Factor Structure and Longitudinal Measurement Invariance of the Achievement Goal Questionnaire with a Korean Adolescent Sample

Abstract

For decades, achievement goal theory has been extensively used, but empirical research still requires a clearer understanding of the underlying factors conceptualized and measured during secondary school periods. In light of the increasing use of longitudinal studies in motivation research, this study aims to investigate the longitudinal measurement invariance of the Achievement Goal Questionnaire (AGQ) with the longitudinal panel data of 5071 adolescents. Findings support the consistent use of the 2×2 model across eighth to eleventh grades, although inter-factor correlations were inflated at eleventh grade. Partial strict longitudinal measurement invariance was supported for testing equivalence between the tenth and eleventh grades. Regarding the relations to other variables, the four individual factors of achievement goals have distinct properties in relation to other variables as theoretically hypothesized; and the patterns of the relationship were stable from eighth to eleventh grades.

Keywords

achievement goals longitudinal measurement invariance confirmatory factor analysis adolescence KELS:2005

Achievement goal theory (Ames, 1992; Dweck & Leggett, 1988; Maehr & Midgley, 1991; Nicholls, 1984), also referred to as goal orientation theory, has been extensively investigated to explain individuals’ achievement motivation and learning processes. During the past four decades, the conceptual framework of the achievement goals has been modified, expanded, and still under debate (e.g., Dweck, 1986; Elliot & McGregor, 2001; Elliot et al., 1999; Nicholls, 1984; Pintrich, 2000). The focus of the debates has been the factor structure of achievement goals. The pioneer researchers of the theory suggested two overarching goals, mastery goals and performance goals, depending on the focus of competence (i.e., dichotomous model). The model has evolved to the trichotomous model, the 2 × 2 model, and the 3 × 2 model by adding other dimensions into the prior models (Elliot & Harackiewicz, 1996; Elliot & McGregor, 2001; Elliot et al., 1999, 2011).

Among the achievement goal models, the 2 × 2 model (Elliot & McGregor, 2001) has been validated with diverse samples across different ages and countries. In the 2 × 2 model, the mastery goals and the performance goals have two subtypes based on the valence of competence, approach and avoidance; thus, the model includes mastery-approach goals (attaining the task-based competence), performance-approach goals (attaining normative competence), mastery-avoidance goals (avoiding task-based incompetence), and performance-avoidance goals (avoiding normative incompetence). The 2 × 2 model has been the most frequently used in the literature of achievement goals, but it has been criticized for its uncertain differentiation among factors, poor item specification, and mixed results regarding the relations between the factors and other variables in educational settings (Elliot & Murayama, 2008; Hulleman et al., 2010).

Furthermore, empirical research still requires a clear understanding of the underlying factors conceptualized and measured during secondary school periods. Previous studies have addressed several important issues concerning the current conceptualizations and measures of the 2×2 achievement goals (e.g., Baranik et al., 2010; DeShon & Gillespie, 2005; Elliot & Murayama, 2008; Hulleman et al., 2010). Mastery-avoidance goals are usually represented in those who have already reached a certain level of competence and are anxious about losing their competence (Bong, 2009; DeShon & Gillespie, 2005; Elliot, 2005). Thus, the perceptions of the factor structure may differ by the experience and the maturity of different age groups of students. Such changes are conceptually associated with response shift, which refers to a change in meaning or structure of the measured constructs over time (Oort, 2005; Sprangers & Schwartz, 1999). In particular, during adolescence, students’ perceptions of achievement goals may change over time regarding their meaning, values, and importance. Therefore, it is necessary to investigate longitudinal changes in perceiving the factor structure of achievement goals during adolescence.

Factor Structure of Achievement Goals

Achievement goal theory aims to explain achievement motivation that drives individuals to develop or demonstrate their competence. The achievement goal theorists have attempted to identify psychological constructs explaining purposes and reasons why individuals engage in a certain task or behavior (Pintrich, 2003). Based on the dichotomous model (Ames, 1992; Dweck, 1986; Maehr & Midgley, 1991), individuals with mastery goals tend to understand concepts, develop new skills, prefer challenging tasks, attribute success to their efforts, and evaluate their success according to self-improvement (Ames, 1992; Anderman & Wolters, 2006; Midgley et al., 1998; Pintrich, 2000). On the other hand, individuals with performance goals are concerned about how others judge them and use comparative social standards desiring to have better grades than others (Ames, 1992; Anderman & Wolters, 2006; Midgley et al., 1998; Pintrich, 2000). However, since the dichotomous model primarily focuses on attaining success (Elliot & Harackiewicz, 1996), individuals’ achievement motivation is not sufficiently explained in cases that avoid a negative possibility or undesirable event (Atkinson, 1957; McClelland, 1951).

Given the limitation of the dichotomous model, Elliot and Harackiewicz (1996) expanded the framework to the trichotomous model by dividing performance goals into performance-approach and performance-avoidance goals; but the mastery goal was yet divided into the two subtypes. Individuals with performance-approach goals aim to show their abilities to others and have better grades than others, and individuals with performance-avoidance goals focus on not showing their lack of abilities to others. Generally, performance-avoidance goals are associated with maladaptive learning outcomes such as low levels of self-efficacy, interest, and enjoyment, high levels of anxiety, and adopting surface learning strategies (e.g., rehearsal and memorization) (Ames, 1992; Anderman & Wolters, 2006; Elliot & Church, 1997; Middleton & Midgley, 1997; Ryan et al., 2001; Skaalvik, 1997; Wolters et al., 1996).

Later, the approach-avoidance notion was applied to mastery goals (Elliot & McGregor, 2001); therefore, the 2 × 2 achievement goal factor structure was proposed (Elliot, 1999; Elliot & McGregor, 2001). Achievement goal theorists have contended that adopting mastery-approach goal is the most optimal for students’ learning because it is significantly related to adaptive learning outcomes such as a high level of academic self-efficacy, school satisfaction, interest, enjoyment, achievement, and using deep cognitive strategies (Ames, 1992; Anderman & Wolters, 2006; Bandalos et al., 2003; Pintrich, 2000; Rawsthorne & Elliot, 1999; Ryan et al., 2001; Wolters et al., 1996). Individuals with mastery-avoidance goals are worried about losing their abilities and not mastering new skills. Generally, the mastery-avoidance goal is associated with maladaptive learning outcomes (e.g., Baranik et al., 2010; Van Yperen et al., 2009). For example, a meta-analysis study (Baranik et al., 2010) showed that mastery-avoidance goal is negatively related to learners’ performance and adaptive help-seeking behaviors (e.g., asking for help and feedback).

Since the 2 × 2 framework was proposed, the constructs have been validated with factor analysis approaches (e.g., Baranik et al., 2007; Bong, 2009; Elliot & Murayama, 2008; Korn & Elliot, 2016; Murayama et al., 2009). Elliot and Murayama (2008) validated the 2 × 2 factor structure at the college level by comparing it to different combinations of the 2 × 2 model factors. The results demonstrated that the 2 × 2 model was more suitable than others (e.g., dichotomous and trichotomous models). This finding has also been replicated to various age ranges, from elementary to college students (e.g., Cury et al., 2006; Fryer & Elliot, 2007; Madjar et al., 2011), and across different cultures, such as individualistic (Baranik et al., 2007; Corker et al., 2013; Meissel & Rubie Davies, 2016; Murayama et al., 2009) and collectivistic cultures (Cheng & Phillipson, 2013; Meissel & Rubie-Davies, 2016; Murayama et al., 2009).

Despite accumulated studies validating the factor structure of the 2 × 2 achievement goals, few studies have investigated perceptual changes in the 2 × 2 structure across different ages with a longitudinal perspective. Some researchers have attempted to investigate how the mean-levels of students’ achievement goals change across different ages (e.g., Anderman & Midgley, 1997; Meece & Miller, 2001; Middleton et al., 2004; Pajares & Cheong, 2003; Shim et al., 2008); yet most of these studies were descriptive or showed the mean changes of achievement goals. Those studies did not show the changes in perceiving and understanding the factors of achievement goals, which can be captured with longitudinal invariance tests (for exceptions, see Corker et al., 2013; Schwinger et al., 2016). Given that adolescence is a critical period during which develop achievement motivation, it is crucial to examine the invariance of the goal constructs to corroborate whether the development of achievement goals is derived from students’ internal changes or measurement issues.

Longitudinal Measurement Invariance

Testing longitudinal measurement invariance is required in longitudinal research to conclude that the mean changes are due to true changes of individuals over time. It is imperative when applying the latent mean comparison techniques (e.g., latent growth curve modeling, autoregressive panel modeling) with longitudinal data. Longitudinal measurement invariance tests examine response shifts, systematic changes in the meaning or the structure of the measured constructs over time (Oort, 2005; Sprangers & Schwartz, 1999). In other words, it examines whether the respondents invariantly perceive the factor structure of a psychological construct across different time points of measures. For example, a four-factor model of the achievement goals is supported by younger individuals while it may not be supported along with their psychological and intellectual growths as their understanding of each factor changes. Thus, this method is appropriate to investigate changes in students’ perceptions and understanding of achievement goal constructs across different grade levels of adolescence.

There are three types of response shifts: reconceptualization is a change in the meaning of the item content, recalibration is a change in the meaning of the scale values for item response, and reprioritization is a change in the importance of the item (Oort, 2005). Oort (2005) discussed analytic procedures of delineating the three types of response shifts using structural equation modeling. Reconceptualization is tested by examining changes in salient factor loadings across time (i.e., configural invariance), recalibration is tested by examining changes in item intercepts (i.e., uniform recalibration or scalar invariance) and residual variances (i.e., non-uniform recalibration), and reprioritization is tested by examining differences in the sizes of factor loadings (i.e., metric invariance). For the analysis of longitudinal measurement invariance based on structural equation modeling, an augmented covariance matrix using a single group approach, which is estimated from the measures across all different time points, is used (Brown, 2015). Such an analytic technique involves examining the lagged correlations among variables measured in different waves as well as within-time covariances (Vandenberg & Lance, 2000).

Studies examining the longitudinal measurement invariance of achievement goals with adolescent data are scarce. Corker et al. (2013) is the only study we found that confirmed strong factorial invariance of the 2 × 2 model with a college student sample. Despite a lack of studies, the significance of testing longitudinal measurement invariance of the achievement goal structure is apparent given that unclear factor structure has been theoretically and empirically suggested with adolescents’ ages. Their perceptions of the achievement goal structure may be significantly different across the ages because of their competency levels to recognize the mastery avoidance or the redundancy of the two dimensions involved in the 2 × 2 model.

Achievement Goal Factors in Relation to Other Variables

The mastery-avoidance goal entails counterintuitive components as shown by the term: a potential negative valence (i.e., avoidance) with task-mastery such as avoiding misunderstanding, losing abilities, and forgetting knowledge (Elliot, 1999; 2005; Elliot & McGregor, 2001; Elliot & Murayama, 2008; Murayama et al., 2011). Jagacinski et al. (2008) argued that the concept of mastery-avoidance goals was redundant with mastery-approach and performance-avoidance goals. Such an unclear factor structure might be associated with “bloated specifics” (Cattell & Tsujioka, 1964), which occurs when the items have inflated intercorrelations because of similar wordings.

To prove the utility of each factor in the 2 × 2 achievement goal model as a distinct construct, the factors of achievement goals should be examined in relation to other variables that are known to relate to the factors of achievement goals theoretically. In a meta-analysis study reviewing 54 empirical studies (Baranik et al., 2010), mastery-avoidance goals correlated more strongly to interests and less to competitiveness than performance-avoidance goals. Compared to approach goals, avoidance goals were positively related to negative affect (e.g., anxiety and stress), but had weaker correlations with the need for achievement (e.g., self-regulation motivation), and perceived competence (e.g., self-efficacy). Mastery-approach and mastery-avoidance goals were associated less with seeking interpersonal competitions than performance goals. Learning strategies have also been examined concerning achievement goals. Approach goals are known to facilitate the use of deep learning, which is characterized by elaboration and metacognition, whereas avoidance goals are associated with surface learning strategies, such as the use of rehearsal (Lau et al., 2008; Liem et al., 2008). To summarize, it is hypothesized that a mastery-avoidance goal relates to negative affect; but it does not relate to self-efficacy, self-regulation motivation, and achievement compared to other constructs of achievement goals.

The conceptual differentiation and prevalence of mastery-avoidance goals among younger people have also been controversial because mastery-avoidance goals are usually represented in those who have already reached a certain level of competence and are anxious about losing their competence. Thus, the construct is less represented in younger people (Bong, 2009; DeShon & Gillespie, 2005; Elliot, 2005). Sideridis and Mouratidis (2008) found that mastery-avoidance was not represented among middle school students in physical education. It is a contrast to the findings of other empirical studies that the conceptual differentiation of mastery-avoidance goals was possible among high school students and college undergraduate students (e.g., Conroy et al., 2003; Finney et al., 2004; Madjar et al., 2011). Therefore, further investigations on how the relationship between mastery-avoidance and other variables changes over time with adolescents would make the utility of mastery-avoidance clearer.

The Present Study

This study aims to investigate the longitudinal measurement invariance of the AGQ and the relations of the factors to other theoretically related variables with a sample of adolescents. We first compared the 2 × 2 factor model with the trichotomous model across eighth to eleventh grades in Korea. Using the longitudinal measurement invariance tests, we also investigated whether adolescents’ perceptions and understanding of the individual factors were invariant and consistent across the different time points. The focus of this study was to examine the factor structure of the achievement goal constructs across different time points; however, we also explored the relations of the four factors to other theoretically related variables. This enabled us to examine the utility of each of the four factors distinctly across the different time points.

The specific purposes of this study were to (1) assess the factor structure of the achievement goal framework using confirmatory factor analysis (CFA) across the four different time points, (2) examine the longitudinal measurement invariance of achievement goal constructs, and (3) explore the unique properties of achievement goals compared to other related variables.

Method

Sample

This study used data from the Korean Educational Longitudinal Study: 2005 (KELS:2005; Kim et al., 2010). KELS:2005 includes nationally representative panel data from Korean secondary school students who were followed regarding their cognitive and affective development until high school graduation. A total of 6908 seventh grade students from 150 public and private schools participated in the initial year of the study, and data were collected annually for the next 6 years, ending in twelfth grade. In Korea, middle school consists of seventh through ninth grades, and high school includes tenth through twelfth grades. We used the KELS:2005 data from Wave 2 (eighth grade) through Wave 5 (eleventh grade) because the Achievement Goals Questionnaire (AGQ) was measured only for the four waves.

Among the panel of 6908 seventh-grade students, about 17% dropped out by Wave 5 (i.e., approximately 83% of the initial panel remained). Using Heckman’s (1979) selection model estimation with covariates (e.g., school type, family income, and gender), the lambda coefficient was not significant (λ = 8.00, p =.96), which implied no selection bias based on the covariates. Therefore, responses from participants who dropped out from the sample before Wave 5 and those who had missing data on one of the dependent variables were excluded from the final sample, which included 5071 students. For the convenience of interpretation, we henceforth refer to Wave 2 of the original dataset as Wave 1 (data of the eighth grade) and Wave 5 of the original dataset as Wave 4 (data of the eleventh grade).

Measures

In addition to the achievement goal constructs, we also measured theoretically related variables to explore the external relationships of achievement goal constructs, including global self-efficacy, external and intrinsic motivation of self-regulated motivation, and elaboration of the study process.

Achievement goals. KELS:2005 includes the AGQ (Elliot & McGregor, 2001), which measures four types of achievement goals: mastery-approach, mastery-avoidance, performance-approach, and performance-avoidance goals. Elliot and McGregor (2001) reported Cronbach’s $α$ estimates ranging from .83 to .92 for the four-factor AGQ with college students samples. Model fit statistics (the root-mean square error of approximation [RMSEA] = .042; Tucker-Lewis Index [TLI] = .99; the comparative fit index [CFI] = .99) supported the 2 × 2 model.

Global self-efficacy. Global self-efficacy is the perception of self-efficacy to individuals’ beliefs about their own ability to perform specific tasks when facing adverse circumstances in general academic domains (OECD, 2019). In the KELS: 2005 data sets, the variable was measured with four items over the 4 years, grades 8 through 11. The items were revised based on the ELS:2002 surveys, and the sample item is “I’m certain I can understand the most complex material presented by my teacher.” The internal consistency reliability (Cronbach’s $α$ ) with the current sampled data was ranged from .81 to .84 for the four waves.

Intrinsic and external regulation. Intrinsic and external regulations were measured with the Korean Academic Self-Regulation Questionnaires (Kaplanet al., 2002) developed based on the Academic Self-Regulation Questionnaires (Ryan & Connell, 1989). The sample items are “I study because it’s fun” for intrinsic motivation; and “I study because my parents will give me a reward” for external regulations. For the first and second waves, six items were used to measure each construct; and for the fourth wave, four items were used per construct. The internal consistency reliability coefficients (Cronbach’s $α$ ) were .76–.87 for intrinsic motivation and .81–.86 for external regulation for the three waves.

Elaboration. Elaboration is a cognitive learning strategy that clarifies and specifies the information connecting to prior knowledge and related information. KELS:2005 uses four items developed based on the Motivated Strategies for Learning Questionnaire (MSLQ; Pintrinch, 2003). A sample item is “when I study, I try to connect with what I already know.” The internal consistency reliability coefficients (Cronbach’s $α$ ) were .63–.77 for the four waves.

Analysis

We compared the trichotomous model (Elliot & Church, 1997; Middleton & Midgley, 1997) with the 2 × 2 model (Elliot & McGregor, 2001), where the mastery-avoidance construct is added to the trichotomous model. The two competing models were estimated with the data of four waves separately. We used multiple model fit indices, including CFI, TLI, SRMR, and RMSEA, to compare the models. Estimated values of CFI and TLI greater than .90 and values of RMSEA smaller than .08 are conventionally regarded as implying adequate model fit (Vandenberg & Lance, 2000; cf. Hu & Bentler, 1999 for stricter criteria when continuous indicators are used).

After confirming the factor structure of the AGQ, we performed longitudinal measurement invariance tests with a single-sample approach. As recommended by Brown (2015) and Chen et al. (2005), we conducted four sequential invariance tests: (a) test of equal form, (b) test of equal factor loadings, (c) test of equal indicator intercepts, and (d) test of equal indicator error variance. Each pair of two sequential testing models was nested; thus, the two sequential models were compared to evaluate the measurement invariance. Given the results indicating a notable discrepancy in model fits and internal consistency estimates between Waves 3 and 4, we focused on comparing the two waves because post-hoc tests and interpretation of measurement invariance tests are cumbersome with three or more groups (Brown, 2015). Due to the sensitivity of chi-square tests to large sample sizes (Sass, 2011), we primarily used difference tests of other model fit statistics. Comparing two sequential nested models, a change greater than .01 in ΔCFI and greater than .015 in ΔRMSEA was regarded as indicating non-invariance of the more restricted model (Chen, 2007). Corrected chi-square difference tests using the DIFFTEST option (Muthén & Muthén, 1998–2015) in Mplus are also presented. Any test indicating non-invariance was followed by partial measurement invariance tests, which allow the indicator with the highest modification index to be subsequently unconstrained (Brown, 2015).

The first step of the testing was a test of equal form, which is used to establish the baseline second-order factor model with no constraint (Figure 1). We conjointly estimated two separate factor models of each wave, specifying each pair of lagged correlations between indicators of Wave 3 and Wave 4. If the baseline model was supported with acceptable levels of model fit, the second and third steps were conducted with constraints. Nonsignificant results indicated that the unit of measurement of the underlying factors is equivalent across the waves. The fourth step placed equal constraints on all indicator intercepts. Invariant results meant that the same origin of measurement exists across the waves (Cheung, 2008). If the tests of factor loadings and indicator intercepts were all invariant, the difference between latent means across the waves could be regarded as a true change in the constructs (Brown, 2015). In the final step, all error variances were restricted to be equal. Nonsignificant results indicated that the items have equal measurement errors. We also estimated stability coefficients across the waves. Stability refers to the strength of association between two or more waves when the same construct is repeatedly measured for the same person, and the across-time correlations in the autoregressive paths are used to estimate the coefficients (Little et al., 2009).

Figure 1.

Single-group testing model of longitudinal measurement invariance across waves 3 and 4. Note. W3 = Wave 3; W4 = Wave4; MP = mastery-approach; MV = mastery-avoidance; PP = performance-approach; PV = performance-avoidance.

Results

Descriptive Statistics

Table 1 presents descriptive statistics and estimates of internal consistency for each of the waves used in this study (α = .73 to .80 for mastery-approach goals; α = .71 to .88 for mastery-avoidance goals; α = .76 to .80 for performance-approach goals; α = .76 to .85 for performance-avoidance goals). Internal consistency coefficients decreased at Wave 4, implying that the participant’s responses for each construct at Wave four were not as consistent as those at other waves. All univariate skewness and kurtosis estimates were in the range of acceptable levels of univariate normality suggested by Kline (1998). However, given the multivariate non-normality (multivariate kurtosis = 48.11–64.23, p < .001), we used a robust maximum likelihood estimator with standard errors and mean- and variance-adjusted chi-square test statistic (MLMV) for further analyses.

Table 1.

Descriptive Statistics and Internal Consistency Coefficients Across Four Waves (N = 5071 for Each Wave)

	Wave 1 (Grade 8)					Wave 2 (Grade 9)					Wave 3 (Grade 10)					Wave 4 (Grade 11)
Item	M	SD	Skew	Kurt	α	M	SD	Skew	Kurt	Α	M	SD	Skew	Kurt	Α	M	SD	Skew	Kurt	α
MP1	2.83	0.68	−0.25	0.06	0.79	2.83	0.67	−0.37	0.37	0.80	3.00	0.62	−0.20	0.25	0.75	2.91	0.64	−0.32	0.46	0.73
MP2	2.91	0.70	−0.29	0.03		2.84	0.69	−0.25	0.02		3.03	0.66	−0.23	−0.11		3.19	0.67	−0.50	0.22
MP3	3.02	0.70	−0.41	0.19		2.95	0.72	−0.39	0.08		3.17	0.66	−0.42	0.15		3.00	0.63	−0.55	1.30
MV1	2.65	0.76	0.02	−0.44	0.86	2.57	0.74	0.07	−0.35	0.88	2.60	0.73	0.18	−0.41	0.87	2.89	0.66	−0.39	0.50	0.71
MV2	2.58	0.77	0.02	−0.41		2.54	0.75	0.00	−0.35		2.59	0.75	0.04	−0.36		2.50	0.66	−0.04	−0.22
MV3	2.47	0.78	0.18	−0.37		2.43	0.75	0.18	−0.28		2.48	0.74	0.20	−0.29		2.81	0.70	−0.29	0.04
PP1	3.14	0.73	−0.55	0.11	0.80	3.08	0.74	−0.53	0.10	0.80	3.29	0.67	−0.63	0.24	0.80	2.54	0.74	0.13	−0.35	0.76
PP2	2.83	0.79	−0.12	−0.60		2.72	0.78	−0.04	−0.51		2.88	0.76	−0.13	−0.58		3.15	0.72	−0.61	0.34
PP3	2.61	0.79	0.15	−0.55		2.54	0.76	0.18	−0.40		2.69	0.73	0.14	−0.53		2.69	0.75	−0.16	−0.27
PV1	2.34	0.75	0.19	−0.26	0.83	2.34	0.77	0.15	−0.32	0.85	2.42	0.76	0.06	−0.36	0.81	2.59	0.76	-0.18	−0.28	0.76
PV2	2.34	0.74	0.18	−0.24		2.34	0.75	0.10	−0.31		2.41	0.74	0.10	−0.27		2.66	0.73	−0.19	−0.19
PV3	2.51	0.79	−0.01	−0.44		2.50	0.79	−0.05	−0.44		2.66	0.75	-−0.21	−0.23		2.46	0.78	0.03	−0.41
	Multivariate kurt.=56.64^***					Multivariate kurt.=61.23^***					Multivariate kurt.=48.11^***					Multivariate kurt.=54.00^***

Note. MP = mastery-approach, MV = mastery-avoidance, PP = performance-approach; PV = performance-avoidance. ^*** p < .001.

Factor Structure of the Achievement Goal Framework

The two competing factor models were fitted to the individual data sets of the four waves. Fit indices for both models are presented in Table 2. Although all model fit statistics indicated acceptable levels of model fit for both models, the four-factor model had a slightly better fit with the data (CFI = .94 to .96; TLI = .92 to .94; RMSEA = .060 to .066; SRMR = .041 – .045) than the three-factor model (CFI = .94 to .96; TLI = .91 to .94; RMSEA = .070 to .082; SRMR = .042 – .051). In addition, inter-factor correlations between mastery-avoidance and three other individual factors imply that mastery-avoidance is not a redundant but reasonably unique factor with the three other factors (Table 3). Standardized coefficients of the inter-factor correlations were .51, .54, .48, and .87 with mastery approach; .49, .50, .46, and .77 with performance approach; .49, .51, .51, and .70 with performance-avoidance, for individual waves. Thus, we concluded that the 2 × 2 model is well fitted with a sample of Korean secondary school students. The estimated factor loadings of the 2 × 2 model overall waves are presented in Appendix 1.

Table 2.

Model Fit Indices for the Factor Models (n = 5071).

Wave	Trichotomous Model						2 × 2 Model
Wave	χ ²	df	CFI	TLI	RMSEA [90% CI]	SRMR	χ ²	df	CFI	TLI	RMSEA [90% CI]	SRMR
1	612.31^***	24	0.96	0.94	0.070 [0.065, 0.074]	0.042	932.01^***	48	0.96	0.94	0.060 [0.057, 0.064]	0.042
2	833.64^***	24	0.95	0.92	0.082 [0.077, 0.086]	0.051	1065.99^***	48	0.96	0.94	0.065 [0.061, 0.068]	0.045
3	692.40^***	24	0.95	0.93	0.074 [0.069, 0.079]	0.045	946.29^***	48	0.96	0.94	0.061 [0.057, 0.064]	0.041
4	760.07^***	24	0.94	0.91	0.078 [0.073, 0.083]	0.049	1104.29^***	48	0.94	0.92	0.066 [0.063, 0.069]	0.045

***p < .001.

Table 3.

Inter-Factor Correlations.

Factors		W1	W2	W3	W4
Trichotomous Model
MP	PP	0.56	0.54	0.54	0.66
MP	PV	0.26	0.27	0.25	0.49
PP	PV	0.51	0.64	0.57	0.97
2 × 2 Model
MP	MV	0.51	0.54	0.48	0.87
	PP	0.55	0.54	0.53	0.67
	PV	0.27	0.27	0.26	0.50
MV	PP	0.49	0.50	0.46	0.77
MV	PV	0.49	0.51	0.51	0.70
PP	PV	0.52	0.64	0.58	0.97

Note. All estimated coefficients are standardized and statistically significant at alpha level of .05. MP = mastery-approach; MV = mastery-avoidance; PP = performance-approach; PV = performance-avoidance.

However, the model fit of Wave 4 (eleventh grade) was remarkably degraded compared to the other waves. Although the estimated factor loadings of Wave 1, Wave 2, and Wave 3 were almost equivalent to each other, the estimates of Wave 4 lightly decreased compared to other waves (Appendix 1). Further, the inter-factor correlations were notably inflated at Wave 4, as presented in Table 3. Given the remarkable changes of internal consistency coefficients, inter-factor correlations, and factor model fits between Wave 3 and Wave 4, we posited that there might be a significant difference in factor structure during the transition from tenth grade (Wave 3) to eleventh grade (Wave 4).

Longitudinal Measurement Invariance and Stability Coefficients

We performed longitudinal invariance tests with the 2 × 2 factor model as the baseline model. Table 4 summarizes the results of the sequential longitudinal factor invariance tests. Equal form tests yielded acceptable levels of model fits, CFI = .94, TLI = .92, RMSEA = .04, implying that the Korean secondary students perceived equivalent conceptual frameworks of achievement goals over Waves 3 and 4. The model of equal factor loadings was invariant (ΔCFI = .009, ΔRMSEA = .011), which supports the weak assumption of longitudinal measurement invariance and implies that the students used equal units of the scale over two waves. However, constraining all indicator intercepts resulted in significant difference in model fits (ΔCFI = .129, ΔRMSEA = .033). Partial measurement invariance tests indicated that the intercepts of four items (MP2, MV2, PP1, and PV3) were non-invariant over the two waves. This result implies that the students used different scale origins for the four items across the two waves. After freely estimating the four indicator intercepts, the partial invariance of equal indicator intercepts was satisfied (ΔCFI = .008, ΔRMSEA = .002). The indicator error variance was also invariant (ΔCFI = .006, ΔRMSEA = .001), which supports the partial strict longitudinal invariance. This implies that the majority of factor loadings, indicator intercepts, and error variances were equivalent across the two waves; thus, we conclude that the AGQ measured the constructs in an invariant (i.e., equivalent and consistent) way when used with Korean secondary school students. The stability coefficients (r) over the two waves were .57 for mastery-approach, .27 for mastery-avoidance, .61 for performance-approach, and .41 for performance-avoidance based on the partial strict longitudinal invariance, which indicates that stability was held between two waves.

Table 4.

Longitudinal Measurement Invariance Test Results.

	Adjusted-χ²	df	Δ χ²	Δdf	CFI	TLI	RMSEA	ΔCFI	ΔTLI	ΔRMSEA
Configural	2938.48***	212			0.940	0.921	0.040
Metric	3331.15***	220	459.32	8	0.931	0.913	0.051	0.009	0.008	0.011
Scalar	9135.21***	228	7452.39	8	0.802	0.761	0.084	0.129	0.152	0.033
Partial scalar	3688.84***	224	442.92	4	0.923	0.905	0.053	0.008	0.008	0.002

Note. For testing partial equal indicator intercepts, all indicator intercepts except MP2, MV2, PP1, and PV3 were constrained. *** p < .001.

Relations to Other Variables

In addition to the factor structure, we explored whether the individual four factors are distinctive in terms of the hypothetical relationships with other variables over the 4 years. Table 5 presents the results. Based on our SEM models, the relations to other variables were consistent through Wave 1 to Wave 3. Mastery-approach was positively associated with global self-efficacy,

β = .43 - .45

; intrinsic motivation,

β = .42 - .46

; and elaboration,

β = .36 - .37

for the three waves. Mastery-avoidance was negatively associated with global self-efficacy,

β = - .08

, implying that mastery-avoidance, avoiding the loss of mastery, at these grade levels (8th–10th) would be related to a lack of confidence in general academic domains. Performance-approach was positively related to global self-efficacy,

β = .11 - .14

. However, in contrast to the majority of the findings of the prior studies, performance-approach was not significantly related to external motivation during eighth to tenth grades. Instead, performance-avoidance was significantly associated with external motivation,

β = .27 - .28

, for the periods. This hypothetical nomological network was well-fitted to the sampled data of Waves 1 to 3, CFI = .96, .96, .95; TLI =.93, .94, .93; RSMEA = .049, .051, .056; SRMR = .03, .03, .03 for the three waves, respectively.

Table 5.

Standardized Path Coefficients.

	W1				W2				W3				W4
	MP	MV	PP	PV	MP	MV	PP	PV	MP	MV	PP	PV	MP	MV	PP/PV
GSE	0.43	-0.08	0.11	−0.02	0.45	−0.08	0.14	−0.05	0.43	-0.08	0.14	-0.05	0.09	0.66	-0.35
EX	−0.26	0.04	0.04	0.27	−0.23	0.03	0.02	0.28	—	—	—	—	-0.31	-0.18	0.51
IN	0.46	0.01	0.04	0.08	0.42	0.08	0.07	0.03	—	—	—	—	0.05	0.87	-0.42
ELB	0.37	0.02	0.03	0.08	0.38	0.05	<0.01	0.07	0.36	0.01	0.02	0.04	0.32	0.28	-0.18

Note. Bold represents statistically significant results at alpha level of .05. GSE = global self-efficacy, EX = external regulation, IN = intrinsic motivation, ELB = elaboration.

Contrary to the results for the three waves, the hypothetical structural equation model did not fit the data of Wave 4 (Grade 11), which involved a non-positive definite of the latent variable covariance matrix. A plausible cause for this problem was an inflated inter-factor correlation between performance-approach and performance-avoidance for Wave 4, std. coefficient = .97, implicating that the two factors may be identical or not significantly differentiated. Thus, we had to merge the items of the two factors into a factor and specify with a three-factor model, consisting of mastery-approach, mastery-avoidance, and performance approach/avoidance (PP/PV in Table 5). The model fits were ranged in adequate levels, CFI = .95, TLI = .90, RSMEA = .057, and SRMR = .03. The combined factor, performance goals (PP/PV), had a relationship consistent to the literature; it was negatively related to global self-efficacy, $β = - .35$ , intrinsic motivation, $β = - .42$ , and elaboration, $β = - .18$ ; and positively related to external motivation, $β = .51$ .

Discussion

We investigated the factor structure of the 2 × 2 achievement goals model using the longitudinal data of Korean adolescents. Findings support the use of the 2 × 2 model across ages with secondary school students, including the controversial mastery-avoidance construct. In addition to the previous findings that high school and undergraduate college students could differentiate mastery goals by valence (Conroy et al., 2003; Elliot & McGregor, 2001; Finney et al., 2004; Madjar et al., 2011), we added to evidence that the conceptual differentiation between mastery-approach goals and mastery-avoidance goals is also manifested among middle to high school students. Mastery-avoidance, despite its complex conceptualization, is a useful and unique construct that can explain adolescents’ motivation to achieve. It is probable that mastery-avoidance goals, or avoiding the loss of one’s skills and abilities, could be an approach that Korean students are encouraged to use in academic settings. The finding is aligned with Bong’s (2009) study that middle school students could differentiate among the four achievement goals in a 2 × 2 framework, unlike earlier grade-level students (i.e., Grades 1 and 2), who could not differentiate among those constructs.

This study also provides empirical evidence of longitudinal measurement invariance of the AGQ. In alignment with the conceptual framework of response shift (Sprangers & Schwartz, 1999), the results support that Korean students hold equivalent meanings of the item contents (i.e., absence of reconceptualization) and the equal importance of the items in the overall questionnaires (i.e., absence of reprioritization) in tenth and eleventh grades. However, in terms of recalibration, the students hold the equal meaning of item values on the scale except for four items (i.e., MP2, MV2, PP1, and PV3) which presented non-invariant indicator intercepts. Nonequivalent indicator intercepts in longitudinal invariance tests theoretically imply changes in the response origin on the scale, which can be explained by systematic response bias across different waves (Vandenberg & Lance, 2000). For example, students might be more sensitive or lenient to rate the value of zero on the four non-invariant items as they grow older. However, it is not yet possible to interpret the extent to which the intercepts are not equal over the two waves given the current theoretical development in the behavioral and social sciences; instead, we can just determine the significance and the sign of the coefficients (Cohen et al., 2003).

Although partial invariance tests are controversial among researchers, freely estimating a small number of indicators based on the established theory is acceptable even from a conservative perspective (Brown, 2015; Vandenberg & Lance, 2000). Given that only one indicator intercept per factor was non-invariant and the foundational theory of the achievement goal framework is well-established, we conclude that the achievement goal framework is partially strict invariant across the two waves. Therefore, the achievement goal framework with the four-factor model can be further used to compare the factor means (e.g., latent growth curve models and autoregressive panel models) using longitudinal data from secondary school students. Thus, the four-factor Achievement Goals Questionnaire is a valid and reliable measure of achievement goals, which can be used to investigate developmental changes in academic motivation, an area of study frequently explored by educational psychologists (Wigfield & Eccles, 2002).

Although the differentiation of mastery-avoidance from the other three factors of the achievement goals was apparent among secondary school students, students’ perceptions of the four individual factors were changed from Wave 3 (tenth grade) to Wave 4 (eleventh grade). The inter-factor correlations for Wave 4 were notably inflated for all pairs of the factors, and the correlation between performance-approach and performance-avoidance was .97 (.52–64 for the other waves), which resulted in a non-positive definite of the latent variable covariance matrix in our structural equation model that was run with the data of Waves 1, 2, and 3 without problems. It is possible that our findings are associated with the unique characteristics and contexts of Korean secondary school students. It is well known that Korean adolescents are placed in highly competitive environments with regard to academic achievement and college entrance (e.g., Kim et al., 2010; Song et al., 2015). Such extremely competitive and achievement-oriented environmental and psychological changes might be the causes for diminishing the boundaries of each factor of achievement goals among eleventh graders in Korea. However, more empirical studies should investigate whether strong inter-factor correlations of the achievement goal factors are prevalent among high schoolers across different countries and cultures.

Regarding relations to other variables, we found that the four individual factors of achievement goals have distinct properties in relation to other variables as they were theoretically hypothesized. Mastery-approach goal was associated with increased self-efficacy, intrinsic motivation, and the use of elaboration, but mastery-avoidance was negatively or not significantly associated with the variables. This finding is aligned with prior studies that avoidance goals are closely related to negative affections and using surface learning strategy (Liem et al., 2008). External regulation was more closely associated with the performance-avoidance goal than with performance-approach and mastery-avoidance goals.

This study has limitations. The sample was limited to Korean secondary school students, so the findings may not be generalizable to younger students or those from other countries or cultures. Samples of students from diverse cultures and ages should be examined to allow for the generalization of the findings. Further, given the recent arguments that various measures and labels of achievement goals might have resulted in different findings (Hulleman et al., 2010; Elliot & Murayama, 2008), we recommend future studies to replicate this study with other measures of achievement goals. In this study, we performed longitudinal measurement invariance tests with only two grade levels because measurement invariance tests with more than two waves provide overall fit indices only and do not allow for the detection of the time point at which the invariance happened. Examining with more waves would strengthen the findings.

Footnotes

Declaration of Conflicting Interests

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

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Soohyun Yi

Nielsen Pereira

Appendix

Item		W1	W2	W3	W4
MP1	I want to learn as much as possible from this course	.64 (.01)	.66 (.01)	.59 (.01)	.67 (.01)
MP2	It is important for me to understand the content of this course as thoroughly as possible	.80 (.01)	.82 (.01)	.77 (.01)	.68 (.01)
MP3	I desire to completely master the material presented in this class	.81 (.01)	.80 (.01)	.77 (.01)	.71 (.01)
MV1	I worry that I may not learn all that I possibly could in this class	.76 (.01)	.79 (.01)	.77 (.01)	.74 (.01)
MV2	Sometimes I’m afraid that I may not understand the content of this class as thoroughly as I’d like	.87 (.01)	.89 (.01)	.88 (.01)	.62 (.01)
MV3	I am often concerned that I may not learn all that there is to learn in this class	.84 (.01)	.86 (.01)	.85 (.01)	.64 (.01)
PP1	It is important for me to do better than other students	.68 (.01)	.65 (.01)	.63 (.01)	.72 (.01)
PP2	My goal in this class is to get a better grade than most of the other students	.85 (.01)	.83 (.01)	.83 (.01)	.64 (.01)
PP3	It is important for me to do well compared to others in this class	.76 (.01)	.81 (.01)	.79 (.01)	.78 (.01)
PV1	My fear of performing poorly in this class is often what motivates me	.77 (.01)	.81 (.01)	.78 (.01)	.69 (.01)
PV2	My goal in this class is to avoid performing poorly	.88 (.01)	.88 (.01)	.85 (.01)	.80 (.01)
PV3	I just want to avoid doing poorly in this class	.72 (.01)	.75 (.01)	.68 (.01)	.66 (.01)

Note. Standard Errors are specified in the parenthesis. MP = mastery-approach, MV = mastery-avoidance, PP = performance-approach; PV = performance-avoidance.

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