Longitudinal effects of educational expectations and achievement attributions on adolescents' academic achievements.
Educational expectations, that is, students' own expectations about the highest level of education they will attain, represent a kind of expectation about future academic success. According to expectancy-value theory (Eccles et al., 1983; Eccles & Wigfield, 2002), expectations of success are a crucial component influencing achievement-related performance and are assumed to be influenced by perceptions of competence and by goals held by individuals. Such perceptions and goals are influenced by individuals' interpretations of their own previous achievements. In other words, expectations of success and outcomes of achievements presumably have a cyclical influence on each other. That is, individuals' expectations of success influence their achievements and their achievements further influence their future expectations. Consistent with the feedback mechanism of the expectancy-value model, adolescents are expected to have better long-term academic achievement outcomes if they have higher educational expectations during earlier periods. Through feedback mechanisms operating over time, educational expectations are assumed to facilitate academic achievements.
Moreover, the causal attributions that individuals offer for previous achievement outcomes (Weiner, 1986, 2000) represent key factors in determining whether they continue to engage in subsequent learning. Weiner (1992) has classified attributions of outcomes into three dimensions: locus of control (internal-external), stability (stable-unstable), and controllability (controllable-uncontrollable). For example, ability was classified as an internal and stable characteristic that was beyond the control of students, whereas effort was classified as an internal, unstable, and controllable characteristic. Anderson (1983) has indicated that individuals who attributed outcomes to effort exhibited higher levels of motivation and performed better than did individuals who attributed outcomes to ability. Similar results were also reported by Schunk (1982), revealing that feedback of attributing previous achievements to effort resulted in more progress and greater skill development in math. When adolescents attribute learning outcomes to ability, they would be expected to be less engaged in learning. When adolescents attribute learning outcomes to effort, they would be expected to spend more time on learning, which is assumed to facilitate academic achievements.
Although previous research has shown that attributions of achievement outcomes influence academic achievements (Anderson, 1983; Schunk, 1982; Weiner, 1986, 2000), and educational expectations can predict future academic achievements (Bui, 2007; Sanders, Field, & Diego, 2001), only a few studies have explored the predictive value of achievement attributions and educational expectations on the academic achievements of adolescents and examined their long-term effects on their academic development. This study used the longitudinal database of the Taiwan Education Panel Survey to explore the long-term effects of the educational expectations and achievement attributions of adolescents on their actual academic achievements.
This study used the database from the publicly released files of the Taiwan Education Panel Survey (TEPS, Chang, 2007), Center for Survey Research, Academia Sinica. The TEPS, a nationwide longitudinal database, was designed to collect Taiwanese longitudinal educational data for basic research from 2001 to 2007. This study used the three waves of data that have been released: (a) the base year, seventh graders in 2001; (b) the first follow-up, ninth graders in 2003; and (c) the second follow-up, eleventh graders in 2005. TEPS is a survey using a multistage stratified sample of Taiwanese secondary school and junior college students. The base-year sample consisted of 20,004 students selected from 333 junior high schools. The first follow-up sample included 18,903 students, and the second follow-up sample included 4,172 students. Subjects in the publicly released files of the TEPS consisted of a randomly selected 70% of the total data. After records with missing data were deleted, a total of 2,000 adolescent subjects were included in the present study.
The variables used in this study addressed educational expectations, achievement attributions, and academic achievements. We used the three waves of data of the Item Response Theory (IRT) scores on the General Analyzing Ability Test obtained from the publicly released file of the TEPS to measure academic achievements. The General Analyzing Ability Test was designed to measure students' general abilities in science, math, inference, and reading. The IRT scores for the base year, the first follow-up, and the second follow up were compared. Items addressing educational expectations and achievement attributions were selected from the Student Questionnaire of the TEPS. Educational expectations included two items: (a) "What educational level do you expect to reach?" and (b) "According to your ability, what educational level can you reach?" The item measuring achievement attributions was: What factor do you think is the most relevant to whether one can perform well in terms of academic achievements?" The coding for the responses to these items is shown in Table 1.
The longitudinal data were analyzed through two phases of two-level hierarchical linear modeling. In the first phase, a random-coefficient regression model was used for testing whether the variances of residual terms were significant. This model was specified as follows:
Model 1. random-coefficient regression model:
Level 1 [Y.sub.ti] = [B.sub.0i] + [B.sub.1i] (Time) + [r.sub.ti]
Level 2 [B.sub.0i] = [G.sub.00] + [u.sub.0i]
[B.sub.1i] = [G.sub.10] + [u.sub.1i]
At level 1, each student's achievements were represented by an individual growth trajectory that depended on his/her own unique set of parameters. Y, represented the achievement at time t for student i. Time was the time point, coded as 0 (in 2001), 1 (in 2003), and 2 (in 2005). [B.sub.0i] was the intercept parameter indicating the initial achievement of student i at Time O. [B.sub.1i] represented the growth rate for student i. We assumed that the errors [r.sub.ti] were independent and normally distributed. At Level 2, the intercept (Be) and growth rate ([B.sub.1i]) of Level 1 served as the dependent variables, where [G.sub.00] and [G.sub.10] represented the intercepts and [u.sub.0i] and [u.sub.1i] represented random errors.
In the second phase, when the variances of the [u.sub.0i] and [u.sub.ti] were found to be significant, students' educational expectations and achievement attributions served as predictors for explaining the variances. The three predicting models were defined as follows: Model 2-1. Educational expectations (EE) and attribution to ability (AA) as predictors:
Level 1 [Y.sub.ti] = [B.sub.0i] + [B.sub.1i] (Time) + [r.sub.ti]
Level 2 [B.sub.0i] = [G.sub.00] + [G.sub.01](EE) + [G.sub.02](AA) + [u.sub.0i]
[B.sub.li] = [G.sub.10] + [G.sub.11](EE) + [G.sub.l2](AA) + [u.sub.1i]
Model 2-2. Educational expectations (EE) and attribution to effort (AE) as predictors:
Level 1 [Y.sub.ti] = [B.sub.0i] + [B.sub.1i] (Time) + [r.sub.ti]
Level 2 [B.sub.0i] = [G.sub.00] + [G.sub.01](EE) + [G.sub.02](AE) + [u.sub.0i]
[B.sub.li] = [G.sub.10] + [G.sub.11](EE) + [G.sub.l2](AE) + [u.sub.1i]
Model 2-3. Educational expectations (EE) and attribution to others (AO) as predictors:
Level 1 [Y.sub.ti] = [B.sub.0i] + [B.sub.1i] (Time) + [r.sub.ti]
Level 2 [B.sub.0i] = [G.sub.00] + [G.sub.01](EE) + [G.sub.02](AD) + [u.sub.0i]
[B.sub.li] = [G.sub.10] + [G.sub.11] (EE) + [G.sub.l2](AD) + [u.sub.1i]
Table 2 shows the means and standard deviations of academic achievements for students with different educational expectation levels in the three waves (seventh grade, ninth grade, and eleventh grade). The academic achievements in all three waves exhibited a tendency toward growth for participants at all levels of educational expectations. From a cross-sectional perspective, the academic achievements of students in each wave increased as a function of the level of educational expectation.
Table 3 presents the means and standard deviations of academic achievements for students in the three waves with different achievement attributions. Irrespective of the kind of achievement attributions, students in the three waves exhibited a tendency toward increasing academic achievements. A cross-sectional analysis of students in each wave showed that the mean academic achievement among those with effort attribution was higher than that of students with non-effort attribution; the mean academic achievement of students with ability attribution was higher than that of students with non-ability attribution; the mean academic achievement of students with other attribution (e.g., teacher instruction, parental discipline, or help from friends) was lower than that of students with non-other attribution.
Phase 1: Random-coefficient regression model.
Table 4 shows that both the intercept of initial achievement ([G.sub.00]) and the intercept of growth rate ([G.sub.10]) were significant; the mean initial achievement of all students was 0.524 and the mean growth rate was 0.688. Table 5 shows that the variance components of random effects in initial achievement and growth rate were significant, indicating that students showed significant differences in initial achievement and growth rate. The educational expectations and the three types of achievement attributions of students were also used for predicting their achievements and growth rates.
Phase 2: Intercepts and slopes as outcomes. In Model 2-1 (see Table 6), both the educational expectation coefficients of initial achievements ([G.sub.01]) and growth rates ([G.sub.11]) were significant, indicating that educational expectations could predict the initial achievements and the learning growth rates of students. The coefficient of [G.sub.01] showed that the mean initial achievement increased by 0.202 when the educational expectations of students increased by one level. For example, the mean achievement of seventh graders who expected to graduate from a university (Level 7 of educational expectation) was relatively higher than that of seventh graders who expected to graduate from a senior or vocational high school (Level 3 of educational expectation) by 0.808. The coefficient of [G.sub.11] indicated that the mean initial achievement increased by 0.022 when the educational expectation of students increased by one level. Higher levels of educational expectation are associated with higher learning-growth rates. By contrast, ability-attribution coefficients of initial achievements ([G.sub.02]) and growth rates ([G.sub.12)] were not significant, indicating that ability attribution did not effectively predict the initial achievements and growth rates of students.
In Model 2-2 (see Table 6), the educational expectation coefficient of [G.sub.01] was significant, whereas the effort-attribution coefficient ([G.sub.02]) was not significant, indicating that only educational expectation predicted initial achievement. Both the educational-expectation coefficient ([G.sub.11]) and the effort-attribution coefficient ([G.sub.12]) were significant in regard to growth rates, which showed that, in addition to educational expectation, effort attribution also influenced the rates at which students learned. The growth rate for students who attributed their achievements to effort was higher than that for students who did not by 0.041.
In Model 2-3 (see Table 6), all coefficients of initial achievements ([G.sub.00], [G.sub.01], and [G.sub.02]) and growth rates ([G.sub.10], [G.sub.11], and [G.sub.12]) were significant. This indicated that both educational expectations and attributions to others could be used to predict students' initial achievements and learning-growth rates. In this context, educational expectations had positive effects on students' initial achievements and growth rates, whereas attributions to others had negative effects. In other words, students who attributed learning achievements to teachers, parents, or friends had lower mean initial achievements and lower learning-growth rates by 0.17 and 0.051, respectively, than did those who did not attribute such achievements to others.
As illustrated in Table 7, the variance components of the random effects for initial achievements and growth rates in Models 2-1, 2-2, and 2-3 were significant. The variance components of the three models, [u.sub.0i] and [u.sub.1i], decreased from the original 0.511 and 0.036, respectively, in the random coefficient regression model to 0.355 and 0.035 in Model 2-1, to 0.354 and 0.034 in Model 2-2, and to 0.352 and 0.034 in Model 2-3. When we added educational expectation and ability attribution to predict initial achievement and growth rates, the variance components decreased by 30.5% and 2.8%, respectively, for Model 2-1. Because the predictive effects of ability attribution on initial achievements and growth rates were not significant, the decreased variance came primarily from the predictive effects of educational expectations. When educational expectation and effort attribution were added as predictors in Model 2-2, the variance components decreased by 30.7% and 5.6%, respectively. Likewise, for Model 2-3, when educational expectation and attribution to others were added as predictors, the variance components decreased by 31.1% and 5.6%, respectively. In summary, educational expectations accounted for a moderate amount of variance in initial achievement (30.5%); when attribution to effort and attribution to others were added, we were able to account for additional variance in the growth rate.
DISCUSSIONS AND CONCLUSIONS
This study used the TEPS longitudinal data to examine the effects of adolescents' educational expectations and achievement attributions on academic achievements and learning-growth rates. Results showed that educational expectations are positively predictive of academic achievement, which is consistent with earlier research (Gill & Reynolds, 1999; Marshall & Brown, 2004; Mau, 1995; Sanders, Field, & Diego, 2001; Seginer & Vermulst, 2002; Smead & Chase, 1981). Mau (1995) analyzed data from the National Educational Longitudinal Study and found that the educational aspirations of eighth graders were significantly related to their current academic achievements. This finding lends support to the expectancy-value theory (Eccles et al., 1983; Wigfield & Eccles, 2000) insofar as educational expectations are a crucial factor in academic achievements. Furthermore, the study also revealed that educational expectations positively predict the growth rates of academic achievements. This result supports the impact of the feedback mechanisms of the expectancy-value theory (Eccles et al., 1983; Wigfield & Eccles, 2000) in which high educational expectations can facilitate the growth of academic achievements over time.
Results show that high educational expectations, attribution to effort, and attribution to others influence learning-growth rates. Educational expectations and attributions to effort have a positive effect on learning-growth rates, while attributions to others have a negative effect on learning growth rate. Consistent with previous research (Georgiou, 1999), attributions of achievements to effort are positively related to actual achievements, whereas attributions to external factors are negatively related to achievements. Such attributional feedback regarding previous achievements influences the long-term academic development of adolescents (Schunk, 1982). This result lends support to Weiner's attributional theory (1986). Students with attributions reflecting an internal sense of control, such as the belief that efforts affect learning outcomes, will work harder to improve themselves in school. On the other hand, when students attribute their success or failure to external factors, such as teacher instruction, parental discipline, or the help of friends, they tend not to invest more time in learning. In addition, the findings demonstrate that the predictive effects of ability attributions on academic achievements were not significant in this study. Tuss, Zimmer, and Ho (1995) reported that Asian students considered effort to be a more essential factor for success than did American students, whereas American students tended to attribute success to ability. Taiwanese students tended to attribute their learning outcomes to effort.
Furthermore, the results show that educational expectations and achievement attributions have less effect on growth rates than on initial achievements. For instance, when educational expectations increased by one level, initial achievements increased by 0.202, but learning-growth rates increased by only 0.022. The reason behind this finding may relate to the ability filtering experienced by the second follow-up sample (2,000 eleventh graders): the Basic Competence Test preceded advancement to senior high schools in Taiwan. Thus, variance in the abilities of the tracked samples diminished, perhaps resulting in the insignificant effects of educational expectations and achievement attributions on growth rates.
Moreover, cross-cultural studies have found that different cultures place different emphases on interpreting academic achievements in terms of such factors as ability or effort (Salili, Chiu, & Hong, 2001; Skaalvik, 1994; Tuss et al., 1995; Yan & Gaier, 1994). Western educational culture, with a tradition based in Socratic ideas (Tweed & Lehman, 2002), emphasizes eliciting innate abilities from individuals. Unlike western culture, Asian cultures have emphasized the value of self-improvement in education. The causal attributions and beliefs related to the academic achievements of children held by parents are influenced by the surrounding culture (Bugental & Happaney, 2002; Crystal & Stevenson, 1991; Holloway, 1988). Western parents attribute their children's success to ability, whereas Asian parents attribute their children's success to effort (Natale, Aunola, Nurmi, 2009; Phillipson, 2006; Rytkonen, Aunola, & Nurmi, 2005, 2007). Chen and Lan (1998) have indicated that Chinese students are willing to follow the educational expectations held by their parents. Current research provides insights into how educational expectations and achievement attributions influence adolescents' long-term academic development in Taiwan. Further research is needed to address the impact of cross-cultural factors and parental expectations on the long-term effects of educational expectations and achievement attributions on adolescents' academic achievements.
In conclusion, this study conducted multilevel analyses to examine the longitudinal effects of educational expectations and achievement attributions on adolescents' academic achievements. The results revealed that educational expectations accounted for a moderate amount of variance in the academic achievements of adolescents. In addition, educational expectations and effort attributions positively predicted growth in academic achievements. In educational practice, we encourage teachers to suggest that adolescents hold higher educational expectations and that they attribute successful learning to effort.
Anderson, C. A. (1983). Motivational and performance deficits in interpersonal settings: The effect of attributional styles. Journal of Personality and Social Psychology, 45(5), 1136-1147.
Bugental, D. B., & Happaney, K. (2002). Parental attributions. In M. H. Bornstein (Ed.), Handbook of parenting Volume 3: Being and becoming a parent (pp. 509-535). Mahwah, N J: Erlbaum.
Bui, K. (2007). Educational expectations and academic achievement among middle and high school students. Education, 127(3), 328-331.
Chang, L. Y. (2007). Taiwan Education Panel Survey: Base year (2001), first follow-up (2003), second follow-up (2005) student data [public release computer file]. Center for Survey Research, Academia Sinica [producer, distributor].
Chen, H., & Lan, W. (1998). Adolescents' perceptions of their parents' academic expectations: Comparison of American, Chinese-American, and Chinese high school students. Adolescence, 33(130), 385-390.
Crystal, D. S., & Stevenson, H. W. (1991). Mothers' perceptions of children's problems with mathematics: A cross-national comparison. Journal of Educational Psychology, 83(3), 372-376.
Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motives (pp. 75-146). San Francisco: Freeman.
Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109-132.
Georgiou, S. N. (1999). Achievement attributions of sixth-grade children and their parents. Educational Psychology, 19(4), 399-412.
Gill, S., & Reynolds, A. J. (1999). Educational expectations and school achievement of urban African American children. Journal of School Psychology, 37(4), 403-424.
Holloway, S. D. (1988). Concepts of ability and effort in Japan and the United States. Review of Educational Research, 58(3), 327-345.
Marshall, M. A., & Brown, J. D. (2004). Expectations and realizations: The role of expectanoes in achievement settings. Motivation and Emotion, 28(4), 347-361.
Mau, W. C. (1995). Educational planning and academic achievement of middle school students: A racial and cultural comparison. Journal of Counseling and Development, 73(5), 518-526.
Natale, K., Aunola, K., & Nurmi, J. E. (2009). Children's school performance and their parents' causal attributions to ability and effort: A longitudinal study. Journal of Applied Developmental Psychology, 30(1), 14-22.
Phillipson, S. (2006). Cultural variability in parent and child achievement attributions: A study from Hong Kong. Educational Psychology, 26(5), 625-642.
Rytkonen, K., Aunola, K., & Nurmi, J. E. (2005). Parents' causal attributions concerning their children's school achievement: A longitudinal study. Merrill-Palmer Quarterly, 51(4), 494-522.
Rytkonen, K., Aunola, K., & Nurmi, J. E. (2007). Do parents' causal attributions predict the accuracy and bias in their children's self-concept of math ability? A longitudinal study. Educational Psychology, 27(6), 771-788.
Salili, F., Chiu, C. Y., & Hong, Y. Y. (2001). The culture and context of learning. In F. Salili, C. Y. Chiu, & Y. Y. Hong (Eds.), Student motivation: The culture and context of learning (pp. 1-14). New York: Kluwer Academic/ Plenum Publishers.
Sander, C. E., Field, T. M., & Diego, M. A. (2001). Adolescents' academic expectations and achievement. Adolescence, 36(144), 795-802.
Schunk, D. H. (1982). Effects of effort attributional feedback on children's perceived self-efficacy and achievement. Journal of Educational Psychology, 74(4), 548-556.
Seginer, R., & Vermulst, A. (2002). Family environment, educational aspirations, and academic achievement in two cultural settings. Journal of Cross-Cultural Psychology, 33(6), 540-558.
Skaalvik, E. M. (1994). Attribution of perceived achievement in school in general and in math and verbal areas: Relations with academic self-concept and self-esteem. British Journal of Educational Psychology, 64(1), 133-143.
Smead, V. S., & Chase, C. I. (1981). Student expectations as they relate to achievement in eighth grade mathematics. Journal of Educational Research, 75(2), 115-120.
Tuss, P., Zimmer, J., & Ho, H. (1995). Causal attributions of underachieving fourth grade students in China, Japan and the United States. Journal of Cross-Cultural Psychology, 26(4), 408-425.
Tweed, R. G., & Lehman, D. R. (2002). Learning considered within a cultural context: Confucian and Socratic approaches. American Psychologist, 57(2), 89-99.
Weiner, B. (1986). An attributional theory of motivation and emotion. New York: Springer-Verlag.
Weiner, B. (1992). Human motivation: Metaphors, theories, and research. Newbury Park, CA: Sage.
Weiner, B. (2000). Intrapersonal and interpersonal theories of motivation from an attributional perspective. Educational Psychology Review, 12(1), 1-14.
Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25, 68-81.
Yan, D., & Gaier, E. (1994). Causal attributions for college success and failure: An Asian-American comparison. Journal of Cross-Cultural Psychology, 25(1), 146-158.
The authors wish to thank Professor Wen-Bin Chiou at the Institute of Education, National Sun Yat-sen University, and Chair Professor Wen-Chung Wang at the Department of Educational Psychology, Counseling and Learning Needs, the Hong Kong Institute of Education, for their insightful comments on earlier drafts of this paper. The database of the Taiwan Education Panel Survey used in the study was sponsored by Academia Sinica, Ministry of Education, National Academy for Educational Research Preparatory Office, and National Science Council.
Kun-Shia Liu, Ying-Yao Cheng, and Yi-Ling Chen, Institute of Education, National Sun Yat-sen University, Taiwan
Yuh-Yih Wu, Department of Special Education, National Kaohsiung Normal University, Taiwan
Requests for reprints should be sent to Ying-Yao Cheng, Institute of Education, National Sun Yat-sen University, 70 Lienhai Rd., Kaohsiung 80424, Taiwan. E-mail: firstname.lastname@example.org
Table 1. Coding for Responses to Items Variables Content of the Items Coding Educational What educational Coding Steps: Expectation level do you expect Step 1. Code the responses of to reach? each item into 5 ordinal variables: 1 = junior high According to your school; 2 = senior high ability, what school/vocational high school; educational level 3 = junior college/technology can you reach? college or university; 4 = university; 5 = graduate school. Step 2. Average the codes of the two items. Then, recode the educational levels into nine levels: junior high school (1) to graduate school (9) as the levels of students' educational expectations. The higher the code is, the higher educational expectation will be. Achievement What factor do you The responses of the item were Attribution think is the most coded into three nominal relevant to whether variables: one can perform 1. Effort (Yes: 1; No: 0) well in terms of 2. Ability (Yes: 1; No: 0) academic 3. Others, such as teacher achievements? instructions, parental discipline, or help from friends (Yes: 1; No: 0) Table 2. Means and Standard Deviations of Academic Achievements for Students with Different Educational Expectations Levels of Number Academic Academic Educational of Achievement Achievement Expectation's Students Wave 1 Wave 2 M SD M SD 1 24 -0.93 0.80 -0.42 0.91 2 24 -0.91 1.02 -0.21 0.95 3 133 -0.27 0.74 0.35 0.98 4 114 0.10 0.81 0.76 0.99 5 327 0.28 0.71 1.05 0.94 6 187 0.41 0.69 1.23 0.85 7 505 0.57 0.67 1.37 0.89 8 302 0.74 0.68 1.63 0.88 9 384 0.91 0.71 1.90 0.90 Total 2,000 0.48 0.80 1.30 1.03 Levels of Academic Educational Achievement Expectation's Wave 3 M SD 1 0.22 0.89 2 0.27 1.11 3 0.92 1.13 4 1.33 1.18 5 1.59 1.10 6 1.80 0.92 7 1.99 0.95 8 2.16 1.01 9 2.38 0.96 Total 1.86 1.11 Table 3. Means and Standard Deviations of Academic Achievements for Students with Different Achievement Attributions Types of Number Academic Academic Academic Achievement of Achievement Achievement Achievement Attributions Students Wave 1 Wave 2 Wave 3 M SD M SD M SD Effort 557 0.43 0.88 1.20 1.10 1.75 1.15 Non-effort 1443 0.50 0.77 1.34 1.00 1.90 1.10 Ability 1747 0.46 0.79 1.28 1.02 1.84 1.11 Non-ability 253 0.60 0.85 1.46 1.07 1.96 1.14 Others 314 0.31 0.85 1.01 1.06 1.59 1.13 Non-others 1,686 0.51 0.79 1.35 1.02 1.91 1.10 Table 4. Final Estimation of Fixed Effects Fixed Effect Coefficient SE t p Initial Achievement, 0.524 0.018 28.504 .000 [G.sub.00] Growth Rate, [G.sub.10] 0.688 0.008 83.256 .000 Table 5. Final Estimation of Variance Components Random Effect Variance Component df [chi square] P Initial Achievement, 0.511 1999 8107 .000 [u.sub.0i] Growth Rate, [u.sub.1i] 0.036 1999 2725 .000 Level Residual, [r.sub.ti] 0.201 Table 6. Final Estimation of Fixed Effects Fixed Effect Coefficient SE Model 2-1 Initial achievement ([B.sub.0i]) Intercept, [G.sub.00] -0.809 0.062 Educational expectation, [G.sub.01] 0.202 0.009 Attribution to ability, [G.sub.02] 0.077 0.051 Growth rate ([B.sub.1i]) Intercept, [G.sub.10] 0.544 0.029 Educational expectation, [G.sub.11] 0.022 0.004 Attribution to ability, [G.sub.12] -0.019 0.026 Model 2-2 Initial achievement ([B.sub.0i]) Intercept, [G.sub.00] -0.856 0.067 Educational expectation, [G.sub.01] 0.203 0.009 Attribution to effort, [G.sub.02] 0.071 0.038 Growth rate ([B.sub.1i]) Intercept, [G.sub.10] 0.514 0.032 Educational expectation, [G.sub.11] 0.022 0.004 Attribution to effort, [G.sub.12] 0.041 0.019 Model 2-3 Initial achievement ([B.sub.0i]] Intercept, [G.sub.00] -0.767 0.063 Educational expectation, [G.sub.01] 0.201 0.009 Attribution to others, [G.sub.02] -0.17 0.046 Growth Rate ([B.sub.1i]) Intercept, [G.sub.10] 0.555 0.029 Educational expectation, [G.sub.11] 0.022 0.004 Attribution to others, [G.sub.12] -0.051 0.024 Fixed Effect t p Model 2-1 Initial achievement ([B.sub.0i]) Intercept, [G.sub.00] -13.028 .000 Educational expectation, [G.sub.01] 22.512 .000 Attribution to ability, [G.sub.02] 1.519 .129 Growth rate ([B.sub.1i]) Intercept, [G.sub.10] 18.721 .000 Educational expectation, [G.sub.11] 5.227 .000 Attribution to ability, [G.sub.12] -0.749 .454 Model 2-2 Initial achievement ([B.sub.0i]) Intercept, [G.sub.00] -12.775 .000 Educational expectation, [G.sub.01] 22.743 .000 Attribution to effort, [G.sub.02] 1.898 .057 Growth rate ([B.sub.1i]) Intercept, [G.sub.10] 15.849 .000 Educational expectation, [G.sub.11] 5.175 .000 Attribution to effort, [G.sub.12] 2.196 .028 Model 2-3 Initial achievement ([B.sub.0i]] Intercept, [G.sub.00] -12.206 .000 Educational expectation, [G.sub.01] 22.493 .000 Attribution to others, [G.sub.02] -3.674 .000 Growth Rate ([B.sub.1i]) Intercept, [G.sub.10] 18.883 .000 Educational expectation, [G.sub.11] 5.070 .000 Attribution to others, [G.sub.12] -2.140 .032 Table 7. Final Estimation of Variance Components Random Effect Variance df [chi square] Component Model 2-1 Initial Achievement, [u.sub.0i] 0.355 1997 6236 Growth Rate, [u.sub.li] 0.035 1997 2687 Level Residual, [u.sub.ti] 0.201 Model 2-2 Initial Achievement, [u.sub.0i] 0.354 1997 6232 Growth Rate, [u.sub.li] 0.034 1997 2681 Level Residual, [u.sub.ti] 0.201 Model 2-3 Initial Achievement, [u.sub.0i] 0.352 1997 6198 Growth Rate, [u.sub.li] 0.034 1997 2681 Level Residual, [u.sub.ti] 0.201 Random Effect P Model 2-1 Initial Achievement, [u.sub.0i] .000 Growth Rate, [u.sub.li] .000 Level Residual, [u.sub.ti] Model 2-2 Initial Achievement, [u.sub.0i] .000 Growth Rate, [u.sub.li] .000 Level Residual, [u.sub.ti] Model 2-3 Initial Achievement, [u.sub.0i] .000 Growth Rate, [u.sub.li] .000 Level Residual, [u.sub.ti]
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|Author:||Liu, Kun-Shia; Cheng, Ying-Yao; Chen, Yi-Ling; Wu, Yuh-Yih|
|Date:||Dec 22, 2009|
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