abstract: Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values. In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2015

This study compared 3 approaches for handling a fourth level of nesting structure when analyzing data from a cluster-randomized trial (CRT). CRTs can include 3 levels of nesting: repeated measures, individual, and cluster levels. However, above the cluster level, there may sometimes be an additional potentially important fourth level of nesting (e.g., schools, districts, etc., depending on the design) that is typically ignored in CRT data analysis. The current study examined the impact of ignoring this fourth level, accounting for it using a model-based approach, and accounting it using a design-based approach on parameter and standard error (SE) estimates. Several fixed effect and random effect variance parameters and SEs were biased across all 3 models. In the 4-level model, most SE biases decreased as the number of level 3 clusters increased and as the number of level 4 clusters decreased. Also, random effect variance biases decreased as the number of level 3 clusters increased. In the 3-level and complex models, SEs became more biased as the weight level 4 carried increased (i.e., larger intraclass correlation, more clusters at that level). The current results suggest that if a meaningful fourth level of nesting exists, future researchers should account for it using design-based approach; the model-based approach is not recommended. If the fourth level is not practically important, researchers may ignore it altogether.

Un nombre grandissant d’études suggère que le soutien maternel à l’autonomie pourrait favoriser une meilleure performance scolaire chez les enfants. Or, peu d’études longitudinales ont examiné l’apport du soutien à l’autonomie précoce dans la prédiction des trajectoires développementales du rendement en mathématiques durant les premières années d’école, bien que l’évolution des habiletés en mathématiques au cours du primaire soit bien documentée. De plus, l’interaction entre le soutien maternel à l’autonomie et les capacités cognitives de base de l’enfant n’a jamais été examinée dans la prédiction de trajectoires de rendement scolaire, bien que de telles interactions soient attendues théoriquement. La présente étude avait pour objectif d’examiner l’interaction entre le soutien maternel à l’autonomie et les capacités cognitives de l’enfant, mesurés durant la petite enfance, dans la prédiction des trajectoires de rendement en mathématiques de la première année à la troisième année du primaire. L’échantillon était constitué de 113 dyades mère-enfant. Le soutien maternel à l’autonomie a été mesuré par observation d’interactions mère-enfant, tandis que les capacités cognitives de base et le rendement en mathématiques de l’enfant ont été mesurés à l’aide d’outils standardisés. Les résultats suggèrent que le soutien maternel à l’autonomie précoce est associé à la performance en mathématiques au cours du primaire, mais que cette relation se présente différemment selon les capacités cognitives de base de l’enfant. Cette étude suggère que le soutien maternel à l’autonomie durant les premières années de vie de l’enfant pourrait potentiellement favoriser le développement de compétences en mathématiques à long terme. / Increasing evidence suggests that maternal autonomy support fosters academic achievement in children. However, despite evidence that mathematical achievement evolves markedly during elementary school years, no study has examined early autonomy support in relation to mathematical achievement trajectories. Moreover, few studies have considered the role of child general cognitive abilities in these associations. With a sample of 113 mother–child dyads, the current study investigated whether patterns of growth in mathematical achievement during the first three years of elementary school were predicted by the interaction between maternal autonomy support and child general cognitive abilities, both assessed in infancy. Maternal autonomy support was assessed based on videotaped mother–child interactions, whereas child general cognitive abilities and mathematical achievement were assessed using standardised tests. Results suggest that early maternal autonomy support predicts later mathematical development in children, although this relation unfolds differently based on children’s baseline cognitive abilities. These findings suggest that maternal autonomy support in the first years of life may confer long-lasting benefits for children’s acquisition of mathematical knowledge.

Although the research literature supports the notion of language growth trajectories, primarily in monolingual English children, the shape and direction of English-language learners' (ELLs) language growth trajectories are largely unknown. The present study examined the shape of ELLs' language growth trajectories by estimating the initial status and the growth rates of specific oral language skills (mean length of utterance in words (MLUw), number of different words (NDW), and words per minute (WPM)) in each language during the first 3 years of formal schooling. This study was framed from the perspective of language as a dynamic system, composed of linguistic subsystems that change over time. This study utilized secondary data from a larger project, the Bilingual Language Literacy Project (BLLP), which collected narrative retell language samples produced in Spanish and English from ELL children. The final longitudinal dataset used in this study consisted of 12,248 oral narrative language samples (6,516 Spanish; 5,732 English) that were produced by 1,723 ELLs. This study examined the effect of three predictors on language growth: academic semester (metric of time), gender, and schooling. Growth curve model (GCM) testing was used to profile the longitudinal growth of the ELLs' oral language skills in Spanish and English over time. This study had a number of important findings regarding change over time, intra- and inter-individual variability, and the impact of initial status on growth. With regard to change over time: MLUw, NDW, and WPM demonstrated growth over time in Spanish and English; the shapes of Spanish (curvilinear, non-monotonic, and continuous) and English growth (linear, non-monotonic, and discontinuous) were similar within-language; language growth in Spanish was predicted by academic semester and gender; and language growth in English was predicted by academic semester, gender, and schooling. With regard to intra- and inter-individual variability: significant intra-individual differences in the growth of all the oral language measures, across each wave of measurement, were found for both languages; significant intra-individual differences in the initial status of participants for all the oral language measures were found for both languages; significant inter-individual differences in the growth rates were found for WPM-Spanish; and significant inter-individual differences in the growth rates were found for all the oral language measures in English. With regard to the impact of initial status on growth: the growth of MLUw-Spanish was systematically related to initial status (lower performers at initial status may not catch up to higher performers); the growth of NDW- and WPM-Spanish were unrelated to its initial status (lower performers at initial status may, or may not catch up to higher performers); and the growth of MLUw-, NDW-, and WPM-English was systematically related to initial status (lower performers at initial status may catch up to higher performers). With regard to the co-development of interconnected subsystems, qualitative observations (non-empirically tested) based on visual inspection and GCM estimates provided initial insight into the possible co-development occurring within- and across-languages. The present study broke new ground by specifying the shape of growth for MLUw, NDW, and WPM in the Spanish and English of ELLs during their first 3 years of formal schooling. The study had a number of methodological limitations that will guide and motivate future work on the language growth of ELLs. / Communication Sciences

Background: While drinking alcohol, one must choose between the immediate rewarding effects and the delayed reward of a healthier lifestyle. Individuals differ in their devaluation of a delayed reward based on the time required to receive it, i.e., delay discounting (DD). Previous studies have shown that adolescents discount more steeply than adults and that steeper DD is associated with heavier alcohol use in both groups. - Methods: In a large-scale longitudinal study, we investigated whether higher rates of DD are an antecedent or a consequence of alcohol use during adolescent development. As part of the IMAGEN project, 2220 adolescents completed the Monetary Choice Questionnaire as a DD measure, the Alcohol Use Disorders Identification Test, and the Timeline Follow Back interview at ages 14, 16, 18, and 22. Bivariate latent growth curve models were applied to investigate the relationship between DD and drinking. To explore the consequences of drinking, we computed the cumulative alcohol consumption and correlated it with the development of discounting. A subsample of 221 participants completed an intertemporal choice task (iTeCh) during functional magnetic resonance imaging at ages 14, 16, and 18. Repeated-measures ANOVA was used to differentiate between high-risk and low-risk drinkers on the development of neural processing during intertemporal choices. - Results: Overall, high rates of DD at age 14 predicted a greater increase in drinking over 8 years. In contrast, on average, moderate alcohol use did not affect DD from ages 14 to 22. Of note, we found indicators for less brain activity in top-down control areas during intertemporal choices in the participants who drank more. - Conclusions: Steep DD was shown to be a predictor rather than a consequence of alcohol use in low-level drinking adolescents. Important considerations for future longitudinal studies are the sampling strategies to be used and the reliability of the assessments.

對偏差行為的解釋有多種理論，不過以後天的角度詮釋偏差行為，則社會控制理論、自我控制理論是最有力的解釋理論。本研究亦欲圖驗證此兩種理論在多變量潛在成長模型的效用。因此，研究者採用臺灣教育長期追蹤資料庫之資料，以自我控制信念、親子關係、同儕關係、學校依附感、教育抱負、學業成就預測偏差行為之變化。此外，並探究性別對潛在成長模型之影響。茲將研究成果陳述如下。 1、偏差行為隨著年級逐漸增加，日益增加，變異數亦逐漸擴大。 2、整體多變量潛在成長模型中，整體模式適配度良好。 3、自變項對偏差行為截距、斜率解釋量分別為.19、.32，顯示模式的解釋量仍有改善空間，其中對截距之預測達顯著者，分別為同儕關係截距、學校依附感截距、學業成就截距、親子關係截距。對斜率之預測力達顯著者，分別為學校依附感斜率、學校依附感截距、同儕關係斜率、同儕關係截距、教育抱負截距。 4、運用多群組分析，發現男女生並無測量不變性。 5、性別對偏差行為有重要影響。 6、預測女生的斜率主要考量其學校依附感和同儕關係，但預測男生偏差行為的斜率除了與學校、同儕的關係外，還要考量其教育抱負。 最後，根據上述的結論，研究者分別提出實務、研究方法、未來偏差行為研究之建議，以作為參考。 / The cause of deviation behavior is explained by many theories. However, social control theory and self control theory are the most famous and important theories. Research would like to confirm the theories which are applied in multivariable latent growth curve model. Therefore, TEPS data are analyzed to investigate the model, and the results are as follows: (1)Deviation behavior gradually increases with time and variety of it also rises. (2)The fit of model is good. (3)The intercept is explained 19% by independent variables and the slope is explained 32%. In addition, it is significant for the intercept of the relation of peer group, attachment feeling of school, parental relation and academic achievement in the regression which is employed to anticipate the intercept. It is significant that the intercept of the relation of peer group, attachment feeling of school, and educational ambition and the slope of peer group, and attachment feeling of school can anticipate slope of deviation behavior effectively. (4)Employing multi-group analysis, there exist gender differences in the model. (5)Sex has influence on deviation behavior. (6)For girls, the slope of deviation behavior is anticipated by social relations, but for boys, besides the peer relationship, it is also included the educational ambition. According the results, some suggestions are proposed for future researches and the administration authority.

過去關於父母參與效果的研究發現：父母參與有助於提升子女的學習成就。由於父母參與被視為一種社會資本或文化資本的延伸，父母參與的愈多，其子女學習效果也愈好。有鑑於此，本研究主要在探討父母參與在家庭社經地位和子女學習成就之間所扮演的角色，並將研究目的細分為三個研究議題。首先，根據智力發展理論與認知能力成長曲線相關研究，第一個議題探討臺灣青少年學生學習成長軌跡的發展與變化情形為何？接著，運用 Bourdieu 的文化資本與 Coleman 的社會資本的概念說明父母參與的重要性，其它兩個議題則探討家庭社經地位對子女學習成長軌跡的影響歷程中，父母參與扮演著中介效果還是交互作用效果？ 原始資料來源取自臺灣教育長期追蹤資料庫（Taiwan Education Panel Survey）公共使用版中的第一波到第四波國中長期追蹤樣本，使用潛在成長曲線模型進行次級資料分析。研究結果發現：1.就整體學習發展型態來看，臺灣青少年學生學習成長軌跡的發展是一種非線性遞增減速的成長曲線，年級愈高，學習成長速率愈慢；2.就個別學習成長軌跡而言，學生間起始狀態與成長速率有個別差異現象，進一步透過潛在成長混合模型的分析，發現學生學習成長軌跡的發展型態並無類別上的差異；3.學生的起始能力會影響學習成長速率的變化而產生馬太效應；4.隨著時間的遞移，高起始能力組的學生，其學習成長速率高於低起始能力組的學生，兩者的學習成就間差距會逐漸擴大而產生扇形擴散效應；5.父母參與對子女學習成就表現有顯著正向的短期立即效果與長期延宕效果，但波段與波段之間的延宕效果則沒有顯著差異；6.在家庭社經地位對子女學習成長軌跡的影響歷程中，父母參與扮演著部份中介而不調節的影響效果。 最後，依據上述研究發現，就研究結果與研究方法兩方面，將提出相關研究建議以供實務參考及後續研究之用。 / The previous research has shown that parental involvement produces measurable gains in student achievement. Since parental involvement is seen as a form of social capital and cultural capital, it is possible that the more a student owns parental involvement, the bigger the effect is. Thus, this study explores what role parental involvement plays between parents’ social-economic status and their children’s academic performance. The major purpose is further categorized into three specific questions. Based on the intelligence developmental theory and growth curve analyses of cognitive ability, the first is to inquire what patterns the development and change of academic growth trajectories of Taiwanese teenager’s academic performance are. Using the concepts of Bourdieu’s cultural capital and Coleman’s social capital to explain the importance of parental involvement, the other two purposes are to explore whether the effects of parental involvement on adolescent academic growth trajectories are mediated or moderated by family socioeconomic status. Using the data from the public released core panel data of the Taiwan Education Panel Survey (TEPS) in 2001, 2003, 2005, and 2007, this study employs the method of the latent growth curve modeling to address research questions. The results are the following: (1) Academic growth trajectory of Taiwan adolescence’s achievement reveals a nonlinear de-accelerating growth curve; (2) There are significant individual differences in both the initial status and growth rate of achievement among students, but further employing different latent growth mixture models shows no individual differences in the patterns of academic growth trajectories; (3) The Matthew Effects occur in the academic growth trajectories of Taiwanese teenagers; (4) Students with lower initial status learn more slowly over time than those with higher initial status do, and the “fan-spread” effect is found; (5) There are positive short-term and longer term effects of parental involvement on the Taiwanese adolescents’ academic achievement performance, but no significant difference among patterns of longer term effects over 6 years; (6) The effects of parental involvement are partially mediated, but not moderated by family SES. Finally, the study discusses the implications of parental involvement and suggests directions for future research.

個人學習動機向來被認為是影響學習成就的重要因素，但是家庭也對學生的學習提供特定的脈絡條件。因此，在探討學生學習成就與時間發展效應之時，若能同時納入個人與家庭因素，並探討其間的交互作用，將能對於兩者的影響力進行客觀的檢驗。本研究的目的主要在探討臺灣青少年學習成就的成長軌跡變化型態，以及家庭文化資本與個人學習動機對於學習成就成長軌跡的影響機制。其中學生的文化資本是來自家庭父母所傳遞下來的先天條件，係屬於一種結構因素；而學生的學習動機則是來自個人後天的努力與學習的正向動力，係屬於一種個人因素。具體而言，本研究目的分為三個主要的研究議題，首先，根據Bourdieu（1977）的文化資本概念，以及Bandura（1977, 1986, 1997）與McInerney和McInerney（1994）的學習動機觀點，探討這兩個重要解釋變數對於各波學生學習成就的影響情形；再者，根據Sternberg（1985, 1986, 1988）的智力三元論觀點探討學生學習成就的成長變化情形；最後，探討文化資本與學習動機對於學生學習成就成長軌跡的交互作用效果。 研究資料取自臺灣教育長期追蹤資料庫（Taiwan Educational Panel Survey）的四波追蹤樣本，以潛在成長曲線模式進行次級資料分析。研究結果發現：1.臺灣青少年的學習成就成長軌跡呈現非線性的遞增漸緩的成長曲線；學生在學習成就的起始能力與成長速率存在個別差異，且學生的起始能力與成長速率具有正向的關係，顯示隨著時間的遞移，起始能力高與低的學生，其能力的差距會逐漸擴大。2.文化資本與學習動機對於學習成就成長軌跡的影響未具交互作用，顯示個人的學習動機並不能減緩或反轉文化資本對於學生學習成就的影響。3.文化資本與學習動機對於學生學習成就的主要效果，在學習的早期階段，存在正向的影響效果，但影響力會隨著時間而逐漸降低。4.文化資本係影響學生學習成就成長軌跡的重要因素，文化資本的豐富與不足會加劇學生學習成就的差距，因而造成強者恆強、弱者恆弱的「馬太效應」現象。最後，依據上述的研究發現，分別提出教育實務上、未來研究與對資料庫研究的建議，以供相關教育人員與研究者參考。 / Individual motivation has always been recognized as the key factor for influencing the students’ learning achievement. However, the family of the students is also considered as an important contextual determinant. As a result, in order to analyze the students’ learning achievement against the temporal effect of time, it is imperative that the factor of family background should be included for understanding the interaction of the factors on the learning achievement. The primary goal of this study is to inquiry the patterns the development and change of learning achievement growth trajectory of the Taiwan adolescent. Particularly, this study explores the effects of family cultural capital and learning motivation on adolescent learning achievement growth trajectory. By definition, family cultural capital which is a structural factor refers to the inherent characteristics that are passed down from the students’ parents. On the other hand, the students’ learning motivation which is a personal factor refers to the extrinsic factor that arises from later days’ hard work and positive learning efforts. In terms of research objectives, this study tries to integrate the Bourdieu’s (1977) perspective of cultural capital, and Bandura’s (1977, 1986, 1997) as well as McInerney and McInerney’s (1994) concept of learning motivation into a framework for examining the effects of the learning growth of different waves of students. Secondly, by applying the Sternberg’s (1985, 1986, 1988) triarchic theory of intelligence to examine the changes of the students’ learning growth trajectory. Finally, to analyze the interaction between the students’ cultural capital and learning motivation on their learning achievement trajectory. The data using in this study was selected from the longitudinal database Taiwan Educational Panel Survey (TEPS). A total of four waves of students’ data were downloaded and analyzed as secondary data using the latent growth curve modeling (LGCM). Major results of the study were followed: First, the learning achievement trajectory of Taiwan adolescents’ seemed to be gradually growing in a non-linear incremental curve; it also shown that at the beginning the students’ learning achievement displayed significant individual differences. Likewise results also revealed a positive relationship between the students’ initial status and growth rate of learning achievement. That is, as the passing of time, the initial status of learning achievement affected the growth of disparity among the students. Second, there were no significant interaction effect between the students’ cultural capital and learning motivation on the learning achievement growth trajectory. This means that the students’ learning motivation cannot moderate the effects of cultural capital towards the learning achievement. Third, results revealed that the main effects of the students’ cultural capital and learning motivation on the learning achievement were occurred on the early stages of learning. A significant positive effect was found in these stages, however, the positive effect gradually decreased along with the passing of time. Fourth, it was found that the minimal effect of students’ cultural capital on their learning achievement growth trajectory was determined by the abundance or deficiency of the former. The amount of cultural capital also determined the distance of the students’ gap. In other words, a phenomenon of the Mathew effect was supported; wherein the students who are in a strong stand will get stronger later on, while the weak shall get weaker. Besides the findings mentioned above, recommendations for further study and limitations of the present study were given at the end.