Translation and Psychometric Evaluation of a Chinese Version of the Behavioral Regulation in Sport Questionnaire (BRSQ) with University Sport Athletes

Abstract

Our aim in this study was to translate and psychometrically evaluate a Chinese version of the Behavioral Regulation in Sport Questionnaire (BRSQ). Participants were Chinese collegiate athletes (N = 361) who were competitive in their respective sports. We examined the construct validity of the Chinese BRSQ using alternative structural equation models and evaluated convergent validity, factor score reliability, and measurement invariance of the optimal model. Due to insufficient score reliability for some subscales, our initial Chinese BRSQ was deemed problematic. A modified version of the questionnaire with a four-factor structure (amotivation, external regulation, introjected regulation, and autonomous motivation) demonstrated excellent construct validity, convergent validity, and score reliability. There was measurement invariance across athlete level and sex. This tool provides a valuable resource for practitioners and sport psychology researchers for assessing sport motivation among competitive university athletes in China.

Keywords

psychometrics motivation self-determination theory validity reliability

Introduction

Athletes’ motivation towards sport participation has been widely studied across the world (Amemiya & Sakairi, 2019; Buonamano et al., 1995; Chan et al., 2015; Chen et al., 2007; Farrell et al., 2004; Smith et al., 2016). A framework frequently relied upon to understand an individual’s motivational processes is Self-determination Theory (SDT, Deci & Ryan, 1986, 2008). SDT holds that human behaviors are driven by different types of motivation, and these fall on a continuum varying in degrees of self-determination (Deci & Ryan, 1986, 2000, 2008). Accumulating evidence has found that more self-determined motivation is positively associated with sport participation (McLoughlin et al., 2017), sport commitment (Zahariadis et al., 2006), deliberate practice (Vink et al., 2015), doping avoidance (Chan et al., 2015), flow experience (Jackson et al., 1998), and level of physical activity in youth sports (Fenton et al., 2016), whereas less self-determined motivation is positively related to sport drop-out (Garcia Calvo et al., 2010), athlete burnout (Barcza-Renner et al., 2016; Jordalen et al., 2016, p. 201; Lemyre et al., 2007; Madigan et al., 2016), and negative emotions during sport participation (Vallerand & Losier, 1999). These associations underlie the critical value of understanding athletes’ sport motivation to determine various positive and negative sport consequences.

The continuum begins with amotivation, which represents the least self-determined form of motivation and is characterized by not acting at all or acting passively toward a specific goal or enterprise. Extrinsic regulation is the next least self-determined type of motivation, and it refers to acting because of various degrees of extrinsically manipulated reasons that can be further divided into four distinct but related types: external regulation, introjected regulation, identified regulation, and integrated regulation. External regulation, the most controlling form of extrinsic regulation, occurs when actions are purely governed by external rewards or avoiding punishment. Introjected regulation is a partially integrated form of extrinsic motivation, but it is still externally controlling. Individuals endorsing this type of motivation tend to pursue ego-oriented outcomes, as exemplified by the pursuit of internal pressures, such as the need to maintain self-respect or avoid guilt, rather than pure enjoyment of the game or external rewards. Identified regulation refers to the internal endorsement of the values associated with taking action, which is somewhat autonomous. Integrated regulation is the most autonomous type of extrinsic regulation because the identified values of an activity is consistent with one’s own values. The continuum ends with intrinsic motivation, the most self-determined type of motivation, characterized by pure enjoyment, pleasure, and volition for engaging in an activity (Deci & Ryan, 1986, 2000, 2008). With the continued development of SDT, some researchers have proposed a revised taxonomy of motivation, that distinguishes between amotivation, controlled motivation (external regulation and introjected regulation) and autonomous motivation (identified regulation, integrated regulation, and intrinsic motivation; Vansteenkiste et al., 2010). The SDT framework is a comprehensive representation of human motivation that has consistently been applied across achievement contexts, including sport. Based on this theoretical substructure, several psychological instruments measuring sport motivation have emerged.

The development of the Sport Motivation Scale (SMS, Pelletier et al., 1995) was the initial attempt to measure sport motivation using an SDT framework. This scale has shown satisfactory validity and reliability, and it has been tested across cultures (Chantal et al., 1996; NÚÑez et al., 2006), gender (Li & Harmer, 1996), age (Zahariadis et al., 2005), and sport type (Pelletier & Dion, 2007). This instrument evaluates all the SDT motivation types, except integrated regulation. As Deci and Ryan (2008) noted, integrated regulation and intrinsic motivation are distinct, even if they appear similar. While the former should be considered an extrinsic motivation in which individuals act to achieve preferable sport outcomes, the latter characterizes motivation driven solely by the internal enjoyment of engaging in a sport. Therefore, with the omission of integrated regulation, some have questioned the content validity of the original SMS (Mallett et al., 2007) and have suggested including of an integrated regulation subscale. The SMS-6 and SMS-II are revised versions of the SMS that included an integrated regulation subscale. These instruments have also demonstrated good construct validity, consistent with SDT (Mallett et al., 2007; Pelletier et al., 2013).

A second scale designed to assess sport motivation and address the content validity concerns of the SMS is the Behavioral Regulation in Sport Questionnaire (BRSQ; Lonsdale et al., (2008). Lonsdale et al. (2008) proposed two different versions of the BRSQ. The BRSQ-6 is a six-factor model in which intrinsic motivation is regarded as a unidimensional construct; the BRSQ-8 is an eight-factor model in which intrinsic motivation is divided into three components (accomplish, knowledge, and stimulation). The BRSQ-6 has been applied more frequently in the sport setting than the BRSQ-8, because it more closely matches SDT (Deci & Ryan, 1986, 2008). The BRSQ-6 has been adapted to address cultural differences and translated into a number of languages, retaining adequate validity and reliability, and these adaptations have included Spanish (Viladrich et al., 2011), English (Hancox et al., 2015), Turkish (Çetinkaya & Mutluer, 2018), and Portuguese (Monteiro et al., 2018). The BRSQ-6 was found to be scalar invariant across gender, age, and competitive level of dancers in the United Kingdom (Hancox et al., 2015). Despite favorable psychometric features identified in various language versions of the BRSQ-6, the external regulation and introjected regulation subscales of the BRSQ-6 were found to be highly correlated (Hancox et al., 2015; Lonsdale et al., 2008), suggesting a possible measurement problem, as the two subscales are meant to be conceptually distinct according to SDT.

Although previous studies have established promising construct validity evidence for different versions of the BRSQ-6, they have failed to integrate the two broad motivation factors into the factor structure of the entire instrument. As motivation can also be subdivided by the degree of the controlling nature of these two broad factors - controlled and autonomous motivation (Vansteenkiste et al., 2010) - it is plausible that both broad and specific motivation dimensions may co-exist and collectively explain different portions of item covariance. Another possibility is that some specific motivation factors may be redundant when considering the two overarching factors. For instance, the high correlation between external regulation and introjected regulation identified in previous BRSQ studies (Hancox et al., 2015; Lonsdale et al., 2008) could be resolved by integrating a broader controlled motivation factor. This factor alone could be sufficient to explain most of the common variance shared by the items under the external regulation and introjected regulation subscales. In fact, Hancox et al. (2015) discovered that, when using a single controlled motivation factor to predict items under the external regulation and introjected regulation subscales, the model fit was comparable to the original factor structure of the BRSQ, and factor loadings were statistically significant and large. This finding suggests that multiple models with and without the addition of broader motivation factors (controlled and autonomous motivation) should be compared to identify the optimal factor structure of the BRSQ.

Two hierarchical models, named higher-order confirmatory factor analysis (HCFA) and bi-factor confirmatory factor analysis (BCFA), can be used in comparative analyses of the BRSQ to allow simultaneous modeling of both its specific and general motivation factors. The primary distinction between HCFA and BCFA is that BCFA requires fewer model constraints than HCFA. Specifically, the HCFA approach requires mediation effects from superordinate factors to items via subordinate factors, whereas the BCFA approach assumes that the common variances among items can be explained by one or more general factors and the remaining covariances can be explained directly by specific factors (Chen et al., 2006). As a result of this relaxed assumption, BCFA often yields a better model fit than HCFA (Chen et al., 2006). Another advantage of the BCFA approach is the independence of latent factors. All the latent factors estimated from the BCFA model are presumed to be uncorrelated, thus making the results easier to interpret (Gignac, 2016). To evaluate a postulated hierarchical factor structure, a BCFA model should be favored in the absence of any theoretical justifications necessitating the employment of a HCFA model. Therefore, in the current research, we utilized a BCFA method to concurrently examine specific and general motivational factors of a Chinese version of the BRSQ, to determine its optimal factor structure.

Despite the broad adoption of the BRSQ in different countries, no corresponding Chinese BRSQ has been developed. Although the Chinese SMS-II (Li et al., 2018) is available to measure athletes’ sport motivation in China, Lonsdale et al. (2014) showed that both the SMS-II and the BRSQ demonstrated strengths and weaknesses for measuring sport motivation and advised additional comparisons between these two scales to determine which is preferable. Moreover, the identified regulation, integrated regulation, and intrinsic motivation subscales of the Chinese SMS-II were found to be highly correlated (Li et al., 2018), indicating that the translation of items under these subscales may be problematic if they are to have similar meanings in Chinese. Given that the BRSQ and SMS-II employ entirely different item pools, translating the BRSQ into Chinese may alleviate this issue. Therefore, we believed it was imperative to develop a Chinese BRSQ to provide an alternative measure of sport motivation for the Chinese population. As the merits and limitations of the SMS-II and BRSQ identified in Western cultures may not apply to a different culture, the availability of a Chinese BRSQ allows sport motivation researchers and practitioners in China to compare it with the SMS-II to determine which instrument is best suited for implementation in the Chinese culture.

Our primary purpose in the present study was to translate and assess the construct validity, convergent validity, and factor score reliability of the Chinese BRSQ-6 among Chinese collegiate athletes. Considering the high correlation between external regulation and introjected regulation subscales found in previous BRSQ studies (Hancox et al., 2015; Lonsdale et al., 2008), as well as the high correlation between identified regulation, integrated regulation, and intrinsic motivation subscales of the Chinese SMS-II (Li et al., 2018), we utilized alternative CFA and BCFA models to determine the optimal factor structure for the Chinese BRSQ-6. Specifically, we tested all the possible combinations of the general and specific motivation factors including: (a) a CFA with six specific motivation factors (M1); (b) a CFA with amotivation and two general motivation factors (M2); (c) a BCFA with two general motivation factors and six specific motivation factors (M3); (d) a BCFA with two general motivation factors, amotivation, external regulation, and introjected regulation (M4); (e) a BCFA with two general motivation factors, amotivation, identified regulation, integrated regulation, and intrinsic motivation (M5); (f) a CFA with amotivation, controlled motivation, identified regulation, integrated regulation, and intrinsic motivation (M6); and (g) a CFA with amotivation, external regulation, introjected regulation, and autonomous motivation (M7). In addition to determining the optimal factor structure, we examined convergent validity, reliability of the factor scores, and measurement invariance of the best factor structure across sex and athlete level.

Method

Participants

Chinese undergraduate student-athletes (N = 361) from several public universities participated in this study. As the BRSQ-6 requires the respondents to be at least at a competitive level in their specialized sport (Lonsdale et al., 2008), we recruited students majoring in athletic training or physical education because these majors require students to be competitive in their specialized sports. In order to enroll in these majors, students must pass a special college admission exam in which they must display extraordinary competence in their specialized sports. On average, the participants were aged 20.45 years (SD = 1.41) and had been involved in their respective sports for 5.67 years (SD = 3.44). The sample consisted of 269 men and 92 women. A majority of the participants were freshmen (n = 123) and sophomores (n = 155), along with a smaller number of juniors (n = 59) and seniors (n = 24). Approximately two-thirds of these students were professional athletes (n = 232), with the remainder being competitive athletes (n = 129, see Instrumentation section for categorization details).

Ethical Considerations

This study received approval from the first author’s second institution’s Institutional Review Board (approval number: 2382122). Upon approval, a letter requesting access to students was sent to college professors in China who were selected through the primary researcher’s personal network. Following these professors’ permission, students in their classrooms were asked to participate in this study. All participants gave their consent to participate in this study before answering the questionnaires.

Instrumentation

Demographic Questionnaire

We collected the participants’ demographic information using a brief demographic questionnaire that included questions about school year, age, sex, and years playing their primary sport. Participants were also asked the question, “What is your certification in your main sport?” with response options: (a) no certification; (b) national level 3; (c) national level 2; (d) national level 1; (e) national player; (f) international player. Because people with certificates higher than national level 2 are widely considered professional players in China, those who responded with “a” or “b” were regarded as competitive players and those who responded from “c” to “f” were considered professional players.

Behavioral Regulation in Sport Questionnaire

The BRSQ-6 (Lonsdale et al., 2008) consists of 24 items and measures six different types of behavioral regulation: amotivation (e.g., “I participate in my sport but the reasons why are not clear to me anymore”); external regulation (e.g., “I participate in my sport because if I don’t other people will not be pleased with me”); introjected regulation (e.g., “I participate in my sport because I would feel ashamed if I quit”); identified regulation (e.g., “I participate in my sport because it teaches me self-discipline”); integrated regulation (e.g., “I participate in my sport because it’s a part of who I am”); and intrinsic motivation (e.g., “I participate in my sport because I enjoy it”). Respondents rate items on a Likert scale ranging from 1 (not at all true) to 7 (very true). The score for each type of behavioral regulation was calculated by averaging the scores of the items within the same subscale. The initial study on BRSQ-6 has confirmed the structural validity evidence (χ² (237) = 385.44, p < .01, CFI = .99, and TLI = .99) and good internal consistency (Cronbach’s alpha ranging from .79 to .92) of this scale (Lonsdale et al., 2008).

Chinese Basic Needs Satisfaction in Sport Scale

We used the Chinese Basic Needs Satisfaction in Sport Scale (BNSSS; Ng et al., 2011) to measure participants’ basic psychological needs satisfaction in sport. The BNSSS consists of 20 items measuring competence (e.g., “I am skilled at my sport”), autonomy-choice (e.g., “In my sport, I get opportunities to make choices”), autonomy-internal perceived locus of causality (e.g., “In my sport, I feel I am pursuing goals that are my own”), autonomy-volition (e.g., “I feel I participate in my sport willingly”), and relatedness (e.g., “In my sport, I feel close to other people”). Individuals record their response to each item using a 7-point Likert scale ranging from 1 (not true at all) to 7 (very true). The score for each subscale was calculated by averaging the scores of the items within the same subscale. The BNSSS has demonstrated good structural validity (χ² (160) = 341.70, p < .01, NNFI = .96, CFI = .97, SRMR = .07) and internal consistency (Cronbach’s alpha values range between .76 and .82 for all subscales, with the exception of the autonomy-volition subscale, which has an alpha of .61) among college athletes (Ng et al., 2011).

Questionnaire Translation

The English version of BRSQ-6 was translated into Chinese by three bilingual students according to the method recommended by Beaton et al. (2000). All students had been studying in the United States for two-to-three years. Each of the three individual translations was evaluated by the other two students, and any inconsistencies in item translation were discussed collectively. This process continued until all students agreed on a final version of the Chinese BRSQ-6. The translated instrument was then back-translated into English by a Chinese immigrant who has lived in the United States for over 15 years and is a college psychology professor. The differences between the back-translated and original versions of the instrument were evaluated by two monolingual English speakers with expertise in sport psychology. If any discrepancy was found, the monolingual speakers gave detailed feedback to the three forward-translators who then rewrote the troublesome items, and the back-translator translated the corrected items into English again. This process continued until the two monolingual speakers considered the items identical.

Data Collection Procedures

The implied consent form, Chinese-translated version of the BRSQ-6, and the BNSSS were electronically sent to students through Wen Juan Xing (Ranxing, Changsha), an online questionnaire management application. Students completed these questionnaires independently at their preferred time and location. The completion of all instruments took around 10 minutes. The completed surveys were automatically stored in Wen Juan Xing online and were downloaded by the first author.

Data Analysis

We used the statistical software program, R, for data preparation and Mplus for data analysis. We evaluated the univariate and multivariate normality of the item scores using the Shapiro-Wilk test and the Mardia estimate of multivariate kurtosis, respectively. Items having a z score exceeding 3.29 or less than −3.29 were deemed to be outliers (Warner, 2012) and were removed from further data analysis. The maximum likelihood robust (MLR) estimator was used to estimate the parameters, as it provides a more precise parameter estimation for Likert scale with five or more response categories, and is robust when the multivariate normality assumption is violated (Finney & DiStefano, 2006). In the CFA model, items were specified to regress on their specific latent factors that are allowed to correlate with each other. In the BCFA model, items were specified to regress on two general latent factors (controlled motivation and autonomous motivation) as well as on their specific factors. The latent factors in the BCFA model were not allowed to correlate with each other. Figure 1 shows the graphical representation of all the proposed models.

FIGURE 1.

Graphical Representation of the Tested Measurement Models.

The chi-square ( $χ$ ²), comparative fit index (CFI, Bentler, 1990), Tucker-Lewis index (TLI, Tucker & Lewis, 1973), and root mean square error of approximation (RMSEA, Steiger, 1990) were utilized as goodness of fit indices. Cut-off values for acceptable model fit were: χ² (p > .05), CFI >.90, TLI >.90, and RMSEA <.08 (Vandenberg & Lance, 2000). CFI and TLI values larger than .95 and RMSEA value less than .06 indicate excellent fit (Hu & Bentler, 1999). Due to its sensitivity to sample size, the chi-square test alone should not be used to establish the acceptance or rejection of a model (Schermelleh-engel et al., 2003). Akaike information criterion (AIC, Sakamoto et al., 1986), Bayesian information criterion (BIC, Raftery, 1986), and Akaike’s Bayesian information criterion (ABIC, Akaike, 1998) were used to assess if model fit surpassed model complexity. No rule of thumb was utilized to establish the appropriateness of AIC, BIC, and ABIC values. However, lower values typically reflect a better trade-off between model fit and model complexity (Van de Schoot et al., 2012).

Measurement invariance testing was conducted in accordance with Putnick and Bornstein’s (2016) recommendation. The best-fitting model was first fitted separately to each subgroup to test for model fit. A multi-group model was conducted to test the measurement invariance across sex and athletic level. The configural (no equality constraints), metric (equality of factor loadings across groups), scalar (equality of factor loadings and intercepts across groups), and strict invariance (equality of factor loadings, intercepts, and residual variances across groups) tests were performed. A decrease in CFI less than .01 and an increase in RMSEA less than .015 from less-constrained model to more-constrained model were used as evidence of group invariance (Cheung & Rensvold, 2002).

Convergent validity evidence, defined by the extent of agreement between two instruments that measure theoretically relevant constructs, was evaluated by correlating BRSQ factor scores with the factor scores from BNSSS. According to a previous study that found more controlling types of motivation had a more negative relationship with the BNSSS factors and more autonomous types of motivation had a more positive relationship with the BNSSS factors (Ng et al., 2011), similar relationships were hypothesized to be found in the present study.

The composite omega (ω_c) was adopted to evaluate the model-based reliability for all the models. The composite omega measures the proportion of explained total score variance that can be attributed to all common factors. Composite omega with a value greater than .80 indicates that the factor score is satisfactorily reliable (Nájera, 2019). The hierarchical omega (ω_h) was used to measure the proportion of explained score variance that is only attributable to a single latent factor for the BCFA models. A hierarchical omega greater than .80 indicates the factor score is essentially unidimensional (Rodriguez et al., 2016). The explained common variance (ECV) was used to determine the extent to which a general factor explains the common variance among a set of items. The percentage of uncontaminated correlations (PUC) was used to determine the number of correlations that can be described by the general factor in the absence of specific factors (Rodriguez et al., 2016). When both the ECV and PUC values are greater than .70, it implies that the items represent an essentially unidimensional latent construct (Rodriguez et al., 2016). Item explained common variance (I-ECV) was used to assess the item common variance that is attributable to a general factor. I-ECV greater than .80 indicates an item essentially reflects the general factor (Stucky & Edelen, 2014).

Results

Data Screening

Except for item 11 with six outliers, no outliers were found for other items. The Shapiro-Wilk test indicated that none of the item scores met univariate normality (all ps <.05). The Mardia estimate of multivariate kurtosis indicated deviation of the item scores from multivariate normality (p < .05). The potential biases introduced by outliers and non-normality were addressed using the MLR estimator (Zhong & Yuan, 2011).

Goodness of Fit Indices

Table 1 shows the goodness of fit statistics for all the models tested. The M1 model showed an excellent fit (CFI and TLI >.95, RMSEA <.06), except for the p value of the chi-square test (p < .001). The M3 and M7 models showed acceptable evidence of construct validity (CFI and TLI >.90, RMSEA <.08). All of the other models showed poor fit to the data (CFI and TLI <.90, RMSEA >.08). The M1, M3, and M7 models had lower AIC, BIC, and ABIC values than other models, indicating a better trade-off between model fit and model complexity. Because solely relying on fit indices may overlook model misspecification at a micro level, we proceeded to scrutinize the factor loadings and factor score reliability estimates for M1, M3, and M7 models to determine the optimal model.

Table 1.

Goodness of Fit of Alternative Measurement Models.

Models	χ² (df)	p	CFI	TLI	RMSEA (90%CI)	AIC	BIC	ABIC
M1	382.17 (237)	<.001	.98	.97	.041 (.033–.049)	24260.11	24598.44	24322.43
M2	1566.67 (249)	<.001	.78	.75	.121 (.115–.127)	26112.67	26404.34	26166.40
M3	637.36 (232)	<.001	.93	.92	.070 (.063–.076)	24603.65	24961.43	24669.55
M4	955.45 (244)	<.001	.88	.86	.090 (.084–.096)	25127.13	25438.24	25184.44
M5	1409.37 (240)	<.001	.80	.77	.116 (.110–.122)	25738.60	26065.27	25798.78
M6	1264.80 (242)	<.001	.83	.80	.108 (.102–.114)	25594.71	25913.60	25653.45
M7	719.88 (246)	<.001	.92	.91	.073 (.067–.079)	24773.93	25077.26	24829.81

Table 2 shows the standardized factor loadings, score reliability estimates, and factor correlations for the M1 model. All the standardized factor loadings were high and significantly loaded on their specified factors. Composite omega was satisfactory across all the factors (ω_c > .80). Consistent with the motivation continuum proposed by SDT, the factor correlations for amotivation, external regulation, and introjected regulation became higher as factors became theoretically closer to each other and lower as they were theoretically distant to each other. The continuum assumption was not supported for the identified regulation, integrated regulation, and intrinsic motivation factors as they all had similar correlations with other motivation factors and showed extremely high correlations with each other (ranging from .86 to .91).

Table 2.

Standardized Factor Loadings, Score Reliability Estimates, and Factor Correlations for the M1 Model.

Items	Amo	Exter	Intro	Ident	Integ	Intri
21	.926***
22	.941***
23	.961***
24	.958***
17		.921***
18		.873***
19		.891***
20		.893***
13			.870***
14			.896***
15			.786***
16			.925***
9				.825***
10				.903***
11				.945***
12				.902***
5					.826***
6					.901***
7					.916***
8					.912***
1						.929***
2						.941***
3						.860***
4						.941***
ω_c	.97	.94	.93	.94	.94	.96
Exter	.74***
Intro	.22***	.42***
Ident	−.03	.10*	.54***
Integ	−.03	.11*	.56***	.91***
Intri	−.09	.02	.45***	.86***	.88***

Note. Amo = amotivation; Exter = external regulation; Intro = introjected regulation; Ident = identified regulation; Integ = integrated regulation; Intri = intrinsic motivation; *** = p < .001; * = p < .05; ω_c = composite omega.

Table 3 shows the standardized factor loadings and score reliability estimates for the M3 model. All the items significantly loaded onto their general as well as specific factors, except for item 8 under the integrated regulation subscale. The standardized factor loadings for the items under the general controlled motivation factor were comparable to that of these items under their specific motivation factor (external regulation and introjected regulation). The factor loadings of the items under the general autonomous motivation factor were relatively high compared to those under their specific motivation factors (identified regulation, integrated regulation, and intrinsic motivation). The composite omegas were satisfactory for all the factors (ω_c > .80). The hierarchical omega for the controlled motivation and autonomous motivation indicated that 56% and 94% of the reliable sources of score variance could be explained solely by these two factors alone, respectively. While the hierarchical omega for external regulation and introjected regulation were comparable to that of controlled motivation, it became substantially less for identified regulation, integrated regulation, and intrinsic motivation compared to the autonomous motivation. The ECV and PUC values were low for the controlled motivation (ECV and PUC <.70) and high for the autonomous motivation (ECV and PUC >.70). The I_ECV values for the items under the controlled motivation factor were relatively low and were high for the items under the autonomous motivation factor.

Table 3.

Standardized Factor Loadings and Score Reliability Estimates for the M3 Model.

Items	CM	AM	Amo	Exter	Intro	Ident	Integ	Intri	I_ECV
21			.923***
22			.942***
23			.963***
24			.957***
17	.718***			.602***					.587
18	.666***			.568***					.579
19	.499***			.753***					.305
20	.560***			.703***					.388
13	.569***				.657***				.429
14	.534***				.730***				.349
15	.477***				.611***				.379
16	.540***				.753***				.340
9		.774***				.289***			.878
10		.837***				.372***			.835
11		.899***				.274***			.915
12		.851***				.293***			.894
5		.789***					.253***		.907
6		.841***					.404***		.813
7		.872***					.263*		.917
8		.898***					.144		.975
1		.844***						.403***	.814
2		.883***						.312***	.889
3		.798***						.318***	.863
4		.860***						.388***	.831
ω_c	.95	.98	.97	.95	.93	.94	.94	.96
ω_h	.56	.94		.51	.58	.11	.08	.14
ECV	.42	.88
PUC	.57	.73

Note. CM = controlled motivation; AM = autonomous motivation; Amo = amotivation; Exter = external regulation; Intro = introjected regulation; Ident = identified regulation; Integ = integrated regulation; Intri = intrinsic motivation; ω_c = composite omega; ω_h = hierarchical omega; ECV = explained common variance; I_ECV = item explained common variance; * = p < .05; *** = p < .001.

Table 4 shows the standardized factor loadings and score reliability estimates for the M7 model. All the standardized factor loadings were high and significantly loaded on their specified factors. Composite omega was satisfactory across all the factors (ω_c > .80). The factor correlations seemed to be consistent with the continuum assumption proposed by SDT as they became stronger with theoretically closer factors and weaker with distant factors.

Table 4.

Standardized Factor Loadings, Score Reliability Estimates, and Factor Correlations for the M7 Model.

Items	Amo	Exter	Intro	AM
21	.926***
22	.941***
23	.961***
24	.958***
17		.921***
18		.873***
19		.891***
20		.893***
13			.869***
14			.897***
15			.785***
16			.926***
9				.792***
10				.853***
11				.907***
12				.863***
5				.804***
6				.855***
7				.876***
8				.894***
1				.874***
2				.905***
3				.825***
4				.887***
ω_c	.97	.94	.93	.97
Exter	.74***
Intro	.22***	.42***
AM	−.05	.08	.54***

Note. Amo = amotivation; Exter = external regulation; Intro = introjected regulation; AM = autonomous motivation; *** = p < .001; ω_c = composite omega.

Although the standardized factor loadings and reliability estimates were excellent in the M1 model, the factor correlations revealed that the identified regulation, integrated regulation, and intrinsic motivation factors were highly correlated with each other, indicating the possibility that they were measuring a unidimensional construct. The M3 model revealed that after including a general autonomous motivation factor, the factor loadings for the items under the identified regulation, integrated regulation, and intrinsic motivation factors dropped substantially. In addition, the hierarchical omega, ECV, and I_ECV values indicated that a general autonomous motivation factor explained almost all the reliable sources of covariance among the items under the identified regulation, integrated regulation, and intrinsic motivation factors, indicating that these items essentially represented a single autonomous motivation. In contrast, the standardized factor loadings for the items under the external regulation and introjected regulation factors remained relatively high after introducing a general controlled motivation factor. The hierarchical omega, ECV, and I_ECV values for the controlled motivation factor indicated that a single controlled motivation was inadequate to explain the common covariances among the items under the external regulation and introjected regulation factors, indicating these items essentially represented a multidimensional construct (external regulation and introjected regulation). As M7 encompassed the factor structure of amotivation, external regulation, introjected regulation, and autonomous motivation and demonstrated adequate fit statistics, factor loadings, and score reliability estimates with no extremely high factor correlations, M7 was chosen as the best model.

Considering that it is unnecessary to use all 12 items to measure a single autonomous motivation factor and preferable to have a more parsimonious model, we proceeded to reduce the number of items under the autonomous motivation factor in the M7 model to four by referencing the modification indices. The items (item 3, item 5, item 8, and item 9) with the first four lowest modification indices were retained. Another CFA was run using the M7 factor structure, but it only included the retained items under the autonomous motivation factor. The final model showed excellent fit to the data, except for the significant result of the chi-square test (χ² (df) = 180.81 (98), p < .001, CFI = .98, TLI = .97, RMSEA (90%CI) = .048 (.037–.059)). Figure 2 shows the factor structure of the final model.

FIGURE 2.

Graphical Representation of the Final Measurement Model.

Table 5 shows the standardized factor loadings, score reliability estimates, and factor correlations for the final model. All the items significantly load onto their specified factors. The composite omega shows that all the factors have satisfactory score reliability (ω_c > .80). The correlations between the latent factors show that the adjacent factors typically have a higher correlation than distal ones.

Table 5.

Standardized Factor Loadings, Score Reliability Estimates, and Factor Correlations for the Final Model.

Items/Factors	Amo	Exter	Intro	AM
21	.926***
22	.941***
23	.961***
24	.958***
17		.921***
18		.873***
19		.891***
20		.893***
13			.870***
14			.897***
15			.785***
16			.925***
3				.799***
5				.811***
8				.895***
9				.792***
ω_c	.97	.94	.93	.90
Exter	.738***
Intro	.222***	.418***
AM	−.035	.106*	.561***

Note. Amo = amotivation; Exter = external regulation; Intro = introjected regulation; AM = autonomous motivation; * = p < .05; *** = p < .001.

Table 6 shows the measurement invariance test across sex and athlete level for the final model. The final model fits men and women groups, the competitive and professional groups satisfactorily. The relatively small change in CFI and RMSEA values from less to more restrictive models indicate that configural, metric, scalar, and strict invariance was established across sex and athlete level.

Table 6.

Measurement Invariance Test Across Sex and Athlete Level for the Final Model.

Models	χ² (df)	p	CFI	TLI	RMSEA (90%CI)	ΔCFI	ΔRMSEA
Sex
Men (n = 269)	146.993 (98)	.001	.98	.98	.043 (.028–.057)	—	—
Women (n = 92)	157.482 (98)	<.001	.93	.91	.081 (.057–.104)	—	—
Configural invariance	303.766 (196)	<.001	.97	.96	.055 (.043–.067)	—	—
Metric invariance	318.375 (208)	<.001	.97	.97	.054 (.042–.066)	0	−.001
Scalar invariance	351.457 (220)	<.001	.96	.96	.058 (.046–.069)	−.01	+.004
Strict invariance	402.753 (236)	<.001	.96	.95	.063 (.052–.073)	0	+.005
Athlete level
Competitive (n = 129)	141.805 (98)	.003	.97	.96	.059 (.036–.079)	—	—
Professional (n = 232)	156.054 (98)	<.001	.97	.97	.051 (.035–.065)	—	—
Configural invariance	298.174 (196)	<.001	.97	.97	.054 (.041–.066)	—	—
Metric invariance	311.358 (208)	<.001	.97	.97	.052 (.040–.064)	0	−.002
Scalar invariance	336.329 (220)	<.001	.97	.97	.054 (.042–.065)	0	+.002
Strict invariance	363.210 (236)	<.001	.97	.97	.055 (.043–.065)	0	+.001

Table 7 shows the convergent evidence of validity of the final model. As expected, amotivation negatively predicted all the other covariates. External regulation and introjected regulation did not predict any of the covariates with the exception that external regulation positively predicted relatedness. Autonomous motivation positively predicted all the covariates. The final version of the translated Chinese BRSQ can be found in Appendix 1.

Table 7.

Standardized Regression Coefficients for Covariates Regressed on Types of Motivation.

Covariates	Amo	Exter	Intro	AM
Competence	−.152**	.098	.115	.687***
Autonomy-choice	−.141*	.094	.082	.710***
Autonomy-IPLOC	−.170**	.057	.097	.718***
Autonomy-volition	−.417***	−.099	.118	.476***
Relatedness	−.206***	.150**	.084	.681***

Note. IPLOC = internal perceived locus of causality; Amo = amotivation; Exter = external regulation; Intro = introjected regulation; AM = autonomous motivation; * = p < .05; ** = p < .01; *** = p < .001.

Discussion

The purpose of this study was to translate and evaluate the psychometric properties of the Chinese BRSQ-6. This study included 361 Chinese undergraduate sport athletes. Several alternative structural equation models revealed that the four-factor structure solution for the Chinese BRSQ (amotivation, external regulation, introjected regulation, and autonomous motivation) was optimal. This instrument is hence named Chinese BRSQ-4. Following the elimination of some items under the autonomous motivation factor, the modified Chinese BRSQ-4 demonstrated adequate construct validity, score reliability, strict invariance across sex and athlete level, and adequate convergent evidence of validity.

Our most salient finding in this study was that an autonomous motivation factor was sufficient to explain most item covariances under the identified regulation, integrated regulation, and intrinsic motivation subscales. In other words, the conceptual distinction of the identified regulation, integrated regulation, and intrinsic motivation should be deemed redundant because of their psychometric similarities with one another. Our factor structure for the Chinese BRSQ-4 is similar to the original BRSQ study that found an exceptionally high correlation between identified regulation and integrated regulation (Lonsdale et al., 2008). Furthermore, our result precisely duplicated the finding of the Chinese SMS-II which also found the identified regulation, integrated regulation, and intrinsic motivation subscales to be substantially correlated among university sport athletes (Li et al., 2018). Since the Chinese BRSQ-4 and Chinese SMS-II used different item pools, these identical findings are unlikely to have been the result of item-level misspecification. Rather, the unidimensional characteristic of the autonomous motivation subscale among Chinese university students should be viewed as robust and independent of the selection of measuring instrument.

Although none of the following BRSQ studies replicated the unidimensional finding of the autonomous motivation, previous researchers who explored the psychometric features of the Behavioral Regulation in Exercise Questionnaire (BREQ) revealed that a general autonomous motivation score should be calculated for the Chinese BREQ-2 (Chen et al., 2018) and Chinese BREQ-3 (Luo et al., 2022). Similar to BRSQ, BREQ-2 and BREQ-3 (two revised versions of BREQ) were developed, based on SDT, in an effort to evaluate motivation in an exercise context. Taken together, these findings led to the conclusion that the lack of distinction between specific autonomous motivation factors was prevalent in both the Chinese sport and exercise settings. Potential explanations are that: (a) it is empirically inappropriate to divide autonomous motivation into specific motivation factors, as proposed by SDT, in the context of sport and exercise motivation for Chinese university students (i.e., this population conceptually perceives only a single autonomous motivation); and/or (b) the semantic nuances of the various autonomous motivations are difficult to convey in Chinese due to language constraints. Future research should investigate these possibilities to have a deeper comprehension of the unidimensionality of the autonomous sport and exercise motivation among Chinese university students.

Utilizing an array of reliability indices inherent to bi-factor modeling, we were able to determine that the subscale scores for identified regulation, integrated regulation, and intrinsic motivation lacked reliable information, thus favoring the adoption of a single autonomous motivation. Considering the literature’s predominant use of traditional confirmatory factor analysis for evaluating the BRSQ’s factor structure, practitioners and researchers in applied sport psychology should exercise caution when using the factor scores derived from the specific autonomous motivation factors in different language versions of the BRSQ. It is imperative that subsequent research investigates the disparities between models that either include or exclude controlled and autonomous motivation factors, in order to ascertain the most suitable factor solution for the BRSQ.

Instead of using latent factor scores which correct for measurement error, manifest factor scores (e.g., the scores calculated by summing or averaging the observed item scores) are commonly used in sport psychology research and practice. To compare manifest factor scores across groups, item residual variances, as well as factor loadings and item intercepts, should be constrained equal across groups (Marsh et al., 2013). To accommodate the use of the manifest factor scores for the purpose of group comparison, the present study tested and established strict measurement invariance for the Chinese BRSQ-4 across sex and athlete level. This result provided justification for researchers and practitioners to compare manifest factor scores of any of the motivation factors of the Chinese BRSQ-4 across sex and athlete level.

Limitations and Directions for Further Research

Several limitations of the present study must be acknowledged. First, although the degree of social desirability (i.e., participants providing answers they perceive to be viewed as positive by others) was reduced by notifying participants that their responses were anonymous, studies have highlighted the importance of incorporating social desirability scales into surveys like ours to ensure accurate interpretation of individual test outcomes (Perinelli & Gremigni, 2016; Schumm, 2015). The primary aim of our research was to assess the psychometrics of an existing tool (BRSQ) for its suitability with Chinese participants. Nevertheless, we highly encourage future researchers to further develop both the original instrument and its Chinese adaptation to investigate the degree to which respondents are influenced by social desirability when providing their responses. For instance, student-athletes might portray overly positive attitudes towards their sports to appease teachers or coaches when responding to the BRSQ. To mitigate this bias, we suggest the inclusion of a specialized social desirability scale for athletes. This scale could feature contextually relevant items such as: “I worry that admitting discouragement in my sport might cause issues with authority figures” or “I feel compelled to show my sports attitudes positively.” These items, answered with a simple yes or no and more yes responses indicating higher social desirability, can help reduce survey response bias. For data analysis, the frequency of yes responses can serve as a covariate, or separate analyses can be conducted for groups with varying levels of social desirability. Second, it is possible that the basic assumption of independence of observations for CFA models might be violated due to the restricted participant sample (i.e., participants may know each other personally). If participants completed the online survey together in person, their answers to the survey questions may have been affected by one another. Finally, the sample sizes for men and women in the measurement invariance test across sex were uneven. The sample size for men’s group was nearly three times that of women’s group. As the chi-square statistics used in the measurement invariance test were weighted by sample size, an imbalanced sample size may influence the results (Yoon & Lai, 2018). The higher sample size of the men’s group contributed more to the determination of the final chi-square values, potentially reducing the effect of measurement non-invariance on the women’s group.

Conclusion

The present study translated and investigated the psychometric properties of the Chinese BRSQ-6. Our findings suggested that four factor scores should be calculated for the Chinese BRSQ, including amotivation, external regulation, introjected regulation, and autonomous motivation (item 3, 5, 8, and 9). We named this modified instrument Chinese BRSQ-4. The Chinese BRSQ-4 exhibited satisfactory construct validity, convergent validity, and score reliability. Its manifest subscale scores permit comparisons based on sex and athlete level. This instrument is a valuable tool for sport scholars and practitioners in China to assess the sport motivation of university student athletes.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Yan Luo

Data Availability Statement

Data available on request from the authors.

Appendix

中文版运动自我决定量表 (BRSQ-4).

Chinese	English
起始问题: 我参加我的运动项目…	Stem: I Participate in my sport…	1 (完全不正确)	2	3	4 (有些正确)	5	6	7 (非常正确)
		1 (not at all true)	2	3	4 (somewhat true)	5	6	7 (very true)
1.因为它很好玩	1.Because it’s fun
2.因为它是我的一部分	2.Because it’s a part of who I am
3.因为它可以让我以符合我的价值观的方式生活	3.Because it allows me to live in a way that is true to my values
4.因为运动的好处对我很重要	4.Because the benefits of sport are important to me
5.因为如果我放弃我会感到羞愧	5.Because I would feel ashamed if I quit
6.因为如果我放弃我会觉得自己是个失败者	6.Because I would feel like a failure if I quit
7.因为我感到有义务去继续	7.Because I feel obligated to continue
8.因为如果我放弃我会感到内疚	8.Because I would feel guilty if I quit
9.因为如果我不参与其他人将会对我不满意	9.Because if I don’t other people will not be pleased with me
10.因为我感觉到来自其他人的压力	10.Because I feel pressure from other people to play
11.因为别人一直催着我去参加	11.Because people push me to play
12.使那些想让我进行这项运动的人满意	12.To satisfy people who want me to play
13.但我不知道参与的意义是什么	13.But I wonder what’s the point
14.但我质疑为什么我要继续	14.But I question why I continue
15.但我不再清楚参与这项运动的原因了	15.But the reasons why are not clear to me anymore
16.但我质疑为什么我要让自己经历这些	16.But I question why I am putting myself through this

Calculate the average scores for the following subscales.

Amotivation (13,14,15,16)

External Regulation (9,10,11,12)

Introjected Regulation (5,6,7,8)

Autonomous Motivation (1,2,3,4).

Author Biographies

Yan Luo, Ph.D., serves as an Assistant Professor in the Department of Physical Education at Shanghai Jiao Tong University, Shanghai, China. He earned his Ph.D. in Physical Education from Springfield College, Massachusetts, USA. and pursued post-doctoral research in the Department of Kinesiology and Community Health at the University of Illinois at Urbana-Champaign. His research adopts an interdisciplinary approach, integrating quantitative techniques from psychology, epidemiology, and medicine into the study of sports and exercise. Additionally, he concentrates on adapting psychological questionnaires for cross-cultural applications.

Kathleen T. Mellano, Ph.D., serves as an Assistant Professor in the Department of Exercise Science and Athletic Training at Springfield College, Massachusetts, USA. She earned her doctorate in Kinesiology at Michigan State University, Michigan, USA. Her research revolves around social and motivational processes in youth sport with particular attention to relationships among teammates and other key agents. She has a particular interest in the influence of dyadic and group-level constructs in shaping the quality of athlete experiences.

Elizabeth M. Mullin (she/they) is an Associate Professor and department chair of Exercise Science and Athletic Training at Springfield College. She encourages her graduate students to think and write critically about what data do and do not say. In her scholarship, she explores how gender and sexual orientation impact experiences in sport. She is a fellow for SHAPE America and the Association for Applied Sport Psychology. Mullin was a fellow of the American Kinesiology Association Leadership Institute and is an alumnae of HERS Weekend Leadership Institute.

Juan Zhong, Ph.D., is an Assistant Professor in the Department of Psychology at Springfield College, Massachusetts, USA. She earned her Ph.D. in Developmental Psychology from Clark University, Massachusetts, USA. The key question guiding her research is how people experience adulthood in different cultural contexts by using mixed methods.

Yi Zhou, D.Ed., is currently an Assistant Professor in Sports Training School at Chengdu Sport University, Chengdu, China. He obtained his doctorate from Beijing Sport University and was a visiting scholar at Springfield College in the United States. His study is centered on teaching methods and training in physical education.

Yanru Sha, M.Ed., is an Assistant Professor in the Institute of Physical Education at Ningxia University, Yinchuan, China. She received her master’s degree in Physical Education from Xi’an Physical Education University. Her research focuses on teaching and training in physical education.

Yingqiu Zhang, D.Ed., is a Professor in Sports Coaching College at Beijing Sport University, Beijing, China. She obtained her doctorate from Beijing Sport University. Her study concentrates on instructional and training approaches in racket sports programs.

Shenyue Luo, M.Ed., is currently an Assistant Professor in the Department of Sports at the University of Electronic Science and Technology of China, Chengdu, China. She obtained her master's degree in Physical Education from Beijing Sport University. Her research focuses on applying the research methods of sports training and biomechanics in the field of sports science.

Nan Guo, M.Ed., is currently an Assistant Professor in Sports Coaching College at Beijing Sport University, Beijing, China. He obtained his master's degree in Athletic Training from Beijing Sport University. His study centers on the techniques used for training in table tennis.

References

Akaike

(1998). Likelihood and the bayes procedure (pp. 309–332). Springer.

Amemiya

Sakairi

(2019). The effects of passion and mindfulness on the intrinsic motivation of Japanese athletes. Personality and Individual Differences, 142, 132–138. https://doi.org/10.1016/j.paid.2019.01.006

Barcza-Renner

Eklund

R. C.

Morin

A. J. S.

Habeeb

C. M.

(2016). Controlling coaching behaviors and athlete burnout: Investigating the mediating roles of perfectionism and motivation. Journal of Sport & Exercise Psychology, 38(1), 30–44. https://doi.org/10.1123/jsep.2015-0059

Beaton

D. E.

Bombardier

Guillemin

Ferraz

M. B.

(2000). Guidelines for the process of cross-cultural adaptation of self-report measures. Spine, 25(24), 3186–3191. https://doi.org/10.1097/00007632-200012150-00014

Bentler

P. M.

(1990). On the fit of models to covariances and methodology to the Bulletin. Psychological Bulletin, 112(3), 400–404. https://doi.org/10.1037/0033-2909.112.3.400

Buonamano

Cei

Mussino

(1995). Participation motivation in Italian youth sport. The Sport Psychologist, 9(3), 265–281. https://doi.org/10.1123/tsp.9.3.265

Çetinkaya

Mutluer

(2018). Turkish adaptation of behavioral regulations in sports questionnaire and reviewing psychometry properties: Validation and reliability study. International Journal of Higher Education, 7(5), 185–193. https://doi.org/10.5430/ijhe.v7n5p185

Chan

D. K. C.

Dimmock

J. A.

Donovan

R. J.

Hardcastle

Lentillon-Kaestner

Hagger

M. S.

(2015). Self-determined motivation in sport predicts anti-doping motivation and intention: A perspective from the trans-contextual model. Journal of Science and Medicine in Sport, 18(3), 315–322. https://doi.org/10.1016/j.jsams.2014.04.001

Chantal

Guay

DobrevaMartinova

Vallerand

(1996). Motivation and elite performance: An exploratory investigation with Bulgarian athletes. International Journal of Sport Psychology, 27(2), 173–182.

10.

Chen

F. F.

West

S. G.

Sousa

K. H.

(2006). A comparison of bifactor and second-order models of quality of life. Multivariate Behavioral Research, 41(2), 189–225. https://doi.org/10.1207/s15327906mbr4102_5

11.

Chen

Dai

Liu

J. L.

(2018). An integrative perspective of validating a simplified Chinese version Behavioral Regulation in Exercise Questionnaire-2. Measurement in Physical Education and Exercise Science, 22(3), 213–223. https://doi.org/10.1080/1091367x.2017.1417127

12.

Chen

Jin

Lau

K. O.

Chen

(2007). Motivation of sport participation in elite athletes with physical disabilities in mainland China. Research Quarterly for Exercise & Sport, 78(1), A96–A97.

13.

Cheung

G. W.

Rensvold

R. B.

(2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 9(2), 233–255. https://doi.org/10.1207/s15328007sem0902_5

14.

Deci

E. L.

Ryan

R. M.

(2000). The “What” and “Why” of goal pursuits: Human needs and the self-determination of behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/s15327965pli1104_01

15.

Deci

E. L.

Ryan

R. M.

(1986). Intrinsic motivation and self-determination in human behavior. Plenum.

16.

Deci

E. L.

Ryan

R. M.

(2008). “Facilitating optimal motivation and psychological well-being across life’s domains”: Correction to Deci and Ryan (2008). Canadian Psychology/Psychologie Canadienne, 49(3), 262. https://doi.org/10.1037/0708-5591.49.3.262

17.

Farrell

R. J.

Crocker

P. R. E.

McDonough

M. H.

Sedgwick

W. A.

(2004). The driving force: Motivation in special Olympians. Adapted Physical Activity Quarterly, 21(2), 153–166. https://doi.org/10.1123/apaq.21.2.153

18.

Fenton

S. A. M.

Duda

J. L.

Barrett

(2016). Optimising physical activity engagement during youth sport: A self-determination theory approach. Journal of Sports Sciences, 34(19), 1874–1884. https://doi.org/10.1080/02640414.2016.1142104

19.

Finney

S. J.

DiStefano

(2006). Non-normal and categorical data in structural equation modeling. Structural Equation Modeling: A Second Course, 10(6), 269–314.

20.

García Calvo

Cervelló

Jiménez

Iglesias

Moreno Murcia

J. A.

(2010). Using Self-determination Theory to explain sport persistence and dropout in adolescent athletes. Spanish Journal of Psychology, 13(2), 677–684. https://doi.org/10.1017/s1138741600002341

21.

Gignac

G. E.

(2016). The higher-order model imposes a proportionality constraint: That is why the bifactor model tends to fit better. Intelligence, 55, 57–68. https://doi.org/10.1016/j.intell.2016.01.006

22.

Hancox

J. E.

Quested

Viladrich

Duda

J. L.

(2015). Examination of the internal structure of the behavioural regulation in sport questionnaire among dancers. International Journal of Sport and Exercise Psychology, 13(4), 382–397. https://doi.org/10.1080/1612197x.2014.999347

23.

Bentler

P. M.

(1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55. https://doi.org/10.1080/10705519909540118

24.

Jackson

S. A.

Ford

S. K.

Kimiecik

J. C.

Marsh

H. W.

(1998). Psychological correlates of flow in sport. Journal of Sport & Exercise Psychology, 20(4), 358–378. https://doi.org/10.1123/jsep.20.4.358

25.

Jordalen

Lemyre

P.-N.

Durand-Bush

(2016). Exhaustion experiences in junior athletes: The importance of motivation and self-control competencies. Frontiers in Psychology, 7, 1867. https://doi.org/10.3389/fpsyg.2016.01867

26.

Lemyre

P.-N.

Roberts

G. C.

Stray-Gundersen

(2007). Motivation, overtraining, and burnout: Can self-determined motivation predict overtraining and burnout in elite athletes? European Journal of Sport Science, 7(2), 115–126. https://doi.org/10.1080/17461390701302607

27.

Kawabata

Zhang

(2018). Validity and reliability of the sport motivation scale-II for Chinese athletes. International Journal of Sport and Exercise Psychology, 16(1), 51–64. https://doi.org/10.1080/1612197X.2016.1153130

28.

Harmer

(1996). Testing the simplex assumption underlying the sport motivation scale: A structural equation modeling analysis. Research Quarterly for Exercise & Sport, 67(4), 396–405. https://doi.org/10.1080/02701367.1996.10607971

29.

Lonsdale

Hodge

Hargreaves

E. A.

J. Y. Y.

(2014). Comparing sport motivation scales: A response to Pelletier. Psychology of Sport and Exercise, 15(5), 446–452. https://doi.org/10.1016/j.psychsport.2014.03.006

30.

Lonsdale

Hodge

Rose

E. A.

(2008). The behavioral regulation in sport questionnaire (BRSQ): Instrument development and initial validity evidence. Journal of Sport & Exercise Psychology, 30(3), 323–355. https://doi.org/10.1123/jsep.30.3.323

31.

Luo

Mullin

E. M.

Mellano

K. T.

Sha

Wang

(2022). Examining the psychometric properties of the Chinese behavioral regulation in exercise questionnaire-3: A bi-factor approach. PLoS One, 17(3), Article e0265004. https://doi.org/10.1371/journal.pone.0265004

32.

Madigan

D. J.

Stoeber

Passfield

(2016). Motivation mediates the perfectionism burnout relationship: A three-wave longitudinal study with junior athletes. Journal of Sport & Exercise Psychology, 38(4), 341–354. https://doi.org/10.1123/jsep.2015-0238

33.

Mallett

Kawabata

Newcombe

Otero-Forero

Jackson

(2007). Sport motivation scale-6 (SMS-6): A revised six-factor sport motivation scale. Psychology of Sport and Exercise, 8(5), 600–614. https://doi.org/10.1016/j.psychsport.2006.12.005

34.

Marsh

H. W.

Nagengast

Morin

A. J. S.

(2013). Measurement invariance of big-five factors over the life span: ESEM tests of gender, age, plasticity, maturity, and la dolce vita effects. Developmental Psychology, 49(6), 1194–1218. https://doi.org/10.1037/a0026913

35.

McLoughlin

Weisman Fecske

Castaneda

Gwin

Graber

(2017). Sport participation for elite athletes with physical disabilities: Motivations, barriers, and facilitators. Adapted Physical Activity Quarterly: Adapted Physical Activity Quarterly, 34(4), 421–441. https://doi.org/10.1123/apaq.2016-0127

36.

Monteiro

Moutao

J. M.

Cid

(2018). Validation of the behavioral regulation sport questionnaire in Portuguese athletes. Revista de Psicologia del Deporte, 27(1), 145–153.

37.

Nájera Catalán

H. E.

(2019). Reliability, population classification and weighting in multidimensional poverty measurement: A Monte Carlo study. Social Indicators Research, 142(3), 887–910. https://doi.org/10.1007/s11205-018-1950-z

38.

J. Y. Y.

Lonsdale

Hodge

(2011). The basic needs satisfaction in sport scale (BNSSS): Instrument development and initial validity evidence. Psychology of Sport and Exercise, 12(3), 257–264. https://doi.org/10.1016/j.psychsport.2010.10.006

39.

Núñez

J. L.

Martín-Albo

Navarro

J. G.

González

V. M.

(2006). Preliminary validation of a Spanish version of the sport motivation scale. Perceptual and Motor Skills, 102(3), 919–930. https://doi.org/10.2466/pms.102.3.919-930

40.

Pelletier

L. G.

Dion

S. C.

(2007). An examination of general and specific motivational mechanisms for the relations between body dissatisfaction and eating behaviors. Journal of Social and Clinical Psychology, 26(3), 303–333. https://doi.org/10.1521/jscp.2007.26.3.303

41.

Pelletier

L. G.

Rocchi

M. A.

Vallerand

R. J.

Deci

E. L.

Ryan

R. M.

(2013). Validation of the revised sport motivation scale (SMS-II). Psychology of Sport and Exercise, 14(3), 329–341. https://doi.org/10.1016/j.psychsport.2012.12.002

42.

Pelletier

L. G.

Tuson

K. M.

Fortier

M. S.

Vallerand

R. J.

Briére

N. M.

Blais

M. R.

(1995). Toward a new measure of intrinsic motivation, extrinsic motivation, and amotivation in sports: The Sport Motivation Scale (SMS). Journal of Sport & Exercise Psychology, 17(1), 35–53. https://doi.org/10.1123/jsep.17.1.35

43.

Perinelli

Gremigni

(2016). Use of social desirability scales in clinical psychology: A systematic review. Journal of Clinical Psychology, 72(6), 534–551. https://doi.org/10.1002/jclp.22284

44.

Putnick

D. L.

Bornstein

M. H.

(2016). Measurement invariance conventions and reporting: The state of the art and future directions for psychological research. Developmental Review, 41, 71–90. https://doi.org/10.1016/j.dr.2016.06.004

45.

Raftery

A. E.

(1986). A note on Bayes factors for log‐linear contingency table models with vague prior information. Journal of the Royal Statistical Society: Series B, 48(2), 249–250. https://doi.org/10.1111/j.2517-6161.1986.tb01408.x

46.

Rodriguez

Reise

S. P.

Haviland

M. G.

(2016). Applying bifactor statistical indices in the evaluation of psychological measures. Journal of Personality Assessment, 98(3), 223–237. https://doi.org/10.1080/00223891.2015.1089249

47.

Sakamoto

Ishiguro

Kitagawa

(1986). Akaike information criterion statistics. D. Reidel.

48.

Schermelleh-engel

Moosbrugger

Müller

(2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of Psychological Research, 8(8), 23–74.

49.

Schumm

W. R.

(2015). Navigating treacherous waters—one researcher's 40 years of experience with controversial scientific research. Comprehensive Psychology, 4, 17. https://doi.org/10.2466/17.cp.4.24.-CP

50.

Smith

Tessier

Tzioumakis

Fabra

Quested

Appleton

Sarrazin

Papaioannou

Balaguer

Duda

J. L.

(2016). The relationship between observed and perceived assessments of the coach-created motivational environment and links to athlete motivation. Psychology of Sport and Exercise, 23, 51–63. https://doi.org/10.1016/j.psychsport.2015.11.001

51.

Steiger

J. H.

(1990). Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research, 25(2), 173–180. https://doi.org/10.1207/s15327906mbr2502_4

52.

Stucky

B. D.

Edelen

M. O.

(2014). Using hierarchical IRT models to create unidimensional measures from multidimensional data. Handbook of item response theory modeling. Routledge.

53.

Tucker

L. R.

Lewis

(1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38(1), 1–10. https://doi.org/10.1007/bf02291170

54.

Vallerand

R. J.

Losier

G. F.

(1999). An integrative analysis of intrinsic and extrinsic motivation in sport. Journal of Applied Sport Psychology, 11(1), 142–169. https://doi.org/10.1080/10413209908402956

55.

Vandenberg

R. J.

Lance

C. E.

(2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4–70. https://doi.org/10.1177/109442810031002

56.

Van de Schoot

Lugtig

Hox

(2012). A checklist for testing measurement invariance. European Journal of Developmental Psychology, 9(4), 486–492. https://doi.org/10.1080/17405629.2012.686740

57.

Vansteenkiste

Niemiec

C. P.

Soenens

(2010). The development of the five mini-theories of self-determination theory: An historical overview, emerging trends, and future directions. The decade ahead: Theoretical perspectives on motivation and achievement. Emerald Group Publishing Limited.

58.

Viladrich

Torregrosa

Cruz

(2011). Psychometric quality supporting the Spanish adaptation of the behavioral regulation in sport questionnaire. Psicothema, 23(4), 786–794.

59.

Vink

Raudsepp

Kais

(2015). Intrinsic motivation and individual deliberate practice are reciprocally related: Evidence from a longitudinal study of adolescent team sport athletes. Psychology of Sport and Exercise, 16, 1–6. https://doi.org/10.1016/j.psychsport.2014.08.012

60.

Warner

R. M.

(2012). Applied statistics: From bivariate through multivariate techniques. Sage Publications.

61.

Yoon

Lai

M. H. C.

(2018). Testing factorial invariance with unbalanced samples. Structural Equation Modeling: A Multidisciplinary Journal, 25(2), 201–213. https://doi.org/10.1080/10705511.2017.1387859

62.

Zahariadis

Tsorbatzoudis

Alexandris

(2006). Self-determination in sport commitment. Perceptual and Motor Skills, 102(2), 405–420. https://doi.org/10.2466/pms.102.2.405-420

63.

Zahariadis

P. N.

Tsorbatzoudis

Grouios

(2005). The Sport Motivation Scale for children: Preliminary analysis in physical education classes. Perceptual and Motor Skills, 101(1), 43–54. https://doi.org/10.2466/pms.101.1.43-54

64.

Zhong

Yuan

K.-H.

(2011). Bias and efficiency in structural equation modeling: Maximum likelihood versus robust methods. Multivariate Behavioral Research, 46(2), 229–265. https://doi.org/10.1080/00273171.2011.558736