Judul: Mixed effect models for high –dimensional longitudinal data with latent variables
Abstrak: A set of data that consist of repeated measurements on a large number of outcomes and covariates are known as high-dimensional longitudinal data. The high-dimensional longitudinal data may consist of several effects of interest that cannot be directly measured, known as latent factors or latent variables. During the last decade, the multivariate responses or high-dimensional in longitudinal data have been a big issue. The analysis of high-dimensional longitudinal data is complicated due to its complex correlation structures between outcomes. To understand changes over time of outcome variables, having correlations in individuals with explanatory variables is not enough. Hence, complex correlation structures between outcomes need to be considered. One approach that is commonly used to overcome high-dimensional longitudinal data is simultaneous equation modeling. A well-known simultaneous equation modeling method is the structural equation model (SEM). This approach has several appealing modeling abilities and can be used for high-dimensional longitudinal data. Under the SEM framework, the continuous time SEM is developed to avoid some issues associated with autoregressive and cross-lagged problems in SEM. Another simultaneous equation modeling method is by combining factor analysis and multivariate analysis methods to overcome high dimensional longitudinal data, namely latent factor linear mixed model (LFLMM). The factor analysis is used to reduce the high-dimensional outcomes, and the multivariate linear mixed model is used to study the longitudinal trends of several latent factors. One example of high-dimensional longitudinal data is the General Election Study. This study is carried out repeatedly to observe tendencies towards political attitudes and behavior over time in Belgium. The data contain political information, knowledge, perceptions, and preferences of a political party and the level of participation in politics. One of the most interesting things to study from the data is to analyze the change of political attitudes and behavior of respondents over time. Also, the relationship of changes in these outcomes is important to analyze. The General Election Study in Belgium was designed to include a representative sample of the target population under the Belgian electorate, so accurate estimates about the population could be made. This sampling design was created by the Institute for Social and Political Opinion (ISPO) and the Inter-university Center for Political Opinion Research (PIOP). The Belgian data set contained three subsamples, the Flemish (Dutch-speaking), the Walloon (French-speaking), and the Brussels Capital Region (Dutch and French-speaking). Several studies conducted on the Belgium data are carried out to understand the relationships between the latent variables Individualism (I), Ethnocentrism (E), and Authoritarianism (A) in Flanders. Cross-sectional or a longitudinal studies have also been carried out. In such cases, it is critical to capture the trend of the latent variables over time and, more importantly, whether there is any association or relationships between the development of nationalism (N), ethnocentrism (E), individualism (I), and authoritarianism (A) in Belgium. An empirical analysis of CT-SEM has been done to present the interdependencies among the four latent variables mentioned above on the basis of the General Election Studies for Belgium in 1991, 1995, and 1999 (Interuniversitair steunpunt politieke-opinieonderzoek, 1991, 1995, 1999). Although the four variables have been the subject of
Keyword: Belgium, CT-SEM, high-dimensional longitudinal data, LFLMM, Supplemented EM Algorithm

Judul: Enhancing Multivariate Linear Mixed Model with Two-Level Random Effects for Longitudinal Data and Its Application to PISA and National Examination Scores
Abstrak: Increasing the breadth to involve multivariate responses in cross-sectional data analysis becomes essential when examining interconnected and multidimensional phenomena. Including multivariate responses enables researchers to examine relationships and dependencies among numerous variables concurrently. The necessity to analyze multivariate responses in cross-sectional data emerges when researchers seek to understand complex patterns, dependencies, and interactions among various factors within a specific population. In actual scenarios, a series of observations is frequently taken multiple times, a phenomenon commonly known as repeated measurements. Repeated measurements entail evaluating a research subject at different observation points in time. Several researchers have devised alternative methods for analyzing longitudinal data. The linear mixed model is the more prevalent approach (LMM). Another challenge in longitudinal data analysis arises from the presence of multivariate response variables, where multiple responses are observed in the survey. One approach to tackle this is by simultaneously modeling them using a multivariate linear mixed model. The complexity of real-world data sets further increases when random effects are of a multilevel or hierarchical nature. Substantial research questions emerging in longitudinal data structures, where the response variables are multivariate and the random effects are multilevel, often involve issues such as interrelated changes between response variables. An example of hierarchical data with multiple observations is the PISA scores and national exam (UN) data for high school (SMA) students. This research is conducted repeatedly to observe the trend of average PISA scores of Indonesian students and the average national exam scores at the high school level. PISA score data is designed to include a representative sample from the target population, which is the result of a survey conducted by the OECD. There are three test subjects in the OECD survey: reading literacy, mathematics, and science. Meanwhile, the average SMA national exam scores data is sourced from the Basic Education Data. (DAPODIK). Cross-sectional studies have also been conducted to analyze PISA score data. In this case, it is crucial to capture whether there is any association or relationship between students' PISA scores across the three test subjects and also the school as the random effect. Furthermore, longitudinal studies have also been conducted. This study is applied to the average national exam (UN) scores data for high school students majoring in science in the West Java province. In this longitudinal study, it is essential to capture trends among the average UN scores for six subjects: Indonesian language, English language, mathematics, physics, chemistry, and biology over time. Another important aspect is to ascertain whether schools contribute as a random effect to the response variables. Empirical analysis using MLMM has been conducted for both cross-sectional and longitudinal data structures. Although PISA score data has been the subject of several studies in Indonesia, simultaneous analysis of all three PISA score data using MLMM has not been done before. Similarly, simultaneous analysis of average UN scores for high school students majoring in science in West Java with longitudinal data structure and the addition of random effects using MLMM has not been conducted. The results indicate that with the addition of random effects in the model, it is
Keyword: longitudinal data, multiraviate linear mixed model, two-level random effect, multilevel multiraviate linear mixed model

Judul: Karakterisasi Nira Kelapa Sawit (Elaesis guineensis, Jacq) yang Disadap Melalui Bunga Jantan dan Pohon Tumbang
Abstrak: Nira merupakan salah satu produk yang dihasilkan oleh pohon palma dan banyak digunakan dalam pembuatan gula merah dan minuman penyegar. Untuk meningkatkan hasil produksi nira, perlu ditingkatkan jumlah pohon palma penghasil nira atau mencari alternatif pohon palma lain sebagai sumber nira. Kelapa sawit (Elaeis guineensis, Jacq. ) merupakan salah satu diantaranya. Penelitian ini bertujuan untuk mencari metoda penyadapan nira yang paling baik dan melakukan karakterisasi nira. Penyadapan dilakukan melalui bunga jantan yang seludangnya belum membuka, melalui titik tumbuh pohon tumbang yang tidak mengalami pelayuan dan melalui titik tumbuh pchon tumbang yang mengalami pelayuan selama 2-3 minggu. Karakterisasi nira yang dilakukan meliputi pengukuran kadar air, kadar abu, total gula, total padatan terlarut, pH, to~al asam dan identifikasi gula. Sedangkan karakterisasi pada bagianbagian bunga jantan meliputi pengukuran kadar air, kadar abu, total gula, pH, total asam, kadar pati dan serat kasar.
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