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"Partial Least Squares Regression adalah salah satu teknik regresi yang memerhatikan pola hubungan antara variabel respon dan variabel prediktor. Teknik tersebut dapat digunakan saat terdapat korelasi tinggi antara variabel prediktor, banyaknya variabel prediktor yang melebihi jumlah observasi dan efek random pada variabel prediktor. PLSR dengan menggunakan algoritma NIPALS, membentuk komponen yang merupakan kombinasi linier berbobot dari variabel prediktor yang digunakan untuk memprediksi variabel respon dengan metode Ordinary Least Squares, dimana komponen yang terbentuk ortogonal atau tidak saling berkorelasi dan banyaknya komponen yang terbentuk akan lebih sedikit dari banyaknya variabel prediktor.

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Partial Least Squares Regression is one of technique that takes into account the pattern of relationship between response variable and predictor variables. The technique can be used when there is high correlation between predictors variables, the number of predictors variables exceed the number of observation and random effects on predictor variables. PLS using NIPALS algorithm, which is component forming a weigthed linear combination of predictor variables use to predict response variable by the method of Ordinary Least Squares, in which the component are formed orthogonal or not correlated each other and the number will be fewer than the number of predictor variables."

"Prinsip parsimoni adalah prinsip yang menyatakan bahwa jika terdapat beberapa penjelasan untuk suatu fenomena, maka penjelasan paling sederhanalah yang harus dipilih. Prinsip ini digunakan dalam analisis data untuk memilih model yang paling efisien dalam menjelaskan variabilitas data dengan parameter seminimal mungkin. Namun pada beberapa kondisi, data bisa saja melibatkan pengukuran atau variabel yang cukup banyak. Data berdimensi tinggi dapat menyebabkan kompleksitas dan kesulitan dalam analisis, sehingga reduksi dimensi pada data penting untuk dilakukan. Principal Component Analysis (PCA) adalah salah satu metode yang dapat digunakan untuk melakukan reduksi dimensi, dengan mengekstraksi variabel baru dan mengurangi pengaruh dari variabel yang tidak relevan. Namun, metode PCA tidak toleran terhadap missing value, sehingga algoritma Nonlinear Iterative Partial Least Squares (NIPALS) dapat digunakan dalam mengatasi data yang mengandung missing value. Performa dari algoritma NIPALS dievaluasi menggunakan nilai normalized root mean square error (NRMSE) dan koefisien korelasi Pearson. Kemudian, performa dari algoritma ini dibandingkan dengan dua metode lain, meliputi Probabilistic Principal Component Analysis (PPCA) dan SVDImpute. Setelah dilakukan percobaan sebanyak seratus kali pada data survei COVIDiSTRESS, didapatkan hasil bahwa algoritma NIPALS memiliki performa yang lebih baik dan stabil dalam melakukan reduksi dimensi dibandingkan SVDImpute dan PPCA pada data dengan missing value sebesar 1% hingga 15%.

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The principle of parsimony, states that if there are multiple explanations for a phenomenon, the simplest explanation should be chosen. This principle is applied in data analysis to select the most efficient model that explains the variability of the data with minimal parameters. However, in some cases, the data may involve a large number of measurements or variables. High-dimensional data can lead to complexity and difficulties in analysis, therefore dimensionality reduction is important. Principal Component Analysis (PCA) is one method that can be used for dimensionality reduction by extracting new variables and reducing the influence of irrelevant variables. However, PCA is not tolerant to missing values, so the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm can be used to handle data with missing values. The performance of the NIPALS algorithm is evaluated using the normalized root mean square error (NRMSE) and Pearson correlation coefficient. Subsequently, the performance of this algorithm is compared with two other methods, including Probabilistic Principal Component Analysis (PPCA) and SVDImpute. After conducting a hundred trials on the COVIDiSTRESS survey data, it was found that the NIPALS algorithm performed better and was more stable in dimension reduction compared to SVDImpute and PPCA algorithms on data with missing values ranging from 1% to 15%."

"The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the non-specialist."

"Dalam penerapan analisis regresi seringkali terdapat efek dependensi spasial (lokasi) yaitu nilai observasi variabel dependen pada suatu lokasi bergantung pada nilai observasi di lokasi lain. Karateristik ini dinamakan spasial lag. Bentuk dependensi lain adalah spasial error yaitu error pada suatu lokasi dipengaruhi oleh error pada lokasi sekitarnya. Model regresi yang melibatkan efek dependensi spasial disebut model spasial dependen. Dalam kenyataannya tidak tertutup kemungkinan spasial dependen pada data cross section memiliki kedua kararateristik dependensi spasial. Tugas akhir ini membahas tentang prosedur mengestimasi parameter model dengan kedua jenis spasial dependen, yaitu spasial lag sekaligus spasial error dengan metode Generalized Spatial Two Stage Least Squares (GS2SLS). Metode ini menggunakan Two Stage Least Squares, Generalized Moment, dan transformasi Cochrane-Orcutt. Taksiran yang dihasilkan bersifat konsisten. Kata Kunci: Spasial Lag, Spasial Error, Two Stage Least Squares, Generalized Moment, Transformasi Cochrane-Orcutt."

"This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained."

"The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control.In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject."

"Obstructive Sleep Apnea OSA adalah gangguan di mana seseorang sering berhenti bernapas selama tidurnya. OSA ditandai oleh episode henti napas apnea minimal 10 detik/episode. Gejala OSA sering terjadi, namun sulit untuk dideteksi. Hal ini disebabkan OSA terjadi saat pasien tidur. Hal inilah yang menjadikan OSA penyebab terbesar morbiditas dan mortalitas di seluruh dunia. OSA terkait dengan beberapa penyakit, salah satunya adalah Diabetes Melitus DM. Kejadian OSA melalui hipoksemia intermitten dapat menyebabkan intoleransi glukosa, seperti DM tipe 2 dan prediabetes. OSA, DM, dan prediabetes diketahui memiliki faktor risiko bersama antara lain obesitas dan tekanan darah tinggi. Tujuan dari penelitian ini adalah untuk mengetahui model hubungan OSA, DM tipe 2, dan prediabetes secara simultan. Setelah model hubungan antar ketiganya diketahui, maka faktor-faktor risiko OSA, DM tipe 2, dan prediabetes secara bersamaan dapat diketahui. Data yang digunakan dalam penelitian ini adalah data primer yang diperoleh dengan pemeriksaan langsung ke pasien OSA di RSCM. Metode sampling yang digunakan adalah non-probability sampling, yaitu purposive sampling. Jumlah sampel pada penelitian ini didapat sebanyak 205 pasien. Metode Partial Least Squares PLS digunakan untuk mencapai tujuan penelitian. PLS digunakan untuk memodelkan hubungan langsung maupun tidak langsung antara variabel laten dan variabel terukur secara simultan. Selain itu, PLS dipertimbangkan sebagai pendekatan soft modeling yang tidak mensyaratkan asumsi-asumsi yang kuat, seperti ukuran sampel, skala pengukuran, dan asumsi distribusi. Variabel dependen dalam penelitian ini adalah OSA, DM tipe 2, dan prediabetes. Variabel independen dalam penelitian ini adalah jenis kelamin, usia, tekanan darah, obesitas, dan sleep hygiene. OSA dipengaruhi secara langsung oleh obesitas dan sleep hygiene. DM tipe 2 dipengaruhi secara langsung oleh prediabetes, dan dipengaruhi secara tidak langsung oleh jenis kelamin, usia, obesitas, dan OSA. Sedangkan prediabetes dipengaruhi secara langsung oleh jenis kelamin, usia, dan OSA, dan dipengaruhi secara tidak langsung oleh sleep hygiene. Prediabetes dapat dipengaruhi baik secara tidak langsung dan tidak langsung oleh obesitas melalui OSA.

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Obstructive Sleep Apnea OSA is a disorder in which a person frequently stops breathing during his or her sleep. OSA is characterized by episodes of stop breathing apnea at least 10 seconds episode. Symptoms of OSA are common, but difficult to detect. This is because OSA occurs when patient sleeps. That is what causes OSA to be the biggest morbidity and mortality worldwide. OSA has been linked with several diseases, one of which is Diabetes Mellitus DM . Incidence of OSA through hypoxemia intermitten can cause glucose intolerance, such as Diabetes Mellitus type 2 and prediabetes. OSA, DM, and prediabetes are known to have shared risk factor such as obesity and high blood pressure. The purpose of this research is to know the relationship model of OSA, DM type 2, and prediabetes simultaneously. Once the relationship model is known, then the risk factors of OSA, DM type 2, and prediabetes can simultaneously be known. Data used in this research is primary data which obtained by direct examination to patients with OSA at RSCM. Sampling method used in this research is non probability sampling, such as purposive sampling. The number of samples in this research as many as 205 patients. Partial Least Squares PLS method is used to obtain the purpose of this research. PLS is used to modeling a direct and indirect relation between latent variables and manifest variables simultaneously. Moreover, PLS has been considered as soft modeling approach because PLS does not require strong assumptions, such as sample size, measurement scale, and distribusions. OSA, DM type 2, and prediabetes are dependent variables. Independent variables are gender, age, blood pressure, obesity, and sleep hygiene. OSA is directly affected by obesity and sleep hygiene. DM type 2 is directly affected by prediabetes, and indirectly affected by gender, age, obesity, and OSA. Gender, age, and OSA have direct effect to prediabetes, meanwhile sleep hygiene has indirect effect to prediabetes. Obesity has direct and indirect effect to prediabetes, through OSA. "

"This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigor, it advances readers understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms."