Parentification is a process where children or adolescents assume adult roles before they are emotionally or developmentally ready, which, in turn, disrupts the development of healthy, secure attachment in childhood. Using 1,001 men and women from South Korea and the United States with equal division between males and females and multiple group comparison technique in structural equation modeling, this paper examined the relationship between parentification during childhood and depression during adulthood. It explores the cross-sectional long-term effects of parentification into adulthood, using a retrospective survey technique. This study also confirmed previous research findings that attachment, physical health and family-of-origin dysfunction, parental addiction in particular, significantly predict depression. This study is one of the few studies, using clinical data, that allows a direct comparison between different sample groups in two different countries and by gender.

本研究的主要目的是藉由實徵的PISA資料庫資料將多層次結構方程式模型的方法學介紹到台灣的教育領域。多層次結構方程式模型適合應用在大型且具階層或巢狀結構的資料，可以解決因群集性抽樣設計所導致的樣本點相依的問題。 本研究中包含三個小研究。在研究一中，實徵的資料經由多層次結構方程式模型步驟化的分析，並與傳統的結構方程式模型的分析結果相互比較。一共有五個構念及其測量指標從PISA 2003資料庫中被選取來建構多層次結構方程式模型。樣本包含948個學校共26,884位15歲來自加拿大的學生。研究結果顯示某些結構係數的正負向關係在組內層次與組間層次是十分不同的，這也彰顯出多層次結構方程式模型與傳統結構方程式模型比較下的價值。研究一的發現指出，在數學興趣與數學工具性動機控制的條件下，教師的支持對學生的數學成績及數學自我效能在組間層次並無效果，但教師的支持對學生的數學自我效能在組內層次具有正向顯著的效果。此外，除了在組間層次上數學興趣對數學成績有顯著的負向效果以及數學工具性動機對數學自我效能沒有顯著效果外，數學興趣與數學工具性動機對數學成績及數學自我效能具有顯著的正向效果。另外，數學成績對數學自我效能具有很大的效果，特別是在組間層次。 在研究二中，藉由評估跨越不同層級二樣本大小（即120、240、360、480、600、720、840、948個學校）時的模式適配度及參數估計值的穩定性，來決定一個最小較佳的層級二樣本數相對於層級二估計參數數目的比值。研究結果顯示，該比值大約至少8：1是較可以被接受的結果。在研究三中，藉由多群組多層次結構方程式模型進行跨國家的比較。根據研究二的較佳最小比例以及亞洲國家在PISA 2003資料庫中有限的層級二樣本數，一個將焦點集中在數學興趣對數學成績的不同層次預測關係之新多層次結構方程式模型被提出。由再次隨機取樣的加拿大145所學校作為西方國家的代表樣本，而由只有143所學校的日本樣本作為東方國家的代表。研究結果顯示，跨越加拿大與日本樣本，在任一層級中出現十分不同的預測效果。數學興趣對數學成績的預測效果在加拿大樣本中的兩層級皆是正向地顯著，但在日本樣本中卻都是負向地顯著。這意謂著未來某些重要的教育及心理學變項之間關係的跨國研究應該在被重視。 / The main purpose of this research was to introduce multilevel structural equation modeling methodology to Taiwan education field by applying empirical example from PISA 2003 database. Multilevel structural equation modeling was suitable to be applied to the large-scale and hierarchical or nested data structure. It could solve the problem of dependency among sample units resulted from clustered sampling design. There were three studies in the research. In study one, the empirical data dealt with multilevel structural equation modeling analysis was undertaken step by step and compared with conventional structural equation modeling analysis. There were five constructs and their measurement indicators from PISA 2003 database mapped to form the multilevel structural equation model. The sample was 948 schools with 26884 15-year-old students from Canada. The result showed the valences of some structural coefficients were quite different in between-level and within-level structural equation models, which characterisized the value of multilevel structural equation modeling when compared with the outcomes from conventional structural equation modeling analysis. The findings of study one indicated that teacher support had no effect on students’ mathematics grades and mathematics self-efficacy in between-level part but had a significant positive effect on mathematics self-efficacy in within-level part when both interest in mathematics and instrumental motivation to mathematics grades were considered in the model. Besides, interest in mathematics and instrumental motivation had positive effects on mathematics grades and mathematics self-efficacy except for negative effect from interest in mathematics to mathematics grades and no effect from instrumental motivation to mathematics self-efficacy in between-level part. In addition, mathematics grades had great influences on mathematics self-efficacy, especially in between-level part. In study two, a better minimum ratio of the number of level-2 units relative to the number of parameter estimates in between-level part was searched by evaluating the model-fit and stability of parameter estimates across several Canada samples with 120, 240, 360, 480, 600, 720 ,840, and 948 schools. The result showed that the ratio at least about 8:1 was appreciated. In study three, cross-national comparisons were processed by multiple group multilevel structural equation modeling. Based on the better minimum ratio from study two and limited level-2 sample sizes from Asian countries in PISA 2003, a new multilevel structural equation model was proposed focusing on the structural coefficient of mathematics grades regressed on interest in mathematics in each level. A random resampling Canada sample with 145 schools was served as the representative of the West nations and the Japan sample with only 143 schools was on behalf of the East nations. The result showed that quite different predictive effect in either level across the Canada sample and the Japan sample. The predictive effects of the interest in mathematics to mathematics grades were positively significant in the Canada sample in each level but were negatively significant in the Japan sample in each level, which implied that cross-national studies in some important relationships among educational and psychological variables should be emphasized in the future.

Dans ce mémoire, nous considérons un modèle épidémiologique multigroupe dans une population hétérogène, pour décrire la situation de l’épidémie de la COVID-19 dans une résidence pour personnes âgées. L’hétérogénéité liée ici à l’âge reflète une transmission élevée dûe à des interactions accrues, et un taux de mortalité plus élevé chez les personnes âgées. Du point de vue mathématique, nous obtenons un modèle SEIR multigroupe d’équations intégro-différentielles dans lequel nous considérons une distribution générale de la période infectieuse. Nous utilisons la méthode des fonctions de Lyapunov et une approche de la théorie des graphes pour déterminer le rôle du nombre de reproduction de base \(\mathcal{R}_0\) : l’état d’équilibre sans maladie est globalement asymptotiquement stable et l’épidémie s’éteint dans les deux groupes lorsque \(\mathcal{R}_0 \leq 1\), par contre elle persiste et l’état d’équilibre endémique est globalement asymptotiquement stable lorsque \(\mathcal{R}_0>1\). Les simulations numériques illustrent l’impact des stratégies de contrôle de la santé publique. / In this thesis, we consider a multiple group epidemiological model in a heterogeneous population to describe COVID-19 outbreaks in an elderly residential population. Age-based heterogeneity reflects higher transmission with enhanced interactions, and higher fatality rates in the elderly. Mathematically, we analyse a SEIR model in the form of a system of integro-differential equations with general distribution function for the infectious period. Lyapunov functions and graph-theoretical methods are employed to establish the role played by the basic reproduction ratio \(\mathcal{R}_0\) : global asymptotic stability of the disease-free equilibrium and no sustained outbreak when \(\mathcal{R}_0 \leq 1\), as opposed to persistent outbreak and globally asymptotic endemic equilibrium when \(\mathcal{R}_0>1\). Numerical simulations are presented to illustrate public health control strategies.