Testing associations between global and specific levels of student academic motivation and engagement in the classroom

Figures & data

Figure 1. Schematic representation of the potential predictive models of academic motivation predicting engagement in the classroom.

Note. G: Global factor; INT: Intrinsic motivation; EIN: Extrinsic-identified regulation; EID: Extrinsic-introjected regulation. ER: External regulation. A: Amotivation. BE: Behavioral engagement: Effort/attention; BB: Behavioral engagement: Boredom/distraction; ES: Emotional engagement: Social; EL: Emotional engagement: Learning; CS: Cognitive engagement: Strategies; CA: Cognitive engagement: Autoregulation.

Table 1. Sample descriptive statistics (N = 4047).

Variable	N	%
Country
Country 1 (France)	1011	25.0
Country 2 (Belgium)	1591	39.3
Country 3 (Luxembourg)	1445	35.7
Gender
Male	2013	49.7
Female	2034	50.3
Age
14 or under	922	22.8
15 or 16	1330	32.9
17 or over	1790	44.3
Foreign language spoken at home
Yes	1202	29.8
No	2845	70.2
With grade retention (at least one year)
Yes	1567	38.9
No	2480	61.1

Figure 2. Alternative measurement models of academic motivation and engagement in the classroom.

Note. CFA: Confirmatory Factor Analysis. ESEM: Exploratory Structural Equation Model; G: Global factor; INT: Intrinsic motivation; EIN: Extrinsic-identified regulation; EID: Extrinsic-introjected regulation. ER: External regulation. A: Amotivation. BE: Behavioral engagement: Effort/attention; BB: Behavioral engagement: Boredom/distraction; ES: Emotional engagement: Social; EL: Emotional engagement: Learning; CS: Cognitive engagement: Strategies; CA: Cognitive engagement: Autoregulation.

Table 2. Alternative measurement models.

Models	Chi-square	df	CFI	TLI	RMSEA [90% CI]	AIC	CAIC	BIC	SSBIC
Academic motivation
1. Correlated factors CFA	2422.015*	160	.899	.880	.059 [.057; .061]	235683.784	236195.306	236125.306	235902.876
2. Correlated factors ESEM	884.072*	100	.965	.934	.044 [.041; .047]	233587.407	234537.377	234407.377	233994.294
3. Bifactor-CFA	3067.130*	150	.870	.835	.069 [.067; .071]	236449.088	237033.684	236953.684	236699.479
4. Bifactor-ESEM	635.851*	85	.975	.945	.040 [.037; .043]	233208.142	234267.723	234122.723	233661.977
Student Engagement
5. Correlated factors CFA	948.789*	120	.957	.945	.041 [.039; .044]	222202.209	222706.304	222637.304	222418.052
6. Correlated factors ESEM	189.686*	60	.993	.983	.023 [.019; .027]	221339.616	222282.056	222153.056	221743.150
7. Bifactor-CFA	861.005*	117	.961	.949	.040 [.037; .042]	222087.366	222613.378	222541.378	222312.594
8. Bifactor-ESEM	107.264*	48	.997	.990	.017 [.013; .022]	221254.237	222284.345	222143.345	221695.309
9. Partial Bifactor-CFA	754.740*	112	.966	.954	.038 [.035; .040]	221951.393	222513.935	222436.935	222192.262

Note. * p ≤ .01; CFA: Confirmatory Factor Analysis. ESEM: Exploratory Structural Equation Model; df: degrees of freedom; CFI: Comparative Fit Index; TLI: Tucker-Lewis Index; RMSEA: Root Mean Square Error of Approximation; CI: Confidence Interval; AIC: Akaike Information Criterion; CAIC: constant AIC; BIC: Bayesian Information Criterion; SSBIC: Sample-Size adjusted BIC.

Table 3. Standardized factor loadings (λ) and uniquenesses (δ) of the bifactor-CFA and bifactor-ESEM solutions: academic motivation.

Items	G (λ)	S-INT (λ)	S-EID (λ)	S-EIN (λ)	S-ER (λ)	S-A (λ)	δ
1. INT
Item 1	.745 (.011)**	.556 (.088)**	-.055 (.014)**	-.051 (.011)**	-.098 (.016)**	-.043 (.014)**	.119
Item 2	.557 (.018)**	.284 (.038)**	-.030 (.020)	.005 (.017)	-.057 (.021)**	.159 (.016)**	.579
Item 3	.655 (.014)**	-.070 (.022)**	-.054 (.019)**	.007 (.020)	-.093 (.021)**	.035 (.016)*	.554
Item 4	.753 (.011)**	.006 (.020)	-.096 (.019)**	-.116 (.019)**	.005 (.020)	-.006 (.015)	.410
Item 5	.780 (.012)**	-.154 (.019)**	-.103 (.022)**	-.084 (.019)**	.015 (.023)	.034 (.013)**	.348
Item 6	.749 (.011)**	-.233 (.046)**	.064 (.028)*	.045 (.019)*	-.129 (.026)**	.016 (.014)	.362
Item 7	.666 (.012)**	-.004 (.020)	-.106 (.029)**	.116 (.019)**	-.021 (.021)	.094 (.014)**	.522
Item 8	.627 (.013)**	-.088 (.021)**	.043 (.021)*	.368 (.019)**	-.027 (.022)	.098 (.015)**	.452
ω		.368
2. EID
Item 12	.534 (.013)**	.007 (.017)	.294 (.028)**	.020 (.020)	.324 (.028)**	-.130 (.016)**	.506
Item 13	.490 (.015)**	-.055 (.017)**	.393 (.033)**	-.019 (.020)	.433 (.025)**	-.124 (.015)**	.399
Item 14	.508 (.014)**	-.029 (.012)*	.651 (.075)**	.126 (.016)**	.159 (.032)**	-.088 (.014)**	.269
ω			.604
3. EIN
Item 9	.562 (.015)**	-.013 (.021)	-.019 (.036)	.338 (.028)**	.307 (.025)**	.010 (.015)	.475
Item 10	.584 (.015)**	-.079 (.019)**	.097 (.020)**	.448 (.025)**	.058 (.020)**	.053 (.014)**	.436
Item 11	.526 (.014)**	-.033 (.016)*	.074 (.018)**	.576 (.022)**	.086 (.019)**	.068 (.013)**	.373
ω				.591
4. ER
Item 15	.280 (.021)**	-.054 (.020)**	.133 (.033)**	.051 (.021)*	.449 (.036)**	-.018 (.015)	.696
Item 16	.416 (.016)**	-.036 (.013)**	.308 (.028)**	.079 (.016)**	.654 (.029)**	-.098 (.012)**	.288
Item 17	.241 (.019)**	.036 (.024)	.268 (.025)**	.258 (.023)**	.403 (.028)**	.042 (.017)*	.638
ω					.583
5. A
Item 18	-.329 (.018)**	-.019 (.016)	-.089 (.016)**	-.010 (.016)	-.015 (.018)	.640 (.017)**	.474
Item 19	-.143 (.021)**	.001 (.016)	-.090 (.019)**	.033 (.016)*	-.001 (.018)	.687 (.017)**	.498
Item 20	-.180 (.020)**	.017 (.013)	-.036 (.018)*	.070 (.015)**	-.064 (.016)**	.708 (.017)**	.456
ω	.923					.744

Note. * p ≤ .05; ** p ≤ .01; ESEM: Exploratory Structural Equation Model; INT: Intrinsic motivation; EID: Extrinsic-Identified regulation; EIN: Extrinsic-Introjected regulation; ER: External regulation; A: Amotivation; G: Global dimension; S: Specific facet; Target (main) factor loadings are marked in bold.

Table 4. Standardized factor loadings (λ) and uniquenesses (δ) of the partial bifactor-CFA solution: student engagement.

Items	G (λ)	S (λ)	δ
1. BE
Item 1	.615 (.021)**	.518 (.028)**	.353
Item 2	.697 (.019)**	.635 (.027)**	.111
Item 3	.691 (.017)**	.311 (.029)**	.425
ω		.707
2. BB
Item 4	-.338 (.025)**	.558 (.020)**	.575
Item 5	-.480 (.023)**	.584 (.021)**	.428
Item 6	-.487 (.021)**	.728 (.019)**	.232
ω		.739
3. ES
Item 7		.841 (.011)**	.293
Item 8		.793 (.013)**	.371
Item 9		.695 (.015)**	.517
ω		.821
4. EL
Item 10		.790 (.021)**	.375
Item 11		.638 (.021)**	.593
Item 12		.506 (.020)**	.744
ω		.686
5. CS
Item 13	.535 (.017)**	.223 (.026)**	.664
Item 14	.525 (.019)**	.474 (.029)**	.499
Item 15	.609 (.018)**	.561 (.038)**	.315
ω		.517
6. CA
Item 16	.571 (.020)**	.244 (.028)**	.614
Item 17	.497 (.021)**	.662 (.039)**	.315
Item 18	.566 (.019)**	.531 (.034)**	.397
ω	.848	.609

Note. * p ≤ .05; ** p ≤ .01; CFA: Confirmatory Factor Analysis. ESEM: Exploratory Structural Equation Model; BE: Behavioral engagement: Effort/attention; BB: Behavioral engagement: Boredom/distraction; ES: Emotional engagement: Social; EL: Emotional engagement: Learning; CS: Cognitive engagement: Strategies; CA: Cognitive engagement: Autoregulation; G: Global dimension; S: Specific facet.

Table 5. Latent associations between academic motivation and school engagement.

	Academic motivation						Emotional engagement		R^2
Outcomes	G-factor β (SE)	Specific-INT β (SE)	Specific-EID β (SE)	Specific-EIN β (SE)	Specific-ER β (SE)	Specific-A β (SE)	ES β (SE)	EL β (SE)
Model 1 – Without mediation
Engagement G-factor	.712 (.075)**	.014 (.065)	-.133 (.057)*	.278 (.052)**	.011 (.079)	-.232 (.074)**			.657
Specific-BE	-.195 (.193)	.038 (.076)	.144 (.066)*	-.300 (.075)**	-.003 (.092)	-.137 (.103)			.169
Specific-BB	-.167 (.126)	-.125 (.047)**	-.065 (.049)	.111 (.055)*	.098 (.058)	.155 (.058)**			.094
Specific-CS	-.371 (.245)	-.153 (.092)	.174 (.089)	-.384 (.084)**	-.069 (.128)	.105 (.137)			.355
Specific-CA	-.366 (.192)	-.167 (.073)*	.137 (.075)	-.335 (.076)**	.150 (.091)	-.132 (.126)			.333
ES	.232 (.024)**	.116 (.033)**	.065 (.030)*	-.020 (.025)	.039 (.029)	-.168 (.027)**			.102
EL	.150 (.022)**	-.051 (.030)	-.039 (.029)	.155 (.026)**	-.007 (.028)	.058 (.028)*			.054
Model 3 – With mediation
Engagement G-factor	.642 (.075)**	.007 (.059)	-.130 (.057)*	.242 (.051)**	.015 (.079)	-.224 (.069)**	.114 (.052)*	.210 (.057)**	.689
Specific-BE	-.189 (.185)	.049 (.072)	.151 (.069)*	-.294 (.073)**	-.009 (.097)	-.130 (.098)	-.098 (.071)	-.118 (.060)	.209
Specific-BB	-.174 (.136)	-.148 (.049)**	-.087 (.055)	.118 (.058)*	.097 (.065)	.157 (.061)*	.226 (.054)**	.172 (.039)**	.152
Specific-CS	-.322 (.226)	-.159 (.089)	.159 (.089)	-.344 (.079)**	-.076 (.125)	.110 (.123)	-.016 (.095)	-.167 (.075)*	.353
Specific-CA	-.352 (.175)*	-.189 (.070)**	.118 (.076)	-.301 (.073)**	.137 (.091)	-.106 (.112)	.106 (.088)	-.156 (.063)*	.346
ES	.233 (.024)**	.128 (.035)**	.069 (.031)*	-.021 (.025)	.034 (.029)	-.170 (.027)**	–	–	.106
EL	.149 (.022)**	-.057 (.031)	-.039 (.029)	.155 (.026)	-.006 (.028)	.060 (.028)*	–	–	.055

Note. * p < .05; ** p < .01; β: Standardized regression coefficient; SE: standard error of the coefficient INT: Intrinsic motivation. EID: Extrinsic-Identified regulation; EIN: Extrinsic-Introjected regulation; ER: External regulation; A: Amotivation; BE: Behavioral engagement: Effort/attention; BB: Behavioral engagement: Boredom/distraction; ES: Emotional engagement: Social; EL: Emotional engagement: Learning; CS: Cognitive engagement: Strategies; CA: Cognitive engagement: Autoregulation.

Figure 3. Result summary from the final predictive model (partial mediation).

Note. Only statistically significant paths are shown (p ≤ .05); positive paths are represented by full arrows whereas negative paths are represented by dotted-arrows; G: Global factor; INT: Intrinsic motivation; EIN: Extrinsic-identified regulation; EID: Extrinsic-introjected regulation. ER: External regulation. A: Amotivation. BE: Behavioral engagement: Effort/attention; BB: Behavioral engagement: Boredom/distraction; ES: Emotional engagement: Social; EL: Emotional engagement: Learning; CS: Cognitive engagement: Strategies; CA: Cognitive engagement: Autoregulation.