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: Multivariate Multilevel Modeling (MVMM) to Analyze Student's Cognitive Achievement in the 2019 AKSI Survey
Abstrak: Pemodelan regresi linier merupakan metode statistika yang digunakan untuk mengidentifikasi pola hubungan linier antara peubah respon dan peubah penjelas. Untuk menghasilkan penduga dan kesimpulan yang sah, pemodelan regresi linier harus memenuhi beberapa asumsi, yaitu sisaan menyebar normal dengan nilai harapan sama dengan nol dan ragam homogen, serta kebebasan antar sisaan. Asumsi tersebut umumnya dapat terpenuhi jika data antar individu saling bebas. Pada suatu penelitian, data yang diperoleh terkadang tidak bebas dan menyebabkan beberapa penyimpangan asumsi. Misalnya data survei Asesmen Kompetensi Siswa Indonesia (AKSI) yang dibahas dalam penelitian ini. Data survei AKSI terdiri dari beberapa tingkatan atau membentuk struktur data berjenjang. Siswa-siswa yang terambil sebagai sampel tersarang dalam sekolah-sekolah berbeda. Respon pengamatan siswa dari sekolah yang sama cenderung tidak bebas dan variasi antar sekolah menyebabkan ragam tidak homogen. Analisis data berjenjang seperti model linier berhierarki atau pemodelan multilevel menjadi salah satu alternatif menyelesaikan masalah tersebut. Pemodelan multilevel terdiri dari satu peubah respon dan satu atau lebih peubah penjelas yang berjenjang. Apabila jumlah respon lebih dari satu dan saling berkorelasi maka dapat digunakan Multivariate Multilevel Modeling (MVMM). Data AKSI memiliki korelasi antar siswa dalam sekolah yang sama, selain itu data AKSI juga memiliki tiga peubah respon yang saling berkorelasi. Dengan demikian, dalam penelitian ini analisis dilakukan melalui pendekatan multivariate multilevel modeling (MVMM). Tujuan dari penelitian ini adalah mengkaji multivariate multilevel modeling (MVMM) dan memilih model MVMM terbaik untuk mengidentifikasi faktor-faktor yang berpengaruh terhadap capaian kognitif siswa pada survei AKSI 2019 yang diukur melalui skor matematika, literasi membaca dan sains. Pada taraf 5%, pengaruh tetap yang berpengaruh secara simultan terhadap capaian kognitif siswa adalah jenis kelamin, lama pendidikan ayah, indeks ketersediaan perangkat digital, indeks penggunaan perangkat digital sekolah, indeks penggunaan ICT untuk aktifitas mengerjakan tugas sekolah, indeks penggunaan ICT untuk aktifitas selain mengerjakan tugas sekolah, indeks pembatasan ICT di sekolah, indeks mengenai pandangan terhadap manfaat penggunaan ICT, skor akreditasi sekolah, serta interaksi antara lama pendidikan ayah dan skor akreditasi sekolah., Linear regression is a statistical method used to identify the linear relationships between the response and explanatory variables. To produce the best linear unbiased estimators and valid conclusions, The linear models assume the residual has normal distribution with expected value equal to zero and the variance is constant, and independent of each other. This assumption can generally be fulfilled if the data between individuals are mutually independent. In some study, the data obtained are sometimes not independent and causes the assumptions to be not fulfill in the models. For example, the Indonesian Student Competency Assessment (AKSI) survey data discussed in this study. The AKSI data consists of several levels or has a hierarchical data structure. The students taken as the sample were nested in different schools. The responses of students from the same school tend not to be independent and variations between schools cause the variance of residual is not constant. Hierarchical data analysis such as hierarchical linear modeling or multilevel modeling is an alternative to solve this problem. Multilevel modeling consists of one response variable and one or more explanatory variables at each level. If the study has two or more responses variables and
Keyword: Hierarchical data, ICT literacy, Indonesian Student Competency Assessment, MVMM

Judul: Pembuatan Minuman Ringan Berkarbonat dari Teh
Abstrak: Teh merupakan minuman penyegar karena dengan meminumnya baik pada saat udara panas maupun dingin, orang akan merasa lebih segar. Selain memberikan kesegaran, teh juga telah ditemukan mencegah beberapa jenis penyakit.
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