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Utami Dyah Syafitri
Department Of Statistics, Faculty Of Mathematics And Natural Sciences, IPB University, Jl. Meranti Kampus IPB Dramaga, Bogor 16680, Indonesia
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Journal : InPrime: Indonesian Journal Of Pure And Applied Mathematics

 1 
N-Level Structural Equation Models (nSEM): The Effect of Sample Size on the Parameter Estimation in Latent Random-Intercept Model Eminita, Viarti; Saefuddin, Asep; Sadik, Kusman; Syafitri, Utami Dyah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 6, No 1 (2024)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v6i1.38914

Abstract

Multilevel Structural Equation Modeling (MSEM) is claimed to address hierarchical data structures and latent response variables, but it becomes unstable with an increasing number of levels. N-Level SEM (nSEM) is an SEM framework designed to handle a growing number of levels in the model. The nSEM framework uses the Maximum Likelihood Estimation (MLE) method for parameter estimation, which requires a large sample size and correct model specification. Therefore, it is essential to consider the necessary minimal sample size to ensure accurate and efficient parameter estimation in the nSEM model. This study examined how sample size affects the performance of parameter estimators in nSEM models. We propose a method to evaluate the effect of many environments to estimate the results of factor loadings and environmental variance produced by the model. In addition, we also assess the impact of environment size on the estimation results of factor loadings and individual variance. The results were then applied to actual data on student mathematics learning motivation in Depok. The findings show that neither the number of environments nor the size of the environment affects the performance of fixed parameter estimation in the nSEM model. nSEM indicates excellent performance in estimating environmental variance at level 2 when the number of environments increases. Conversely, increasing the size of the environment worsens the performance of estimating individual variance parameters. Overall, the nSEM framework for the latent random-intercept (LatenRI) model performs well with increasing sample sizes. The application data on LatenRI models show almost similar estimation results.Keywords: Hierarchical data; Latent random intercept model; Multilevel structural equation modeling; n-Level structural equation modeling.AbstrakMultilevel Structural Equation Modeling (MSEM) diklaim dapat mengatasi struktur data hierarki dan variabel respons laten, namun menjadi tidak stabil dengan bertambahnya jumlah level. N-Level SEM (nSEM) adalah kerangka kerja SEM yang dirancang untuk menangani semakin banyak level dalam model. Kerangka kerja nSEM menggunakan metode Maximum Likelihood Estimation (MLE) untuk estimasi parameter, yang memerlukan ukuran sampel yang besar dan spesifikasi model yang benar. Oleh karena itu, penting untuk mempertimbangkan ukuran sampel minimal yang diperlukan untuk memastikan estimasi parameter yang akurat dan efisien dalam model nSEM. Studi ini menguji bagaimana ukuran sampel mempengaruhi kinerja penduga parameter dalam model nSEM. Kami mengusulkan metode untuk mengevaluasi pengaruh banyak lingkungan dalam memperkirakan hasil factor loadings  dan varians lingkungan yang dihasilkan oleh model. Selain itu, kami juga menilai dampak ukuran lingkungan terhadap hasil estimasi factor loadings dan varians individu. Hasilnya kemudian diterapkan pada data aktual motivasi belajar matematika siswa di Depok. Hasil menunjukkan bahwa baik jumlah lingkungan maupun ukuran lingkungan tidak mempengaruhi kinerja estimasi parameter tetap pada model nSEM. nSEM menunjukkan kinerja yang sangat baik dalam memperkirakan varians lingkungan pada level 2 ketika jumlah lingkungan meningkat. Sebaliknya, peningkatan ukuran lingkungan akan memperburuk kinerja pendugaan parameter varians individu. Secara keseluruhan, kerangka nSEM untuk model intersepsi acak laten (LatenRI) bekerja dengan baik dengan meningkatnya ukuran sampel. Data penerapan model LatenRI menunjukkan hasil estimasi yang hampir serupa.Kata Kunci: Data hirarki; Model intersep acak laten; Model persamaan structural multilevel; Model persamaan structural n-level. 2020MSC: 62D99
Co-Authors Aam Alamudi Abdul Rohman Abdul Rohman Agus Mohamad Soleh Agustin Faradila Aidi, Muhammad Nur Aji Hamim Wigena Akbar Rizki Alfi Hudatul Karomah ALIU, MUFTIH ALWI Anang Kurnia Andreas Nicholas Gandaputra Simbolon Andrew Donda Munthe Anggrahini, Ervina Dwi Anggraini Sukmawati Anik Djuraidah Anissa Permatasari Antonio Kautsar ASEP SAEFUDDIN Auliya Ilmiawati Aziza, Vivin Nur Azkiya, Azka Al Baehera, Seta Bagus Sartono Bambang - Riyanto Bambang Prajogo Eko Wardoyo Bambang Riyanto Bartho Sihombing Bayu Pranata, Bayu Budi Susetyo Christin Halim Cici Suhaeni Dea Amelia, Dea Dwi Agustin Nuriani Sirodj Dwi Putri Kurniasari Eka Dewi Pertiwi Eka Winarni Sapitri Eminita, Viarti Endina Fatihah Yasmin Erfiani Erfiani Erfiani, Erfiani Erlinda Widya Widjanarko Ernawati, Fitrah Eti Rohaeti Evita Choiriyah Fadhila Hijryani FAHREZAL ZUBEDI Farit M Afendi Fatimah, Zahra Nurul Fitrianto, Anwar Gusti Tasya Meilania Hari Wijayanto I Made Sumertajaya Idqan Fahmi Immatul Ulya Indahwati Indonesian Journal of Statistics and Its Applications IJSA Intan Lukiswati Irmanida Batubara Irzaman, Irzaman Isti Rochayati Izzati, Mumpuni Nur Joko Santoso Jumansyah, L. M. Risman Dwi Khairil Anwar Notodiputro Kusman Sadik Laradea Marifni Lidiasari, Melisa Lismayani Usman M. Iqbal M. Rafi Meilania, Gusti Tasya Mohamad Rafi Mohamad Rafi Mohamad Rafi Mohammad Masjkur Muhamad Insanu Muhammad Bachri Amran Muhammad Nur Aidi Muhammad Nursid Mulianto Raharjo Muslim, Muhammad Irfai Muthahari, Wadudi Nanik Siti Aminah Nariswari Karina Dewi Ni Kadek Manik Dewantari Noer Endah Islami Nofrida Elly Zendrato Novia Yustika Tri Lestari. YR Nur Aidi, Muhammad Nurhajawarsi Nurhajawarsi Nursifa Mawadah R, Arifuddin Rifki Husnul Khuluk Ririn Fara Afriani Riswan Riswan Sanusi, Ratna Nur Mustika Sari, Mutia Dwi Permata Septaningsih, Dewi Anggraini Setyowati, Silfiana Lis Sifa Awalul Fikriah Siwi Haryu Pramesti Soleh, Agus M Soni Yadi Mulyadi Sony Hartono Wijaya Sri Sulastri Sri Wahyuningsih Syam, Ummul Auliyah Syifa Muflihah Tania Amalia Darsono Thasya Putri Topan . Ruspayandi Triyani Oktaria Vega, Iliana Patricia Vivin Nur Aziza Weisha, Ghea Wini - Trilaksani Wulan Tri Wahyuni Yenni Angraini Yuan Millafanti Yuni Suci Kurniawati Yuniar Istiqomah