Self-Concept Contributes to Winning Gold Medals: Causal Ordering of Self-Concept and Elite Swimming Performance

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1 JOURNAL OF SPORT & EXERCISE PSYCHOLOGY, 2005, 27, Human Kinetics Publishers, Inc. Self-Concept Contributes to Winning Gold Medals: Causal Ordering of Self-Concept and Elite Swimming Performance Herbert W. Marsh and Clark Perry University of Western Sydney Elite athlete self-concepts contributed to championship performances in two international swimming championships beyond that which could be explained by previous personal best (PPB) performances for 257 of the world s top swimmers from 30 countries. Responses to the Elite Swimmer Self-Description Questionnaire (ESSDQ) completed at the start of each championship (prior to competition) were psychometrically strong and resulted in a well-defined factor structure. Whereas championship performance was highly related to PPB performance (r =.90), structural equation models demonstrated that elite athlete self-concept also contributed significantly to the prediction of subsequent championship performance, explaining approximately 10% of the residual variance after controlling for PPB. For swimmers who competed in two events, results based on the first event were replicated in the second. The results have important theoretical, substantive, and practical implications for mentors and educators. Key Words: elite athlete self-concept, swimming championship performance Seligman and Csikszentmihalyi (2000), Vallerand et al. (2003), and many others have argued that there is a revolution sweeping psychology, one that emphasizes a positive psychology and focuses on how normal, healthy individuals can get the most from life. Consistent with this emphasis, a positive self-concept is valued as a desirable outcome in many disciplines of psychology such as sport/exercise, health, development, mental health, social psychology, personality, and educational psychology. In sport psychology, as is the case in many disciplines, self-concept is frequently posited as a mediating variable that facilitates the attainment of other desired outcomes such as physical skills, health-related physical fitness, physical activity, and exercise adherence (Fox & Corbin, 1989; Marsh, 1997, 2002; Sonstroem, 1978) in non-elite settings, and improved performance in elite sports. The rationale behind this expectation is that individuals who perceive themselves to be more effective, confident, and able can accomplish more than individuals with a less positive self-perception elite swimmers in this study and are more likely to pursue and achieve desirable outcomes in that domain than equally com- The authors are with the SELF Research Centre, University of Western Sydney, Bankstown Campus, Penrith South DC, New South Wales 1797, Australia. 71

2 72 / Marsh and Perry petent individuals who have a less positive self-concept (I believe, therefore I am). We begin by briefly reviewing an extensive body of literature that supports this contention in educational settings, then test its generalizablity to elite swimming. The Causal Ordering of Self-Concept and Achievement What is Self-Concept? Interest in self-concept has a long and controversial history and is one of the oldest areas of research in the social sciences. In the last 25 years particularly, there has been a resurgence in self-concept research, reinforced in part by the classic review article by Shavelson, Hubner, and Stanton (1976; also see Marsh & Hattie, 1996). Shavelson et al. integrated features of various definitions of self-concept to form their definition of self-concept as a person s self-perceptions that are formed through experience with and interpretations of one s environment. These self-perceptions are influenced especially by evaluations by significant others, reinforcements, and attributions for one s own behavior, and influence future behavior. Consistent with this perspective, Shavelson et al. noted that self-concept is important both as an outcome and as a mediating variable that helps to explain other outcomes. Shavelson et al. (1976) emphasized that self-concept is multifaceted and hierarchically organized, with perceptions of personal behavior in specific situations at the base of the hierarchy, inferences about self in broader domains (e.g., social, physical, and academic) at the middle of the hierarchy, and a global, general self-concept at the apex. Consistent with a large amount of subsequent research in support of the Shavelson et al. model, Marsh argued for the importance of a multidimensional perspective of self-concept in which researchers focused on specific components of self-concept most logically related to goals of particular research study rather than relying on a unidimensional approach that only considered a single global self-concept scale, typically referred to as self-esteem. Fortunately, in sport and exercise research (Fox & Corbin, 1989; Marsh, 1997, 2002; Sonstroem, 1978) there is broad acceptance of this multidimensional perspective in which researchers focus on physical self-concept and particular components of physical self-concept in addition to, or instead of, measures of self-esteem. Self-concept incorporates self-perceptions of self-confidence and competency, but differs somewhat from other self-perceptions such as self-efficacy, depending on how the terms are operationalized. Although self-efficacy measures typically refer to a more narrowly defined domain than self-concept measures, Marsh (1993; also see Bong & Skaalvik, 2003) noted that this in not an inherent difference; selfconcept can be defined in relation to very specific domains and self-efficacy can be defined more globally. Whereas self-concept represents one s general perceptions of the self in given domains of functioning, self-efficacy represents individuals expectations and convictions of what they can accomplish in given situations. For example, the expectation that one can high-jump 6 feet in a particular situation is an efficacy judgment, not a judgment of whether one is competent in high-jumping in general or whether succeeding at this event is a worthwhile accomplishment relative to an athlete s personal standards of what is good performance. Thus, Bong and Skaalvik (2003) emphasized that the separation of competence and affect distinguishes self-concept from self-efficacy. In support of the importance of this distinction, Marsh (1993) argued that

3 Self-Concept and Elite Swimming / 73 the self-perceived worthiness of performance expectations in relation to personal and external standards that are implicated in self-concept responses are likely to contribute to ongoing and future performance beyond the non-evaluative description of what one is able to accomplish. Hence, if one accomplishes something and feels positive about having accomplished something worthwhile, one is more likely to pursue the activity than if the accomplishment is not accompanied by a positive feeling or sense of having accomplished something worthwhile. However, these theoretical distinctions between self-efficacy and self-concept may not always exist in measures that are given the label of self-concept and self-efficacy (see Marsh, 1994b, for discussion of jingle-jangle fallacies about the labels given to the same or different constructs). Theoretical Models of the Causal Ordering of Self-Concept and Achievement Do changes in self-concept lead to changes in subsequent performance? The causal ordering of self-concept and performance is perhaps the most vexing question in self-concept research. This critical question has important theoretical and practical implications and has been the focus of considerable research, particularly in educational settings. Byrne (1984) emphasized that much of the interest in the academic self-concept/achievement relationship stems from the belief that academic self-concept has motivational properties such that changes in academic self-concept will lead to changes in subsequent academic achievement. Calsyn and Kenny (1977) contrasted self-enhancement and skill development models of this relationship. The self-enhancement model posits self-concept as a primary determinant of academic achievement (i.e., self-concept > achievement) and would support self-concept enhancement interventions. In contrast, the skill development model implies that academic self-concept emerges principally as a consequence of academic achievement (i.e., achievement > self-concept) so that the best way to enhance academic self-concept would be to develop stronger academic skills. Due largely to limitations in statistical techniques for testing these models in the 1980s, researchers argued for either-or conclusions. In a review and critique of this research, Marsh (1990a, 1990b, 1993; Marsh, Byrne, & Yeung, 1999) argued that much of this research was methodologically unsound and inconsistent with self-concept theory. He emphasized that according to both common sense and theory, prior academic achievement was one determinant of academic self-concept. Hence the critical question was whether there also exists a significant path from prior academic self-concept to subsequent achievement, regardless of whether or not this path was larger than the path from prior academic achievement to subsequent academic self-concept. Marsh (1990a; Marsh et al., 1999) further argued that a more realistic compromise between the self-enhancement and skill-development models was a reciprocal effects model in which prior self-concept affects subsequent achievement, and prior achievement affects subsequent self-concept. A growing body of research reviewed by Marsh et al. (1999) has established support for the reciprocal effects model of a relationship between academic self-concept and academic achievement. In a recent meta-analysis of relevant research, Valentine, DuBois, and Cooper (2004) also concluded that there was clear support for predictions based on the reciprocal effects model over those derived from self-enhancement and skill development models.

4 74 / Marsh and Perry Generalizability to the Physical Domain A large body of research in support of the reciprocal effects model of the causal ordering of self-concept and performance is based on academic self-concept and academic achievement in traditional school subjects. However, there apparently are few applications of this model to a physical context with appropriate measures of physical self-concept and physical outcomes. Reflecting historical trends in selfconcept research more generally, self-concept instruments used in early physical education and sport/exercise research focused on global self-esteem (Marsh, 1997, 2002). More recently, however, there has been a stronger emphasis on physical selfconcept measures designed specifically for physical education, sport, and exercise settings (e.g., Fox & Corbin, 1989; Marsh, 1997, 2002), providing clear evidence for their convergent and discriminant validity in relation to other self-concept domains (e.g., academic) and to different physical outcome measures. This follows more general trends in sport/exercise psychology for researchers to develop sport/exercise-specific instruments and to evaluate them within a construct validity framework. Thus for example, Gill, Dzewaltowski, and Deeter (1988) argued that Within sport psychology the most promising work on individual differences involves the development and use of sport-specific constructs and measures (pp ) and urged the construction of multidimensional instruments based on theory, followed by item and reliability analysis, exploratory and confirmatory factor analysis, tests of convergent and divergent validity, validation in relation to external criteria, and application in research and practice. This concern has important implications for sport/exercise research, but it also has important theoretical implications for the generalizability of the reciprocal effects model and self-concept theory. Following from this emphasis on domain specificity of physical self-concept, we summarize the results from two recent studies that apparently represent the first studies to test the generalizability of the reciprocal effects model to the physical domain. Gymnastics Self-Concept and Achievement in Physical Education Classes Marsh, Chanal, and Sarrazin (2004) pursued tests of the reciprocal effects, self-enhancement, and skill development models in relation to physical self-concept and performance skills in physical education classes. More specifically, they evaluated predictions about the effects of T1 gymnastics self-concept and T1 gymnastics performance skills collected at the start of a gymnastics training program on T2 gymnastics self-concept and T2 gymnastics performance skills collected at the end of the 10-week program conducted as part of normal physical education classes. Achievement was based on videotapes of each student s performance on a standardized gymnastics performance test that was evaluated independently by each of three expert judges. Structural equation models based on responses by 376 junior high school students collected at the start (T1) and end (T2) of a gymnastics training program supported a reciprocal effects model. The effect of T1 gymnastics self-concept on T2 gymnastics achievement (.20) and the effect of T1 gymnastics achievement on T2 gymnastics self-concept (.14) were both highly significant. In summary, gymnastics self-concept and gymnastics performance were both determinants and consequences of each other. The results also provide further evidence in favor of

5 Self-Concept and Elite Swimming / 75 the multidimensional perspective of self-concept and the generalizability of the reciprocal effects model to sport/exercise settings. Physical Self-Concept and Physical Activity Associated With Physical Education Classes As emphasized by Hagger, Chatzisarantis, Culverhouse, and Biddle (2003), one aim of physical education in school is to get students to participate in healthrelated physical activity outside of school and to develop lifelong healthy lifestyles. Although physical education teachers and programs are in a unique position to pursue this aim, there is little research on how effective they are at accomplishing it. In order to address these issues, Marsh, Papaioannou, and Theodorakis (2004) adapted the reciprocal effects model in a study of the causal ordering of physical self-concept and exercise behavior. Based on a large sample of Greek physical education classes (2,786 students, 200 classes, 67 teachers) collected early (T1) and late (T2) in the school year, analyses supported a reciprocal effects model in which prior (T1) physical self-concept and exercise behavior both influence subsequent (T2) physical self-concept and exercise behavior. Consistent with the predictions from the reciprocal effects model, the effect of T1 physical self-concept on T2 exercise behavior (.17) and the effect of T1 exercise behavior on T2 physical self-concept paths (.10) were both highly significant. Extended models that included gender and age showed that for both T2 physical self-concept and exercise behavior, girls had systematically lower scores than boys, and the scores declined with age. There were, however, no significant age gender interactions. Although the pattern of results in support of the reciprocal effects models was still evident (all paths are statistically significant), the sizes of these effects were somewhat smaller when controlling for age and gender. The Present Study: Generalizability to Championship Performances in Elite Swimming Support for the benefits of a positive self-concept on subsequent performance and achievement, as reviewed by Marsh et al. (1999) and Valentine et al. (2004), is based substantially on the effects of academic self-concept on school performance and achievement. Recent physical education research (Marsh, Chanal, & Sarrazin, 2004; Marsh, Papaioannou, & Theodorakis, 2004) provides an important extension of this research to a physical context in which the focus is on physical components of self-concept and desirable physical outcomes. Demonstration of the generalizability of support for predictions based on academic self-concept and achievement has important theoretical implications for self-concept research as well as substantive and policy implications for physical education. Nevertheless, this more recent research into physical self-concept, like most of the research in the Marsh et al. and the Valentine et al. reviews, is based on responses by general populations of students in school settings. In the present study we extended this research to test the causal ordering of self-concept and performance of a large sample of many of the best swimmers in the world competing at international swimming championships. For purposes of this study, we modified the Elite Athlete Self Description Questionnaire (EASDQ) instrument to reflect elite swimming (called the ESSDQ). In collaboration with the Australian Institute of Sport and Australian Swimming,

6 76 / Marsh and Perry we measured elite swimming self-concepts of participants in the Pan Pacific swimming championships in Australia and the World Short Course Championships in Greece. Top swimmers (N = 257) from 30 countries completed this instrument on the first day for each championship prior to actually competing in any events. Also available for all participants were PPBs in each of their events. Following from the reciprocal effects model, we predicted a priori that elite swimmer self-concept would contribute to subsequent championship performance even after controlling for the substantial effects of PPB performances. Participants and Procedures Methods Participants were 257 elite swimmers from 30 nations participating at the Pan Pacific Championships (Sydney, Australia, August 1999) and the 5th World Short Course Championships (Athens, Greece, March 2000). Countries represented and the number of swimmers from each country were: Algeria (1), Australia (67), Brazil (1), Bulgaria (1), Canada (17), China (4), Chinese Taipei (14), Costa Rica (2), Cuba (2), Denmark (3), Fiji (2), Finland (1), Germany (5), Great Britain (14), Greece (13), Hong Kong (8), Italy (4), Japan (37), Malaysia (4), New Zealand (19), Nigeria (1), Northern Marianas (1), Norway (3), Poland (4), Seychelles (2), Slovakia (6), Slovenia (2), South Africa (15), Spain (2), Switzerland (2). Swimmers were 14 to 35 years of age (M = 20.8, SD = 3.6) and were about equally divided in terms of gender (53% males). No swimmer was included in both samples. Any swimmer included in the first sample was not asked to participate as part of the second sample, and so there was no overlap in swimmers in the two samples. Prior to the competition, national swimming federations were given an outline of the project and approval was sought for participation. Swimmers were sought from all performance levels, as long as they had achieved the qualifying time for the respective championships. Upon arrival of each national swimming team that had agreed to participate, a cohort of researchers arranged with officials how best to distribute the Elite Swimmer Self Description Questionnaire (ESSDQ) to athletes from their country. Athletes were given an introductory letter explaining the purpose of the study and an ESSDQ instrument was completed prior to the first event. Because we only approached swimmers whose national swimming team had already agreed to participate in the study, nearly all swimmers who were approached agreed to participate. Swimmers identified their preferred events (up to four) within the current competition, completed the ESSDQ in relation to each event, and put materials into sealed envelopes that were returned to researchers. Measures In the design of the original EASDQ, overall performance by elite athletes was hypothesized to be a function of skill levels, body suitability, aerobic fitness, anaerobic fitness, and mental competence. Based on this theoretical model, Marsh and colleagues (Marsh, Hey, Johnson, & Perry, 1997; Marsh, Hey, Roche, & Perry, 1997) developed the EASDQ to measure these six factors the five specific factors and one global factor (overall performance). For each scale they developed a pool of items that was then evaluated by sport psychology staff at the Australian Institute of Sport for their suitability for elite athletes. Pilot studies were conducted to select the best items to represent each factor. A compromise between brevity and

7 Self-Concept and Elite Swimming / 77 psychometric soundness was achieved, with acceptable levels of reliability (e.g., all scales having reliability estimates of at least.8) based on scales having a relatively small number of items. In his reviews, Marsh (1997, 2002) indicated that EASDQ responses were reliable and had a well-defined factor structure as shown by CFA. The ESSDQ used in the present investigation (see Appendix) is a modified version of the EASDQ in which the wording of the items was altered slightly to refer to elite swimmers rather than elite athletes in general. As with the original version, participants responded to the items using a 6- point true-false response scale. Although participants were asked to complete the ESSDQ for up to four events, most analyses are based on responses to only the first event (N = 257 swimmers) or, in the final set of analyses, for swimmers who had responses for two events (N = 216 swimmers). Whereas most elite swimmers were able to read the English version of the instrument, the ESSDQ was also translated into Spanish, German, Italian, Korean, Japanese, and Chinese. In each case a professional translator translated the EASDQ and a native speaking psychologist then checked the translation. Also, nearly all of the athletes were reasonably fluent in English and they had access to both English and native-language versions of the instrument. In addition, when the EASDQ was administered, there was at least one person (typically a sport psychologist from the swimmer s country) who spoke both English and the native language who could answer questions from non-englishspeaking participants. Because the ESSDQ is so similar to the original instrument, we expected the good psychometric strengths based on the original EASDQ to generalize to the ESSDQ. In support of these expectations, preliminary analyses indicated that coefficient alpha estimates of reliability were greater than.9 for all six scales based on the new ESSDQ for the total sample as well as for responses by men and women considered separately (see Appendix). A more thorough evaluation of the psychometric properties of the ESSDQ is presented as part of the present study. Swimming performance was represented by an international point score (IPS) so as to provide comparable performance measures across different events. The IPS is an internationally recognized standard, determined by averaging the five fastest all-time performances in a particular event and setting that time to a standard of 1,000 points. The IPS system scores events with values from 0 to 1,100 points, more points for world-class performances (typically 1,000 or more) and fewer points for slower performances. The IPS charts are revised yearly, allowing for comparisons among various events, swimmers of different sex, age, and so forth. We computed IPS scores for PPB performances by each swimmer prior to the championship as well as his or her subsequent championship performances (the best score recorded by each swimmer at the championship in each event). The events selected, and the number of athletes selecting each as their best event (i.e., first event in the present study) were: 50m free (22), 100m free (17), 200m free (22), 400m free (11), 800m free (9), 1500m free (9), 100m back (20), 200m back (23), 100m breast (19), 200m breast (22), 100m fly (21), 200m fly (18), 200m individual medley (11), 400m individual medley (18), 50 breast (3), 50 back (6), 50 fly (4), and 100 individual medley (2). Statistical Analyses CFAs and SEMs were conducted with LISREL (Version 8.54) using maximum likelihood estimation (for further discussion see Bollen, 1989; Byrne, 1998; Jöreskog & Sörbom, 1996). Following Marsh, Balla, and Hau (1996; Marsh, Balla,

8 78 / Marsh and Perry & McDonald, 1988), we considered the Tucker-Lewis index (TLI), the relative noncentrality index (RNI), and the root mean square error of approximation (RMSEA) to evaluate goodness of fit as well as presenting the Normal Theory χ 2 test statistic (the default in LISREL) and an evaluation of parameter estimates. The TLI and RNI vary along a 0-to-1 continuum in which values greater than.90 and.95 are typically taken to reflect acceptable and excellent fits to the data. RMSEA values of less than.05 and.08 are taken to reflect a close fit and a reasonable fit. There was no missing data for swimming performances and little missing data for responses to the ESSDQ (less than 0.1% missing responses). Although missing data was not an important problem, we used the Expectation Maximization Algorithm, a widely recommended approach to imputation for missing data, as operationalized in SPSS (Version 11.5). First-Order (FO) and Higher-Order (HO) Models. A critical aim of this study was to evaluate whether the a priori 6-factor model is able to fit the data and the size of factor correlations. Also important was the question of whether or not correlations among ESSDQ factors could be explained by one higher-order (HO) factor (see Bollen, 1989; Marsh, 1987; Marsh & Hocevar, 1985; Marsh & Jackson, 1999). Because the number of HO factor loadings is typically much smaller than the number of correlations among first-order factors, a HO model is more parsimonious. Differences between nested models, under appropriate conditions, can be tested for statistical significance (Bentler, 1990) or can be compared in terms of indices of fit like those emphasized here. However, particularly in applied research, the statistical significance of the chi-square statistic is rarely used as the basis for evaluating goodness of fit of a single model. As noted by many researchers, no model is ever true and will be shown to be false with a sufficiently large sample size. Also, the chi-square test is well known to be overly sensitive to sample size (e.g., Marsh, Hau, Balla, & Grayson. 1998; Marsh, Hau, & Grayson, in press). If the chi-square test of statistical significance is not appropriate for the evaluation of a single model, it is clearly inappropriate for the evaluation of the difference in fit of two models for the same reasons. Furthermore, because the chi-square difference test assumes that the baseline model is able to fit the data, the statistical justification for the chi-square difference tests is typically dubious. In this sense it is better to evaluate changes in goodness-of-fit indexes and, in particular, evaluate differences in critical parameter estimates. We also note that the relative ability of models testing more or fewer invariance constraints is of greater importance than the absolute level of fit of any one model. Thus for example, Cheung and Rensvold (2002) suggested that for incremental fit indices (e.g., TLI and RNI), decreases in fit greater than.01 might be important. If more parsimonious HO models are able to fit the data as well as less parsimonious first-order (FO) models, then there is support for the HO models. In the present investigation we were particularly concerned with whether the influence of the six FO factors on subsequent swimming performances could be explained in terms of one HO factor. Factorial Invariance. In SEMs it is possible to test the invariance of any one, any set, or all parameter estimates across parallel administrations of the same materials to the same individuals. Such tests of invariance are the within-subject counterpart of the more typical between-group comparisons (i.e., multiple group comparisons of invariance over responses by two or more independent groups). Although the most common use of within-group invariance comparisons is to evalu-

9 Self-Concept and Elite Swimming / 79 ate the invariance of parameter estimates over time, here we used this approach to evaluate the replicability of results over responses to the first and second events chosen by each elite swimmer. Tests of factorial invariance (see Bollen, 1989; Byrne, 1998; Jöreskog & Sörbom, 1996; Marsh, 1994a; Meredith, 1993) traditionally posit a series of nested models in which the endpoints are the least restrictive model with no invariance constraints, and the most restrictive (total invariance) model with all parameters constrained to be the same across all groups. In applying this approach, there is a well-developed methodology in which the goodness-of-fit indexes for alternative models are compared, including the least restrictive model that does not require any of the parameter estimates to be the same in different groups and the most restrictive model that requires all parameter estimates to be the same in the different groups. Typically, the minimal condition for factorial invariance is the equivalence of all factor loadings in the multiple groups, and this is usually the first test of invariance (following the test with no invariance constraints) in the sequence of invariance models. There is no clear consensus in recommendations about the ordering of subsequent invariance constraints (e.g., Bentler, 1988; Bollen, 1989; Byrne, 1998; Jöreskog & Sörbom, 1996), although Bentler (1988) and Byrne (2003) noted that the equality of parameters associated with measurement errors is typically the least important hypothesis to test and is unlikely to be met in most applications. The relative importance of invariance tests for different parameters also depends in part on the intent of the study. In the present study, for example, we are particularly interested in the invariance of path coefficients that are the basis of predictions used to test the reciprocal effects model. In preliminary (unreported) analyses, we demonstrated strong support for the invariance of the ESSDQ factor structure over responses to Events 1 and 2. In these tests we compared the fit of first-order models constraining various sets of parameters (factor loadings, factor correlations, factor variances, and measured variable uniquensesses) to be invariant across responses to the two events. Included in these models were correlations among the six EASDQ factors representing Event 1 and Event 2, and residual covariances (correlated uniquenesses) relating the uniqueness terms for the same items for Events 1 and 2 (for further discussion on why correlated uniquenesses should be included, see Marsh & Hau, 1996; also Jöreskog, 1979). Because these parameters represented relationships between responses to Events 1 and 2, they were not included in tests of invariance of parameters specific to Event 1 with those specific to Event 2. There was strong support for total invariance for all parameters (factor loadings, factor variances and covariances, and uniquenesses) across responses to each of the two events. In the present study we extended these preliminary analyses to include PPB performance in each event and subsequent championship performance to test whether the effects self-concept and PPB performance were the same for the two events. Hence, support for the invariance of these parameters provides a strong test of the generalizability of the results based on the first event that was the main focus of our analyses. Effects of Gender and Age. Although the effects of gender and age were not a focus of the present study, we considered their effects on the six ESSDQ scales in unreported, preliminary analyses. We began by showing that the ESSDQ factor structure (factor loadings, factor correlations, and uniquenesses) was invariant over age. Gender was only related to one ESSDQ factor (anaerobic, r =.16, favoring women) and no age gender interaction was significant. Whereas age was significantly related to three scales (skill, r =.16; anaerobic, r =.16; mental, r =.13), none

10 80 / Marsh and Perry of these relationships was significant after controlling for the positive relationship between age and PPB (r =.32). Importantly, when championship performance was predicted by PPB and the six ESSDQ factors, the effects of the six ESSDQ factors did not interact with gender, age, nor the age gender interaction; the size and pattern of significant effects of the EESDQ scales was unaffected by inclusion of age, gender, and these interaction terms. Because the effects of gender, age, and their interaction were largely nonsignificant and did not interact with ESSDQ factors in predicting championship performance and in order not to detract from the main focus of the present study these results are not considered further here. First-Order Factor Structure Results We began by testing an a priori, first-order CFA model (Model 1A in Table 1) in which we posited six ESSDQ factors based on responses to the 29 ESSDQ items, and two swimming performance factors based on PPB and championship performances. Each performance score was used to represent a separate factor, inferred from a single variable and assumed to be measured without error. Model 1A provided an excellent fit to the data (e.g., TLI =.980; RNI =.982). Each of the six ESSDQ factors was well defined in that the factor loading relating each item to its corresponding factor was substantial, varying from.72 to.96 (Md =.87). Whereas correlations among six ESSDQ factors varied from.25 to.83 (Md r =.50), only the correlation between the mental competence and overall performance factors was greater than.6. Also, many of the largest correlations were between specific factors and the overall performance factor, which is intended to reflect a global factor incorporating the more specific components. The two performance factors were very highly correlated (r =.90) to each other, indicating that most of the variance in championship performances was determined by PPBs established prior to the championships. Correlations between the six ESSDQ factors and the two performance factors varied from.16 to.36 (Table 2). Interestingly, although the two performance factors are very highly correlated, ESSDQ responses tend to be more highly correlated with (posttest) subsequent championship performances than (pretest) PPB performances. Also, note that the skill self-concept was most highly correlated with both performance factors, followed by aerobic fitness self-concept. Somewhat surprisingly perhaps, the overall performance self-concept factor was not most highly correlated with either of the performance scores (see Table 2). In summary, results based on Model 1A provide strong support for the a priori factor structure based on the design of the ESSDQ. Higher-Order Factor Structure Next we evaluated the higher-order factor model (Model 1B in Tables 1 and 2) in which the six ESSDQ factors are posited to reflect one (global) higher-order factor. The fit indexes for the first-order model (TLI =.980) and the more parsimonious higher-order model (TLI =.978) were similar. First-order factor loadings relating responses to measured variables to the first-order factors were nearly the same for both models. In Model 1B, the six factor loadings relating the first-order factors to the higher-order factor were all substantial (.58 to.89; Table 2). Consistent with the design of the ESSDQ, the largest higher-order factor loading was

11 Self-Concept and Elite Swimming / 81 Table 1 Summary of Goodness of Fit for All Models Model χ 2 DF TLI RNI RMSEA (90% CI) Description CFA 1st Event (N = 257) 1a ( ) 8 First-order (FO) factors: 6 ESSDQ, Personal best, Championship performance (see Table 2) 1b ( ) 8 FO factors, 1 Higher-order (HO) Self-concept factor (defined by the 6 ESSDQ FO factors) SEM 1st Event (N = 257) 2a ( ) Model 1A as a SEM (see Model 2A in Figure 1 and Table 3) 2b ( ) Model 1B as a SEM (see Model 2B in Figure 1 and Table 3) Invariance of 1st and 2nd Event for Model 2B (N = 216) 3a ( ) No invariance (see Figure 2) 3b ( ) 29 first-order factor loadings (FOFL) invariant (1 FOFL for each factor constrained to be 1) 3c ( ) FOFL, 6 higher-order factor loadings (HOFL) invariant (1 HOFL constrained to be 1) 3d ( ) FOFL, HOFL, 4 path coefficients (PC) invariant 3e ( ) FOFL, HOFL, PC, 9 factor variances (FV) invariant 3f ( ) FOFL, HOFL, PC, FV, uniquenesses invariant (see Table 4) Note: RNI = relative noncentrality index; TLI = Tucker-Lewis index; RMSEA = root mean square error of approximation; 90% CI = 90% confidence interval for the RMSEA; DF = degrees of freedom. All tests of invariance (Models 3A 3F) evaluated the effects of constraining some or all parameter estimates to be the same for results based on the first and second events chosen by each swimmer.

12 82 / Marsh and Perry Table 2 Parameter Estimates Relating Previous Personal Best Performance, Current Elite Athlete Self-Concept, and Subsequent Championship Performance Performance Self-Concept Factors (First-order) Higher- Factors Model Descriptions Skill Body Aero Anaero Ment Perf order PB Champ Models with 6 first-order self-concept (SC) factors Factor Correlations (Model 1A) Personal best (PB).31*.17*.25*.16*.18*.16* 1.00 Championship performance (Champ).36*.24*.28*.20*.25*.26*.90* 1.00 Path Coefficients (Model 2A; see Fig 1) PB > SC (6 factors) and Champ.31*.17*.25*.16*.18*.16*.88* SC (6 factors) > Champ * Models with 1 higher-order (HO) self-concept factor Factor Corr (Model 1B) Corr with HO self-concept factor.71*.58*.58*.60*.89*.89* *.33* Path coefficients (Model 2B; see Fig 1) PB > HO and champ.25*.87* HO > SC and champ.71*.58*.58*.60*.89*.89*.12* Note: Skill = Skill self-concept; Body = Body suitability self-concept; Aero = Aerobic fitness self-concept; Anaero = Anaerobic fitness self-concept; Ment = Mental skills self-concept; Perf = Overall performance self-concept; PB = Previous person best performance (in international point score); Champ = Subsequent performance at this championship (in international point score). The symbol > indicates the direction of causality in the structural equation path model. * p <.05

13 Self-Concept and Elite Swimming / 83 for the overall performance factor (.89), although the corresponding factor loading for the mental self-concept scale (.88) was nearly as high. The factor loading for skill self-concept was also high (.71), whereas those for the remaining three factors varied from.58 to.60. However, it is also important to emphasize that substantial amounts of reliable variance in each first-order factor could not be explained in terms of the higher-order factor. The proportions of unexplained variance (1 minus the square of the completely standardized higher-order factor loading) were modest for the mental and overall performance factors (approx. 20%), but were larger for skill self-concept (approx. 50%) and substantial for the remaining three factors (approx. 65%). Hence, even though the fit of Model 1B is good and nearly as good as Model 1A, there is considerable reliable variance in the first-order factor that cannot be explained in terms of the higher-order factor. Importantly, the higher-order factor correlates.25 with prior PPB and.33 with subsequent championship performance. Thus for example, the first-order skill self-concept factor was somewhat more highly correlated with each of these performance factors (.31 and.36, respectively) than the global higher-order factor. Structural Equation Models The two SEM Models, 2A and 2B (see Figure 1), parallel the two CFA models just considered. The models are parallel in that the number of estimated parameters and goodness of fit are necessarily the same for each pair of models (i.e., 1A and 2A, 1B and 2B; see Table 1). Importantly, however, the models differ in that correlations between the ESSDQ factors and performance measures in the CFA models are represented with path coefficients consistent with the temporal ordering of the constructs (PPB > current self-concept > subsequent championship performance). Hence we focus on tests of the effect of self-concept on championship performance, controlling for the very substantial influence of PPB (r =.90). In Model 2A (Figure 1 and Table 2), championship performance is predicted from PPBs and the six ESSDQ factors. Whereas the strongest predictor is PPB (standardized beta =.88), the ESSDQ factors contribute significantly to the prediction of championship performance. Due in part to multicollinearity associated with the six self-concept factors, only the contribution of overall performance self-concept was statistically significant (standardized beta =.12). The residual variance component of.176 indicates that a remarkable 82.4% (mult R =.91) of the variance in championship performance can be explained by the combination of PPBs and the six ESSDQ factors. Whereas the best predictor was clearly PPB, the six self-concept factors accounted for significant variance beyond that which can be explained by PPBs alone. In evaluating Model 2B (Table 1, Figure 1), it is important to emphasize that this model is nested under Model 2A. In particular, one higher-order global factor in Model 2B cannot explain more variance in championship performance than the entire set of six self-concept factors in Model 2A. However, the two models are nearly identical in this respect: residual variance components (unexplained variance in championship performance) were 17.6% (2A) and 17.7% (2B). In Model 2B the effect of the global elite athlete self-concept factor (.12) was highly significant. There is substantial consistency in the results of the first-order and higher-order SEM models relating PPBs and self-concept factors to championship performance.

14 84 / Marsh and Perry Figure 1 Summary of structural equation models predicting subsequent championship performance on the basis of prior personal best and self-concept responses. Self-concept responses are represented as six first-order factors (Model 2A) or a higher-order global factor (Models 2B and 3A). All paths in gray are not statistically significant. In Model 3A, Model 2B is extended to include results from the first and second event chosen by each swimmer.

15 Self-Concept and Elite Swimming / 85 In each model, PPB was the main determinant of championship performance, but the contribution of self-concept was consistently significant. The amount of variance explained in championship performance was nearly identical in both models, as was the proportion of variance not explained by PPBs that could be explained by self-concept responses. Furthermore, even the actual effects of self-concept were reasonably consistent. In Model 2A the path coefficient relating overall performance self-concept to championship performance was.12 and the effect of none of the other first-order self-concept factors was statistically significant. In Model 2B the path coefficient leading from the global elite athlete self-concept factor to championship performance was also.12. Whereas this global self-concept factor incorporated all six ESSDQ (first-order) factors, the global factor was most strongly related to the first-order performance factor, and these results are consistent with both the design of the ESSDQ and the global nature of the outcome variable (championship performance) in the present investigation. Replicability of the Results Across Two Events Particularly because the present study is apparently the first to test the causal ordering of self-concept and performance in an elite athlete setting and is based on responses to a new elite swimmer self-concept instrument, it is important to replicate the results. In the present study the athletes completed the ESSDQ in relation to all the events in which they competed most competed in at least two events and we collected PPB and championship performances for these other events as well. The main focus of these analyses is to evaluate replicability, particularly of the path coefficients across the two events for the SEM based on Model 2B (Figure 1), but the new models differed in several important features. First, we extended Model 2B to include responses associated with both Events 1 and 2 (Model 3A, Figure 1). Second, whereas Model 2B controlled for the effects of PPB in one event, here we controlled for PPB performances in two events (although we expected the effect of the PPB in the matching event to be stronger than the effect of PPB in a different event). Hence this provided a stronger, more demanding, test of the effects of self-concept. Finally, adapting traditional tests of factorial invariance to this within-swimmer design, we systematically evaluated the invariance of matching pairs of parameters one associated with responses to Event 1 and the other with Event 2 to formally test the replicability of the results across the two events. Although not a focus of the present study, relationships between the ESSDQ factors for Events 1 and 2 provide support for the convergent and discriminant validity of the scales using the logic of multitrait-multimethod analyses (Campbell & Fiske, 1959; Marsh, 1988) in which the multiple ESSDQ factors are the multiple traits and the two events are the multiple methods. Hence, substantial correlations between matching ESSDQ (.78 to.91; Table 3) support convergent validity in relation to different events. In support of the discriminant validity, these correlations between matching ESSDQ factors are consistently much larger than the corresponding correlations between nonmatching ESSDQ factors In Model 3A (Figure 1; also see Tables 1 and 3) we fitted the a priori model with no invariance constraints. Although there were small differences in the sizes of higher-order factor loadings relating the six first-order self-concept factors to the single global higher-order factor, the pattern of results was similar. Importantly, path coefficients relating PPBs and global swimming self-concept to champion-

16 86 / Marsh and Perry Table 3 Selected Parameter Estimates for SEM Relating One Higher-Order Self- Concept Factor to Performance Factors in 1st and 2nd Event Elite Swimmer Self-Concept Factors Performance Variable Skill Body Aero Anaero Ment Perf PBest Champ Factor Correlations a Skill 1.00 Body Aero Anaero Ment Perf PBest Champ Factor Corrs between 1st (col) and 2nd (row) Event b Skill Body Aero Anaero Ment Perf PBest Champ Higher-order factor loadings (HOFL) a HOFL First-order factor residuals (FOFR) a FOFR Path Coefficients (leading to Event 1 performance) PB (Event 1).68 PB (Event 2).20 HO Self Path Coefficients (leading to Event 2 performance) PB (Event 2).68 PB (Event 1).20 HO Self Note: Skill = Skill self-concept; Body = Body suitability self-concept; Aero = Aerobic fitness self-concept; Anaero = Anaerobic fitness self-concept; Ment = Mental skills self-concept; Perf = overall performance self-concept; PBest = Previous person best performance; Champ = subsequent performance at this championship. All parameter estimates, presented in completely standardized form, are statistically significant (p <.05). a Each of these parameters is invariant across responses to the two different events by the same swimmer, so only one set is presented. Thus, factor loadings, uniquenesses, factor correlations among factors associated with the same event, higher-order factor loadings, first-order factor residuals are presented for the first event, but are necessarily the same (because they were held to be invariant) for parallel parameters associated with the second event. b Each of these parameters represents correlations between responses to the first event and the second event so that it is not possible to test for invariance across events.

17 Self-Concept and Elite Swimming / 87 ship performance were nearly the same for Events 1 and 2. For both events the primary determinant of championship performance was PPB in the same (matching) event (.70 and.67 in the two events, respectively) as well as PPB in the other (nonmatching) event (.18 and.21 in the two events, respectively). The effect of global swimmer self-concept on championship performance was highly significant and approximately the same for both events (.13 and.12, respectively). Interestingly, the effect of global self-concept in one event on championship performance in the other event was not statistically significant for either event. In relation to previous results based on Event 1 alone in Model 2B, the total explained variance in championship performance was slightly larger, due mostly to the inclusion of the second measure of PPB; unexplained variance was 14.7% in Model 3A but 17.7% in the corresponding Model 2B. Nevertheless, despite this more demanding test of the effect of self-concept, the effect of global self-concept was essentially unchanged and was even marginally larger here than in the previous results based on Event 1. In Models 3A 3F, we pursued a series of invariance tests that included all the parameter estimates associated with Event 1 with the matching parameter estimates for Event 2. Starting with Model 3A with no invariance constraints, we systematically added constraints for different sets of parameters so that in the final Model 3F all parameters were constrained to be the same across the two events (see Table 1). Although this set of invariance models is complex, the results are easy to summarize. Based particularly on the TLI, which incorporates penalties for model complexity, there is good support for the total invariance of all the parameter estimates in Model 3F (TLI =.983 for all Models 3A to 3F in Table 1). Of particular relevance is the test of invariance for the four path coefficients relating PPB and current self-concept to subsequent championship performance (Model 3C in Table 1). The change in chi-square (2.4) associated with the inclusion of the four invariance constraints requiring these parameters to be the same over events was less than the change in degrees-of-freedom (4, one for each constraint), providing strong support for the invariance of these parameters across the two events. Not surprisingly, the results based on Model 3F (Table 3) are very similar to those already examined in earlier analyses of Event 1 alone and those for the corresponding Model 3A, based on both events in which no invariance constraints were imposed. Thus, for parameters constrained to be equal across the two events (Table 3), the parameter estimates are approximately midway between those of each event separately when no invariance constraints are imposed (Figure 1). Because the differences are small, the fit indexes indicate good support for invariance. In summary, the results based on Models 3A 3F provide very strong support for the replicability of the effects of prior self-concept on subsequent championship performance after controlling for the effects to PPBs. Summary and Discussion Does elite athlete self-concept as inferred from ESSDQ responses (see Appendix) have an effect on the subsequent championship performances of elite swimmers beyond that which can be explained in terms of PPBs? Our results provide a clear affirmative answer to this question. These results are theoretically important for self-concept theory and predictions based on the reciprocal effects model, but also have substantive and practical importance for understanding the