EFA With Parallel Analysis Latent Factor
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EFA With Parallel Analysis Latent Factor
EFA with parallel analysis produced only one latent factor. The measurement literature indicates that a parallel analysis may at times lead to under-factoring if there is (a) a high correlation between factors, (b) a large number of variables, or (c) a primary factor with a large eigenvalue (Hayton et al., 2004; Mulaik, 2009; Turner, 1998). All of these three situations occurred in the current situation. Thus, the traditional approach was deemed more appropriate and was thus adopted, which produced four latent factors, with a total of 63.52% variance explained.
The extracted factor matrix was further rotated using the Geomin rotation technique. Following the aforementioned criteria of retaining items, the fourth factor was removed due to severe double loading of its items. Three factors, with a total of 21 items were retained (Table 4), explained 60.77% of the total variance. The factors were labeled as inner self-merit (11 items), lifestyle pursuance (3 items), and social self-presentation (7 items).
Although these three PDSI dimensions all fall under the overarching domain of socialization, they are clearly distinct. The dimension of inner self-merit emphasizes fundamental human needs (e.g. mental health and sound personality) that are not necessarily involved in interpersonal relationships. In contrast, items under the dimension of social self-expression are more advanced and rely heavily on the existence of interpersonal relation- ships to be meaningful. Differing from the first two dimensions, which are strongly tied to tra- ditional sport images, lifestyle pursuance contains items that are more relevant to recreation, leisure, and health, highlighting the well-being of sport participants.
Phase 3: confirmatory factor analysis and structural equation modeling
Method A new online questionnaire was designed using Qualtrics. In addition to the retained PDSI items, sport participation items, and socio-demographic items, the questionnaire included
Table 3. Major sport activities that survey respondents had most frequently participated.
Sport activities
Survey respondents in Phase 2 (N = 370)
Survey respondents in Phase 3 (N = 483)
N % N %
Badminton 4 1.1 5 1.0 Baseball 14 3.8 12 2.5 Basketball 83 22.4 101 20.9 Bowling 8 2.2 5 1.0 Boxing 4 1.1 3 0.6 Cycling 8 2.2 9 1.9 Football 22 5.9 29 6.0 Frisbee 2 0.5 3 0.6 Golf 23 6.2 22 4.6 Hiking 2 0.5 5 1.0 Hockey 7 1.9 5 1.0 Kickball 2 0.5 5 1.0 Martial arts 2 0.5 4 0.8 Racquetball 3 0.8 2 0.4 Running/Jogging 35 9.5 47 9.7 Soccer 27 7.3 55 11.4 Softball 25 6.8 26 5.4 Swimming 7 1.9 8 1.7 Tennis 26 7.0 47 9.7 Volleyball 20 5.4 28 5.8 Walking 4 1.1 3 0.6 Weight lifting 12 3.2 8 1.7 Yoga 2 0.5 5 1.0
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items to measure sport consumption behavior (e.g. personal involvement, money expen- diture, and time expenditure). The sport involvement inventory used in previous sport marketing studies (e.g. Ko et al., 2008; Koernig & Boyd, 2009; McGehee et al., 2003; Shank & Beasley, 1998) was modified to include seven of the original eight semantic differential items (i.e. boring–exciting, uninteresting–interesting, worthless–valuable,
Table 4. Results of exploratory factor analysis in phase 2 (N = 370). Desired self-image Mean SD Factor 1 ISM Factor 2 LP Factor 3 SSP
Enjoying life 4.07 1.03 .090 .759* −.017 Being athletic 4.04 1.04 .123 .438* .004 Being health-conscious 3.99 1.04 .192* .693* .047 Being physical fit 3.99 .99 .005 .298* .472* Being confident 3.92 1.01 .735* .016 −.033 Being determined 3.88 1.07 .515* .058 .159 Being dedicated 3.85 1.06 .640* .154* −.029 Being optimistic 3.85 1.11 .698* −.066 .110 Being enthusiastic 3.84 1.12 .762* .135* −.041 Being self-motivated 3.84 1.07 .766* .081 −.066 Being skilled 3.83 1.08 .313* −.034 .255 Being capable 3.82 1.07 .580* .018 .149 Being hardworking 3.81 1.07 .676* .108* −.020 Being competitive 3.81 1.17 .060 .046 .380* Having work-life balance 3.81 1.10 −.024 .729* .309* Being happy 3.79 1.11 .556* .047 .121 Being cheerful 3.79 1.10 .273* .051 .475* Being mentally strong 3.77 1.10 .660* .027 .089 Pursuing fair play 3.75 1.14 .018 −.029 .628*
Having a strong sense of teamwork 3.74 1.25 −.224* .010 .759* Being self-disciplined 3.70 1.13 .244* .082 .516* Being perseverant 3.68 1.11 .798* −.030 −.015 Being well-rounded 3.67 1.13 .503* .083 .254* Having good leadership 3.66 1.08 .083 .073 .623* Being respectable 3.66 1.16 .422* −.010 .376* Being successful 3.65 1.18 .443* .065 .238* Being passionate 3.65 1.15 .797* .054 −.118 Being in shape 3.64 1.18 .002 .419* .232* Being friendly 3.63 1.17 .030 −.002 .839* Being reliable 3.62 1.16 .556* −.161* .420* Being quick-thinking 3.62 1.14 .283* −.012 .445* Being down-to-earth 3.62 1.12 .474* .077 .225*
Being willing to learn 3.61 1.17 .479* .003 .380* Being open to experience 3.60 1.14 .346* .094 .381* Being sociable 3.59 1.14 −.090 .054 .793* Being responsible 3.58 1.16 .585* .047 .252* Being goal-driven 3.56 1.18 .109 .297* .429* Being self-sufficient 3.53 1.18 .595* .027 .276* Being tough 3.52 1.20 .360* .118* .045 Being focused 3.52 1.18 .370* −.017 .495* Seeking excitement 3.51 1.22 .133 .190* .392* Being supportive 3.50 1.18 .207 −.077 .676* Being prepared 3.49 1.17 .556* −.105* .369* Having high integrity 3.48 1.24 .476* −.062 .437* Being versatile 3.48 1.19 .368* .016 .436* Being spirited 3.48 1.17 .220* .117* .489* Being fun-loving 3.47 1.20 .253* −.015 .353* Having a good work ethic 3.46 1.16 .141 .041 .729* Having a sound mind 3.43 1.23 .761* −.122* .093 Eigenvalues from sample correlation matrix 26.08 2.05 1.64 Eigenvalues from parallel analysis 1.78 1.70 1.64
Notes: ISM = Dimension of inner self-merit, LP = Dimension of lifestyle pursuance, SSP = Dimension of social self-presen- tation.
*p < .05.
EUROPEAN SPORT MANAGEMENT QUARTERLY 595
unappealing–appealing, useless–useful, irrelevant–relevant, and important–unimportant). Each item was phrased on a 7-point Likert scale. Respondents were asked to estimate their annual money expenditure and weekly time expenditure participating in their chosen sport. Money and time expenditure were evenly anchored across 2000 dollars and 20 hours, respectively, on 10-point scales, with one additional option to capture levels in excess of the maximum.
The online questionnaire was available through Amazon Mechanical Turk for four weeks. Excluding problematic questionnaires with a severe rate of missing values and failure in the attention check questions (two personal involvement items were reserve coded), the data of 483 respondents in the United States were considered valid. Table 5 presented the socio-demographic information of these respondents, who were each rewarded $0.71 through theAmazon Mechanical Turk system. Major sport activities that respondents had most frequently participated are incorporated into the earlier Table 3.
Confirmatory factor analysis (CFA) was first conducted for the PDSI items, and structural equation modeling (SEM) was applied to assess the influence of PDSI on consumer behavior. To examine goodness-of-fit, the following indices were employed: chi-square (χ2), normed chi-square (χ2/df), root mean square error of approximation (RMSEA), 90% confidence interval (CI) of RMSEA, possibility of close fit (PCLOSE), comparative fit index (CFI), Tucker–Lewis index (TLI), and standardized root means square residual (SRMR) (Browne & Cudeck, 1993; Hair et al., 2010; Hu & Bentler, 1999; Kline, 2005).
To examine scale reliability, Cronbach’s alpha (α), construct reliability (CR), and averaged variance extracted (AVE) were calculated. To assess construct validity, convergent validity and discriminant validity were examined. The former was assessed using factor loadings,
Table 5. Socio-demographic information of respondents in phase 3 (N = 483). Variable Category N %
Gender Male 252 52.2 Female 231 47.8
Age 18–25 106 21.9 26–35 206 42.7 36–45 96 19.9 46–55 53 11.0 56 and above 22 4.6
Ethnicity African American 52 10.8 American Indian 9 1.9 Asian 36 7.5 Caucasian 338 70.0 Hispanic 41 8.5 Other 7 1.4
Household income Below $20,000 55 11.4 $20,000–39,999 128 26.5 $40,000–59,999 92 19.0 $60,000–79,999 97 20.1 $80,000–99,999 56 11.6 $100,000–149,999 43 8.9 $150,000–199,999 6 1.2 Above $200,000 6 1.2
Education In high school now 1 .2 High school graduate 78 16.1 In college now 66 13.7 College graduate 252 52.2 Advanced degree 79 16.4 Other 7 1.4
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and the latter was evaluated by using correlations among latent factors (Kline, 2005) and the Fornell and Larcker testing (1981). In the case where model comparison was involved, the indices of Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used. Descriptive statistics about respondents’ socio-demographics and desired self-images were calculated using SPSS 19.0. CFA and SEM were conducted using Mplus 7.0 with the estimator of MLR (i.e., maximum likelihood estimation with robust standard errors).
Results of CFA Goodness of fit indicesof CFA were acceptable: χ2 = 587.308, p < .001; χ2/df = 587.308/186 = 3.158, RMSEA = .067 (90% CI = .061–.073), PCLOSE < .001, CFI = .918, TLI = .907, AIC = 24402.878, BIC = 24678.759, and SRMR = .056. However, two items had factor loadings well below the suggested criterion of .70 (Hair et al., 2010): ‘image of having a sound mind’ (λ = .519) under inner self-merit and ‘image of having a good work ethic’ (λ = .512) under social self-presentation.
Also, the mean values of these two items were 3.30 and 3.22, respect- ively, below the cutoff criterion of 3.4. Therefore, CFA was conducted again without these two items, producing better fit indices: χ2 = 448.127, p < .001; χ2/df = 448.127/149 = 3.008, RMSEA = .064 (90% CI = .058–.071), PCLOSE < .001, CFI = .932, TLI = .922, AIC = 21445.434, BIC = 21696.235, and SRMR = .049. Compared with the initial CFA model, the subsequent one had a smaller chi-square value (Δχ2 = 139.181, Δdf = 37, p < .001) and superior fit indices. In terms of reliability, the Cronbach’s alpha, CR, and AVE values (Table 6) of the revised PDSI model exceeded the suggested criteria: .70 for Cronbach’s alpha, .70 for CR, and .50 for AVE (Hair et al., 2010; Kline, 2005).
As shown in Table 6, except for one item (.691), factor loadings of the PDSI items were above the suggested value of .70 (Hair et al., 2010), indicating good convergent validity. The inter-factor corre- lations were .803 (between inner self-merit and lifestyle pursuance), .784 (between inner self-merit and social self-presentation), and .756 (between lifestyle pursuance and social self-presentation), all below and then superior to the criterion of .85 (Kline, 2005).
As the results of the Fornell-Larcker testing, square root of AVEinner self-merit and AVElifestyle pursuance were larger than the correlation between inner self-merit and lifestyle pursuance; however, the square root of AVEsocial self-presentation was less than correlations between inner self-merit and social self-presentation and between lifestyle pursuance and social self-presentation.
Further, the SEM models were reanalyzed with constraining three correlations to 1, respect- ively. All of three SEM models produced fit indices that are inferior to the original ones. Results of inter-factor correlations and the Fornell-Larcker testing together have showed an acceptable level of discriminant validity in the measurement model.
Results of SEM SEM with a second-order PDSI model was conducted to disclose the role of overall PDSI in sport consumer behavior and to preliminarily examine the nomological validity of the proposed scale (i.e. how well the target construct relates to other theoretically related con- structs) (Churchill, 1995). The fit indices of the initial SEM with a second-order PDSI model were acceptable: χ2 = 1071.896, p < .001; χ2/df = 1071.896/343 = 3.125, RMSEA = .066 (90% CI = .062–.071), PCLOSE < .001, CFI = .893, TLI = .882, and SRMR = .051. Given the superior fit indices of the PDSI model in CFA and the observability of money and time expenditure, the relatively inferior model fit of SEM was likely due to
EUROPEAN SPORT MANAGEMENT QUARTERLY 597
the measure of personal involvement. This assumption was confirmed by the results of CFA for the measurement model of personal involvement (7 items): χ2 = 215.364, p < .001; χ2/df = 215.364/14 = 15.383, RMSEA = .173, CFI = .775, TLI = .663, and SRMR = .083. Based on the modification indices provided by Mplus, two problematic items were dropped from the measurement model, largely improving the fit indices: χ2 = 27.081, p < .001; χ2/df = 27.081/5 = 5.4162, RMSEA = 0.096, CFA = .955, TLI = .911, and SRMR = .037.
With the 5-item personal involvement scale, the model fit indices of SEM were much better: χ2 = 715.351, p < .001; χ2/df = 715.351/292 = 2.450, RMSEA = .055 (90% CI = .050–.060), PCLOSE = .060, CFI = .933, TLI = .925, and SRMR = .043. As shown in Figure 2, all five hypotheses were confirmed. In terms of direct effects, PDSI positively influenced personal involvement (β = .407, p < .01), money expenditure (β = .162, p < .01), and time expenditure (β = .159, p < .01). Personal involvement positively influenced money expenditure (β = .164, p < .01) and time expenditure (β = .147, p < .01). In terms of indirect effects, PDSI positively influenced money expenditure (β = .067, p < .01) and time expenditure (β = .060, p < .01) through personal involvement, signifying that personal involvement partially mediated the relationships between PDSI and two indices of actual consumption (Sobel, 1982).
The standardized total effects of PDSI on personal involvement, money expenditure, and time expenditure were .407 (p < .01), .229 (p < .01), and .219 (p < .01), respectively, providing initial evidence about the nomological validity of the proposed PDSI scale.
Table 6. Mean value, standard deviation (SD), factor loadings (λ), Cronbach’s Alpha (α), construct reliability (CR), average variance extracted (AVE) for the proposed PDSI scale in CFA (N = 483). Factor/Item Mean SD λ α CR AVE
Inner self-merit .957 .957 .693 Being happy 3.79 1.14 .851 Being dedicated 3.88 1.11 .863 Being confident 3.91 1.12 .863 Being self-motivated 4.01 1.07 .819 Being enthusiastic 3.93 1.07 .792 Being hardworking 3.96 1.09 .841 Being passionate 3.88 1.13 .838 Being mentally strong 3.85 1.15 .838 Being perseverant 3.89 1.10 .863 Being optimistic 3.82 1.07 .747
Lifestyle pursuance .851 .854 .661 Enjoying life 4.16 1.02 .815 Having work-life balance 3.77 1.16 .780 Being health-conscious 3.93 1.06 .842
Social self-presentation .876 .876 .541 Pursuing fair play 3.68 1.21 .730 Having a strong sense of teamwork 3.71 1.29 .728 Being friendly 3.72 1.17 .756 Being sociable 3.64 1.20 .743 Having good leadership 3.56 1.19 .752 Being supportive 3.71 1.14 .691
Personal involvement .862 .866 .566 Worthless-valuable 6.13 .96 .699 Unappealing-appealing 6.17 1.17 .638 Useless-useful 5.97 1.07 .833 Irrelevant-relevant 5.95 1.04 .808 Important-unimportant 5.90 1.19 .766
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