Psychometric Properties and Factor Structure of the Spanish Version of the Acceptance and Action Questionnaire-II (AAQ-II) in Ecuador

(1) Background: The Acceptance and Action Questionnaire-II (AAQ-II) is the most well-known self-report measure to assess psychological inflexibility, a transdiagnostic pathological process, and targets for interventions. Objective: The aim of this study was to analyze the psychometric properties and factorial structure of the Ecuadorian Spanish version of the AAQ-II in a large sample of college students in Ecuador. (2) Methods: A total of 7905 students, 46.26% male and 53.75% female, from 11 Ecuadorian universities were surveyed. The AAQ-II was tested for factorial structure, reliability, and correlations with other health-related measures. (3) Results: The AAQ-II showed an unidimensional factorial structure, accounting for 66.87% to 70% of the total variance and showing a good fit of the data to the model (comparative adjustment index (CFI) = 0.995; goodness of fit index (GFI) = 0.992; Standardized Root Mean Squared Residual (SRMR) = 0.037; mean square approximation error (RMSEA) = 0.047, CI90% = 0.038–0.056). Reliability was optimal (Cronbach’s α = 0.919; ω = 0.928), and AAQ-II scores significantly correlated with multiple health indicators. Psychological inflexibility was significantly higher in women than men. (4) Conclusions: The Spanish version of the AAQ-II showed good psychometric properties, which further supports psychological inflexibility, not just as a transdiagnostic process.


Introduction
Psychological inflexibility (PI) is characterized by a tendency to act rigidly, avoiding undesirable aversive events and producing important limitations in a person's life [1][2][3]. PI is composed of a set of the subprocess, including experiential avoidance, in which individuals seek to avoid, escape, or otherwise control the occurrence of difficult thoughts and feelings, despite the harmful consequences of doing so [4,5]. It is transdiagnostic in nature and a core concept in the acceptance and commitment therapy (ACT) model [4], which is probably one of the most representative of the third-generation therapies and has the most empirical support [6,7].
Nowadays, the Acceptance and Action Questionnaire is the gold standard in the measurement of psychological inflexibility (PI) [1]. The first version, developed by Hayes [8], was a short scale that had between 9 and 16 items depending on the version, like a Likertstyle scale. Its internal consistency was just satisfactory (α = 0.70), and the test-retest reliability was 0.64 over 4 months. In other samples (such as people with low academic levels or whose second language was English), the reliability indices were lower. The factorial structure of the Acceptance and Commitment Questionnaire (AAQ-I) was also unstable. For example, Hayes [8] reported a one-dimensional factorial structure for the 9 and 16-item versions, while Bond and Bruce [9] found a bifactorial structure for the 16-item version. Considering the inconsistencies and contradictions in the psychometric results of the first version, Bond et al. [1] proposed the second version of the Acceptance and Commitment Questionnaire (AAQ-II), which achieved better psychometric properties compared to the first version [1] and showed good internal consistency for both clinical and non-clinical samples (α = 0.78-0.88); adequate test-retest reliability at 3 and 12 months (α = 0.81 and 0.79, respectively); a one-dimensional factorial structure; and satisfactory convergent, concurrent, and discriminative validities [1].
The first Spanish translation of the AAQ-I scale (9 items) was carried out by Barraca [17], which presents problems related to internal consistency and factorial structure similar to those reported in the first version of the scale in English by Hayes [8]. Therefore, most studies on PI conducted in Spanish-speaking countries have used the AAQ-II translation [6].
Previous studies have validated the AAQ-II in Spain and Colombia by Ruiz et al. [6,7], but its psychometric properties in Ecuador remain unknown, making both psychological evaluation and research under the acceptance and commitment therapy approach difficult.
The aim of this study is to analyze the psychometric properties of an Ecuadorian-Spanish version of the AAQ-II in a large sample in Ecuador.

Participants
College students enrolled in 11 universities in Ecuador were invited via e-mail to participate in the study, and then they completed a computerized survey within the 3-week assessment period. A total of 7905 participants met the inclusion criteria of being enrolled in at least one whole academic year and completing the entire survey (the average response rate across universities was 47.80%, ranging from 39.10% to 56.30%). The average age was 21.49 years (SD = 3.68). Among the participants, 4249 (53.75%) were female, with an average age of 21.25 (SD = 3.70), and 3656 (46.26%) were male, with an average age of 21.80 (SD = 3.75). Among the participants, 60% came from public universities, 91% were single, and 73% were full-time students.

Measures
Acceptance and Commitment Questionnaire-II (AAQ-II) [1]. This is the most widely used general measure of psychological inflexibility. It consists of 7 items in which participants respond in a 7-point Likert-type scale, from 1 = "never" to 7 = "always". Scores range from 7 to 49. Higher scores indicate a tendency to act under the need to control or avoid aversive thoughts, memories, or feelings. The Spanish version presents a unifactorial structure that explains 57.33% of the total variance of the scale responses, and the internal consistency across the different samples was good (between α = 0.75 and α = 0.93). An example item is "My painful experiences and memories make it difficult for me to live a life that I would value". The AAQ-II scores were significantly related to general psychopathology and quality of life measures [6].
Life Engagement Test (LET) [18]. This 6-item scale measures vital commitment, which is understood as the degree to which the person engages in activities that are valuable to them as opposed to experiential avoidance. The response format consists of five alternatives (1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, 5 = strongly agree). Scores range from 6 to 30, with a higher score indicating a greater life engagement. This scale presents a one-dimensional structure; an adequate internal consistency in different samples ranging from α = 0.72 and α = 0.87; a test-retest reliability in the different samples (0.61 to 0.76); and satisfactory convergent, discriminant, and predictive validities [18]. Medium to strong negative correlations were expected between the AAQ-II and LET.
Patient Health Questionnaire of Depression and Anxiety (PHQ-4) [19]. This questionnaire assesses depression and anxiety associated with functional impairment and disability days. It consists of 4 items and a Likert-type response format with four options (0 = never, 1 = several days, 2 = more than half the days, 3 = almost every day). Scores range from 0 to 12. A higher score indicates a greater anxiety and depression level. The scale presented a two-dimensional structure and optimum reliability (α = 0.84) [20]. An example item is "Feeling nervous, anxious or on edge". Medium to strong positive correlations were expected between the AAQ-II and PHQ-4.
Loneliness Scale Revised-Short (UCLA-3) [21]. This consists of a brief 3-item scale evaluating the subjective feeling of loneliness, understood as the perception of less social support being available than desired. Participants respond based on their agreement with a series of statements, where 1 = "hardly ever", 2 = "sometimes", and 3 = "often". Scores range from 0 to 9. Higher scores indicate a greater feeling of loneliness or lack of social support. The internal consistency was good for both men (α = 0.75) and women (α = 0.84). An example item is "How often do you feel that you lack company?". Medium to strong positive correlations were expected between the AAQ-II and UCLA-3.
Perceived Stress Scale (PSS-14) [22,23]. This scale consists of 14 items to assess the degree to which people perceive a lack of control in their daily lives. Participants respond to a 5-point Likert-type scale ranging from 0 ("never") to 4 ("very often"). Scores range from 0 to 56 points. Higher scores indicate higher levels of psychological stress. In the Ecuadorian version [24], the reliability was optimal with the alpha and omega coefficients (α = 0.85 and ω = 0.80), and it presented a bifactorial structure, which explains 49.46% of the total variance, and satisfactory convergent validity with multiple health indicators. An example item is "In the last month, how often have you been upset because of something that happened unexpectedly?". Medium to strong positive correlations were expected between the AAQ-II and PSS-14.
Brief Resilience Scale (BRS) [25]. This assesses the individual's ability to adapt and recover from stressful and adverse situations. It consists of 6 items with 5 Likert-type alternatives of responses, ranging from 1 = "strongly disagree" and 5 = "strongly agree." This scale presents an adequate internal reliability (α = 0.83); a one-dimensional internal structure; and satisfactory concurrent, convergent, and predictive validities [26]. An example item is "I tend to bounce back quickly after hard times". Medium to strong negative correlations were expected between the AAQ-II and BRS.

Design and Procedure
A descriptive cross-sectional study was conducted. Participation was confidential and fully anonymous. A brief summary of individual scores was freely provided after the completion of the survey to encourage honest answers and a higher response rate. The study was approved by the Ethics Committee for Research in Human Beings (Comité de Ética de Investigación en Seres Humanos, CEISH) of the Ministry of Public Health of the Republic of Ecuador and was conducted according to the principles expressed in the Declaration of Helsinki. Written informed consent was obtained from all participants. A language adaptation of the original AAQ II into Ecuadorian Spanish was carried out by a panel of three experts (see Appendix A). The final Ecuadorian Spanish adaptation was tested on 30 candidates as a pilot trial to test for the clarity and comprehensiveness of the questionnaire.

Data Analysis
The statistical analyses were carried out using the IBM Statistical Package for the Social Sciences (SPSS) software (IBM Inc., Chicago, IL, USA), AMOS version 25.0 (IBM Inc., Armonk, NY, USA), and FACTOR version 10.8.03 for Windows (Rovira I Virgili University, Tarragona, Spain).
Firstly, the factorial structure was analyzed by performing an exploratory (EFA) and confirmatory (CFA) analysis. Following the recommendations of Lloret, Ferreres, Hernández and Tomás [30], and Harrington [31] that indicate that to obtain the factorial structure, both the EFA and the CFA must be performed in different samples, the total sample was divided into two random subsamples through the statistical program SPSS 25.0 (n = 4691) and (n = 3176). The chi-square statistical test did not reveal significant differences in both subsamples, so the random selection helped maintain the same proportion of sociodemographic characteristics in each one of them. Kolmogorov-Smirnov normality and Levene's homoscedasticity tests were also conducted for basic assumptions. Based on scores distribution, a MANOVA test was conducted, which has the advantage of reducing type I error by analyzing the differences by sex of all items in the same analysis.
For the EFA, the principal component method with factor extraction and the oblimin method for the rotation of the component matrix, retaining factor loads greater than 0.40 in the rotated matrix, were used. The two criteria to identify the number of factors of the scales were Cattell eigenvalues greater than the point of change of slope in the sedimentation curve and the number of observed eigenvalues, and the sedimentation curve for the 95th percentile in one series of randomly generated matrices (Optimized Horn Parallel Analysis).
For the CFA, the maximum likelihood method was used, and the estimators of the goodness of fit were the chi ratio square by degrees of freedom (CMIN/DF), the Bentler comparative adjustment index (CFI), the Jöreskog and Sörbom goodness of fit index (GFI), the fit index Bentler-Bonett norm (NFI), the parsimony standard adjustment index (PNFI), Akaike information criterion (AIC), and the mean square approximation error (RMSEA) and its confidence intervals (CI: 90). Good fitness of the model was considered if CMIN/DF ≤ 3; CFI, GFI, and NFI ≥ 0.95; and RMSEA ≤ 0.06.
Secondly, the AAQ-II factorial invariance analysis was performed for the total, male and female, sample: configurational invariance (M1), which indicates a factorial structure without restrictions (baseline); metric invariance (M2), where equivalence restrictions are established between factor loads; strong invariance (M3) or load and intercept equivalence restrictions; and strict invariance (M4), taking into account the equivalence restrictions of factor loads, intercepts, and residuals. The measurement invariance and its levels were evaluated according to the recommendations of Cheung and Rensvold [32]: ∆CFI ≤ 0.01 and ∆RMSEA ≤ 0.015.
Thirdly, internal consistency was analyzed based on the calculation of Cronbach's α and McDonald's ω, considering values of 0.70 acceptable for both cases.
Finally, convergent and divergent validities were analyzed based on Pearson's correlation between AAQ-II score and scores on scales corresponding to different well-established psychological health indicators.

Total and Sex Differences in Acceptance and Action Questionnaire-II Scores (AAQ-II) in Ecuador
Female participants reported significantly higher levels of psychological inflexibility than males on the total score and for each individual item (Table 1).

Confirmatory Factorial Analysis
The initial CFA showed poor fit of the data to the model ( The standardized factorial loads of this solution ranged between 0.704 and 0.844 while being significant (p < 0.05), with an average of 0.766, which is higher than the required value of 0.70 [8]. The intra-item correlations do not exceed the value of 0.90 (there is no multicollinearity), and the average variance extracted (AVE) value was acceptable (0.58) (Figure 1). 0.208-0.226)).

Confirmatory Factorial Analysis
The initial CFA showed poor fit of the data to the model (CMIN/DF = 78.236; CFI = 0.906; GFI= 0.895; NFI = 0.905; PNFI= 0.453; AIC= 1137.298; RMSEA = 0.156 (CI 90%: 0.148-0.164)). However, three correlated errors were reported between items 1 and 4, 2 and 3, and 6 and 7. Considering these correlated errors, a second model was evaluated, reporting an adequate fit of the data (CMIN/DF = 8.787. CFI = 0.993; GFI = 0.993; NFI = 0.992; PNFI = 0.390; AIC = 144.65; RMSEA = 0.050 (CI 90%: 0.041-0.059)). The standardized factorial loads of this solution ranged between 0.704 and 0.844 while being significant (p < 0.05), with an average of 0.766, which is higher than the required value of 0.70 [8]. The intraitem correlations do not exceed the value of 0.90 (there is no multicollinearity), and the average variance extracted (AVE) value was acceptable (0.58) (Figure 1). The adjustment indices of the unifactorial model with correlated errors, both for the total sample and separated by sex, are presented in Table 3, showing an adequate fit in each of them. Next, the configurational invariance (M1) was analyzed, presenting good fit indicators (χ2 (22) = 226.240; CFI = 0.994 and RMSEA = 0.034 (0.030-0.038)). The metric invariance (M2) resulted in good fit indices (CFI = 0.994; RMSEA = 0.031), being similar to the M1 values because they presented minimal differences (ΔCFI = 0.000 and ΔRMSEA = 0.003). These results indicate that the factorial loads are invariant between the groups of men and women, and, therefore, the covariances can be compared. The strong invariance The adjustment indices of the unifactorial model with correlated errors, both for the total sample and separated by sex, are presented in Table 3, showing an adequate fit in each of them. Next, the configurational invariance (M1) was analyzed, presenting good fit indicators (χ 2 (22) = 226.240; CFI = 0.994 and RMSEA = 0.034 (0.030-0.038)). The metric invariance (M2) resulted in good fit indices (CFI = 0.994; RMSEA = 0.031), being similar to the M1 values because they presented minimal differences (∆CFI = 0.000 and ∆RMSEA = 0.003). These results indicate that the factorial loads are invariant between the groups of men and women, and, therefore, the covariances can be compared. The strong invariance (M3) shows indices equal to the previous model (CFI = 0.994; RMSEA = 0.030) without minimal differences (∆CFI = 0.000 and ∆RMSEA = 0.001), accepting the invariance between the thresholds. Finally, the strict invariance (M4) reflects a good fit (CFI = 0.993; RMSEA = 0.029) with minimal differences (∆CFI = 0.001 and ∆RMSEA = 0.001), verifying the invariance of the residuals. The combined results indicate factorial invariance of the AAQ-II across both genders.

Convergent and Divergent Validities
The results presented in Table 4 show positive relationships between PI and perceived stress, loneliness, presence of anxiety and/or depression symptoms (convergent validity), and negative associations with resilience and life engagement (divergent validity), all being statistically significant (p < 0.01). The effect size of PI on the health indicators was moderate or large (r > 0.50).

Discussion
This is the first study to examine the psychometric properties of the golden selfreport measure of psychological inflexibility in an adult Ecuadorian sample. Furthermore, to our knowledge, this is the largest sample assessed with this questionnaire in Latin America. Overall, the results showed adequate psychometric properties, supporting its use in Ecuador.
The Ecuadorian Spanish version of the AAQ-II scale has shown a one-dimensional factorial structure consistent with the original version, high internal consistency, and good convergent and divergent validities. Female participants reported significantly higher psychological inflexibility than males. These results are consistent with those previously reported by Ruisoto et al. [33], Ruiz et al. [7], and Martins and Giardini [16].
Regarding factorial structure, both EFA and PA indicated that the one-dimensional structure accounts for between 66.87% and 70.03% of the total variance. Other indicators, such as UniCo, ECV, and MIREAL, proposed by Ferrando and Lorenzo-Seva [34], also suggested unidimensionality, consistent with the original study [1] and with other versions (Hungary [11], Greece [12], Brazil [16], Spain [6], and Colombia [7]). Moreover, the CFA also reflected a good fit of the data to the one-dimensional structure, consistent with the results of the original study [1]. Interestingly, this study found correlated errors between items 1 and 4, 2 and 3, and 6 and 7.
Previous studies had only detected correlated errors between items 1 and 4 [7,[11][12][13]35], 2 and 3 [11,12], and 2 and 5 [1] but failed to detect errors between items 6 and 7. The incorporation of these correlated errors resulted in a model with a better fit to the data than that originally proposed by Bond et al. [1] and Ruiz et al. [7]. The factorial structure remained invariant in men and women [36]. Gender differences in AAQII scores suggest differences in psychological inflexibility instead of a bias in the measurement itself [37].
The internal consistency was extremely high, with values of α = 0.919 and ω = 0.928, similar or even higher than those reported in the analysis of the internal consistency or reliability of other AAQII versions [7,[11][12][13].
The convergent and divergent validities of the Ecuadorian Spanish AAQ II were also consistent with previous studies, in which AAQ-II scores were positively correlated with the presence of more symptoms of depression [7,12,19,38,39] and anxiety [7,11,16,40], greater psychological stress [11,24,41], and greater loneliness [42], and negatively with resilience [16]. This evidence is important because it empirically supports the hypothesis of psychological inflexibility as a transdiagnostic dimension in the field of mental health.
These results should be considered with caution since the sample corresponds to university students. Future studies should further explore the psychometric properties of the Ecuadorian Spanish version of AAQII in clinical populations and other age ranges.

Conclusions
The Spanish version of the AAQ-II presents a one-dimensional structure, accounting for 67 to 70% of the variance, with good reliability and convergent and divergent validities. The scale is invariant by sex, and, thus, it can be used with guarantees in men and women. These results support the use of this scale to measure psychological inflexibility in Ecuador.
Finally, differences in the AAQ II scores reported between the Spanish and Ecuadorian versions might either shed some light on relevant cultural differences about how to cope or manage adverse private events or how this core transdiagnostic process has changed over time. However, although both implications are clinically relevant from a mental health perspective, further studies are needed to explore this path in depth.