Resolving uncertainties of the factor structures of the Coach-Athlete Relationship Questionnaire (CART-Q)

Figures & data

Figure 1. 3Cs direct -perspective three-factor first-order factor model

Figure 2. 3Cs meta-perspective three-factor first-order factor model

Table 1. Descriptive statistics for the 11-item direct perspective and meta-perspective CART-Qs

Item	Direct Perspective	M	SD	Skewness	Kurtosis
1	I like my athlete/coach	5.70	0.97	−0.58	0.13
2	I trust my athlete/coach	5.72	1.09	−0.78	0.33
3	I respect my athlete/coach	6.05	0.97	−1.14	1.70
4	I appreciate the sacrifices my athlete/coach has experienced to improve his/her performance	5.69	1.10	−0.62	−0.17
5	I am committed to my athlete/coach	5.70	1.10	−0.66	−0.07
6	I am close to my athlete/coach	4.42	1.23	0.01	−0.03
7	I think my coaching/playing career is promising with my athlete/coach	5.13	1.24	−0.05	−0.03
8	I am at ease with my athlete/coach	5.38	1.20	−0.70	0.30
9	I am responsive to my athlete/coach efforts	5.63	1.01	−0.40	−0.49
10	I am ready to do my best	6.11	0.89	−0.86	0.48
11	I adopt a friendly stance	5.97	0.82	−0.69	1.32
Item	Meta-Perspective
1	My athlete/coach likes me	5.23	1.04	−0.09	−0.17
2	My athlete/coach trusts me	5.33	1.05	−0.53	−0.05
3	My athlete/coach respects me	5.64	1.06	−0.90	0.96
4	My athlete/coach appreciates the sacrifices I have experienced to improve performance	5.10	1.18	−0.21	−0.07
5	My athlete/coach is committed to me	5.30	1.07	−0.09	−0.58
6	My athlete/coach is close to me	4.20	1.16	0.20	0.33
7	My athlete/coach believes that his/her career is promising with me	5.06	1.05	−0.36	0.24
8	My athlete/coach is at ease with me	5.17	1.13	−0.33	−0.05
9	My athlete/coach is responsive to my efforts	5.24	1.14	−0.34	−0.27
10	My athlete/coach is ready to do his/her best	6.05	0.91	−0.88	0.56
11	My athlete/coach adopts a friendly stance	5.80	1.01	−1.03	1.40

Model Evaluation via Confirmatory Factor Analysis

Table 2. Fit indices for the alternative three-factor higher-order and single-factor models for the direct and meta items using AMOS and LISREL (n = 251)

Model	df	χ^2	χ^2/df	CFI	TLI	SRMR	RMSEA (90% confidence interval)	AIC	ECVI
AMOS Direct Perspective
M1 3 Factor 1^st Order Original	41	277.82	6.78	0.89	0.84	0.06	0.14-0.17	327.83	1.31
M2 3 Factor 1^st Order Modified	37	165.18	4.46	0.93	0.90	0.05	0.10-0.14	223.18	0.89
M3 Single-Factor Solution	44	293.86	6.68	0.87	0.84	0.07	0.14-0.17	337.86	1.35
Meta-Perspective
M4 3 Factor 1^st Order Original	41	241.74	5.90	0.89	0.86	0.06	0.12-0.16	291.74	1.17
M5 3 Factor 1^st Order Modified	37	173.01	4.68	0.93	0.89	0.05	0.10-0.14	231.01	0.92
M6 Single-Factor Solution	44	257.74	5.86	0.89	0.86	0.07	0.12-0.16	301.74	1.20
LISREL
Direct Perspective
M1 3 Factor 1^st Order Original	41	168.96	4.12	0.98		0.07	0.09-0.13	218.96	0.88
M2 3 Factor 1^st Order Modified	40	132.50	3.30	0.98		0.06	0.08-0.11	184.25	0.74
M3 Single-Factor Solution	44	169.68	3.86	0.98		0.07	0.09-0.12	213.68	0.86
Meta-Perspective
M4 3 Factor 1^st Order Original	41	180.11	4.39	0.97		0.06	0.10-0.13	230.11	0.92
M5 3 Factor 1^st Order Modified	38	132.80	3.49	0.98		0.06	0.82-0.12	188.80	0.76
M6 Single-Factor Solution	44	181.21	4.19	0.97		0.07	0.10-0.13	225.21	0.90

Note. df = Degrees of Freedom, χ² = Chi-square, χ²/df = Chi-square divided by Degrees of Freedom, CFI = Comparative Fit Index, TFI = Tucker-Lewis Index, SRMR = Standardised Root Mean Square Residual, RMSEA = Root Mean Square Approximation of Error, AIC = Akaike Information criterion, ECVI = Expected Cross Validation Index.

Figure 3. Person-item threshold distribution for the CART-Q when constructs were entered as subtests for the direct perspective data

Figure 4. Person-item threshold distribution for the CART-Q when analyses were conducted separately for each construct using the direct perspective. The top panel shows results for Closeness, the middle panel Commitment, and bottom panel Complementarity