.37	0.24	0.54	0.36
D. Free angles + Free communalities	408.23	42	<0.001	0.92	0.87	0.22	0.13

Note: Model B returned an inadmissible solution with a non-positive definite information matrix. Fit indices are not interpretable.

Table 6 summarizes the model comparisons, providing fit statistics for these nested models. Model B yielded an inadmissible solution (non-positive definite information matrix), so its fit indices were not interpretable. Models C and D significantly outperformed the fully constrained Model A (Δχ² > 856, p < 0.001). Moreover, Model D significantly improved upon Model C (Δχ²[13] = 2491, p < 0.001) and was the only model to achieve acceptable comparative fit (CFI = 0.92), despite a still-elevated RMSEA = 0.22. As Browne (1992) noted, RMSEA can become inflated when an orthogonal two-factor CFA is imposed on a circumplex, because small localized residuals accumulate additively around the circle.

No CFA model attained conventional absolute fit criteria (i.e., CFI ≥ 0.95, RMSEA ≤ 0.06; Hu & Bentler, 1999). Nonetheless, Model D emerged as the best-fitting and preserved the two-dimensional Valence × Arousal structure, allowing mild elliptical deviations in both angles and communalities (e.g., Browne, 1992; Fabrigar et al., 1997; Hu & Bentler, 1999). These findings agree with the Procrustes and Structural Summary results from the ipsatized EFA where item-level Tucker’s φ reached ~0.97 and SSM R² = 0.94—demonstrating that while the item structure is broadly circular, albeit with modest distortions that are common in applied affective models. Overall, CFA results provide further confirmation of the proposed circumplex structure, acknowledging minor real-world deviations from ideal assumptions.

4.6. Internal Consistency Evidence

Cronbach’s α indicated good reliability for both Valence (α = 0.81) and Arousal (α = 0.76), exceeding the 0.70 benchmark common in research applications. McDonald’s ω yielded slightly higher estimates for each dimension (ω = 0.88 and ω = 0.84, respectively), suggesting that the items remain coherent even when heterogeneous loadings are accounted for. Given that α presumes equal item loadings and homogeneous covariances, whereas ω allows for differential weightings, the close correspondence between the two metrics (difference ≤ 0.07) implies that item polarities were keyed correctly and that both Valence and Arousal item sets exhibit robust internal consistency. These reliability indices demonstrate that the scale’s dimensions are measured consistently and accurately across items.

5. Discussion

This study developed and validated a 12-item circumplex-based affective-state scale for first year engineering students, contributing to the growing body of research on emotional assessment in engineering education. The validation process yielded strong evidence for the scale’s psychometric properties and theoretical alignment with Russell’s Circumplex Model of Affect. The near-circular structure confirmed through Procustes analysis (Tucker’s congruence coefficients φ = 0.929–1.000) and Structural Summary Modeling (R² = 0.94) demonstrates robust geometric fidelity to the circumplex framework. This alignment supports the theoretical foundation that emotions can be meaningfully organized along valence and arousal dimensions, even within the specific context of engineering education. The strong internal consistency (Cronbach’s α ≥ 0.76, McDonald’s ω ≥ 0.84) indicates that the scale reliably captures both pleasant-unpleasant and high-low activation dimensions of student affect.

This successful validation of this circumplex structure within engineering education is particularly noteworthy given the field’s traditionally limited attention to emotional dimensions. The scale’s ability to capture the continuous interplay between activation and valence addresses a critical gap in assessment tools for engineering contexts, where students often experience complex, ambivalent emotions during high-pressure academic situations. The current validation results align closely with previous circumplex-based affect scale development studies, particularly the work by E. Russell and Daniels (2018) using the Daniels five-factor measure of affective well-being (D-FAW). Like the present study, Russell and Daniels found that short-form circumplex measures maintain robust psychometric properties when validated as standalone instruments, Their 10-item D_FAW demonstrated similar challenges with confirmatory factor analysis fit indices, achieving acceptable but not optimal fit (CFI approaching 0.95), which mirrors the current study’s CFA results where no model met strict absolute fir criteria (CFI ≥ 0.95, RMSEA ≤ 0.06). The Tucker’s congruence coefficients in the present study (φ = 0.929–1.000) exceed those reported by Huelsman et al. (2003) in their validation of multiple affect measures with the circumplex model, who found mixed support for circumplex structure with their Model 2 (two correlated factors) fitting best but not achieving perfect orthogonality. Recent work by Roca et al. (2023) with the Hedonic and Arousal Affect Scale (HAAS) provides additional context, as their 12-item measure showed superior goodness-of-fit compared to longer versions and demonstrated similar two-dimensional structure validation (Roca et al., 2023). The present study’s Structural Summary Modeling results (R² = 0.94, amplitude—0.94) are particularly strong compared to the broader literature on circumplex validation, where researchers like Ekkekakis and Petruzzello (2002) have emphasized the inherent challenges of modeling circular constructs using traditional factor analytic approaches. The consistent finding across these studies including the current work that circumplex measures face systematic challenges in meeting conventional CFA fit criteria reflects the ongoing methodological tension between geometric circumplex assumptions and linear factor analytic models, as noted by Remington et al. (2000) in their comprehensive meta-analysis of 47 circumplex datasets.

Practical and Theoretical Implications

The validated scale offers several applications for engineering education. First, it provides educators with a theoretically grounded tool for systematically assessing student emotional states, enabling more responsive pedagogical approaches. The scale’s concise 12-item format makes it feasible for regular classroom use without imposing excessive burden on students or instructors. Instructors could administer the scale weekly, after exams, or following key project deadlines to monitor students’ emotional states in real time. Results can highlight when students experience heightened anxiety, stress, boredom, or disengagement, enabling timely intervention. For example, instructors might initiate targeted support, adjust course pacing, or incorporate resilience-building activities depending on observed emotional patterns.

Second, the circumplex framework allows for nuanced emotional mapping that can inform targeted interventions, particularly for students experiencing negative high-arousal states (anxiety, stress) or negative low-arousal states (boredom, disengagement). This facilitates a precision approach to emotional support that is informed by continuous mentoring rather than reactive measures. From a theoretical perspective, this work extends the application of circumplex models to engineering education research, demonstrating their utility beyond traditional psychology contexts. The successful validation supports the universality of the valence-arousal framework while acknowledging domain-specific emotional experiences in engineering settings. From a theoretical perspective, this work extends the application of circumplex models to engineering education research, demonstrating their utility beyond traditional psychology contexts. The successful validation supports the universality of the valence-arousal framework while acknowledging domain-specific emotional experiences in engineering settings.

Importantly, the scale content and interpretation are directly informed by emotions documented as distinctive in engineering education such as sustained stress, tolerance for ambiguity, productive struggle, “learning shock,” and the experience of isolation or imposter syndrome. Extensive research shows that engineering students face a culture of heightened academic rigor and competitive environments, leading to high-arousal negative states (stress, frustration) and unique emotional configurations related to teamwork, design thinking, and identity formation. By capturing these domain-specific patterns, the scale empowers instructors and researchers to identify emotionally at-risk students, assess resilience, and tailor interventions that recognize the realities of engineering programs (Josiam et al., 2025; Jensen & Cross, 2021; Kellam et al., 2018; Kostolansky et al., 2023).

6. Limitations

Several limitations should be acknowledged in interpreting these findings. First, the sample was drawn from a single institution and course, which may limit generalizability to other engineering programs, institutions, or cultural contexts. The demographic composition and institutional culture of the study setting may not represent the broader diversity of engineering education settings. This study did not collect ethnicity or international-student status to minimize identifiability in small course sections and reduce survey burden, which limits subgroup analyses; future validation with larger, more diverse samples will incorporate these variables under appropriate privacy safeguards. Second, while the ipsatized data analysis enhanced within-person modeling and reduced response bias, this approach may have obscured important between-person differences that could be relevant for understanding demographic or individual variations in emotional experiences. The choice to prioritize within-person emotional structure, while theoretically justified, may limit the scale’s utility for comparing emotional patterns across different student populations. Third, the confirmatory factor analysis results, while consistent with known challenges in modeling circular structures, did not meet conventional absolute fit criteria (CFI ≥ 0.95, RMSEA ≤ 0.06). This limitation reflects the inherent tension between strict factor-analytic assumptions and the geometric properties of circumplex models, as noted in the circumplex literature (Strack et al., 2013). However, this should be considered when interpreting the scale’s structural validity. Finally, the study employed a cross-sectional design that captured emotional states at a single time point, which may not reflect the dynamic nature of student emotions throughout the academic term or in response to specific academic challenges.

7. Future Research Directions

Several avenues for future research emerge from this work. First, replication and validation studies should examine the scale’s performance across diverse institutional contexts, engineering disciplines, and cultural settings to establish broader generalizability. Cross-cultural validation would be particularly valuable given the international nature of engineering education. Second, longitudinal research incorporating real-time emotion assessment through ecological momentary assessment or experience sampling methods could provide deeper insights into how student emotions fluctuate in response to academic demands, deadlines, and learning experiences. Such studies would enhance the understanding of emotional dynamics and their relationship to academic outcomes. Third, intervention studies should investigate how the scale can be integrated into adaptive learning systems or emotionally responsive pedagogical approaches. Research examining whether emotion-aware interventions improve student engagement, learning outcomes, and retention would demonstrate the practical value of systematic emotional assessment. Fourth, methodological research could explore alternative approaches to modeling circumplex structures that better accommodate geometric constraints while meeting conventional fit criteria. This could include the investigation of specialized circumplex modeling techniques or the development of new fit indices appropriate for circular structures. Finally, integration with other measures should examine how circumplex-based emotional assessment relates to other important constructs in engineering education, such as self-efficacy, belonging, academic achievement, and career intentions. This would position emotional assessment within broader frameworks of student success and persistence.

8. Conclusions

This study developed and validated a 12-item affective-state scale within the Valence × Arousal circumplex framework (J. A. Russell, 1980; Larsen & Diener, 1992). Exploratory factor analyses conducted on both raw and ipsatized data consistently supported a two-dimensional structure (pleasant vs. unpleasant; high vs. low activation). Geometric validation, including Procrustes analysis and Structural Summary Modeling (Zimmermann & Wright, 2017), further confirmed a near-circular configuration, demonstrating alignment with theoretical expectations of circumplex geometry (Acton & Revelle, 2004).

Although confirmatory factor analyses (CFA) did not meet conventional absolute fit criteria (Hu & Bentler, 1999), these results are consistent with longstanding challenges in applying strict CFA models to circumplex structures (Browne, 1992; Fabrigar et al., 1997). Such findings highlight the complexity of modeling perfectly circular constructs under typical factor-analytic assumptions. Internal consistency analyses (Cronbach’s α ≥ 0.76, McDonald’s ω ≥ 0.84) underscored the scale’s reliability for both Valence and Arousal dimensions.

In sum, the final 12-item instrument stands as a theoretically coherent, methodologically sound, and psychometrically stable measure of affect. Future research might replicate these results in broader or more diverse samples, use real-time assessments to capture within-person dynamics, or further investigate how engineering education environments elicit specific affective patterns. Despite the typical measurement complexities of modeling circular constructs, this measure offers a valuable tool for examining the nuanced interplay between valence and arousal, particularly for engineering students and potentially extending to other populations, thereby capturing the rich tapestry of human emotional experiences.