Raju Rimal

• Rimal, Raju; Almøy, Trygve & Sæbø, Solve (2020). Comparison of multi-response estimation methods. Chemometrics and Intelligent Laboratory Systems.  ISSN 0169-7439.  205 . doi: 10.1016/j.chemolab.2020.104093 Full text in Research Archive.
• Rimal, Raju; Almøy, Trygve & Sæbø, Solve (2019). Comparison of multi-response prediction methods. Chemometrics and Intelligent Laboratory Systems.  ISSN 0169-7439.  190, s 10- 21 . doi: 10.1016/j.chemolab.2019.05.004 Full text in Research Archive. Show summary

  While data science is battling to extract information from the enormous explosion of data, many estimators and algorithms are being developed for better prediction. Researchers and data scientists often introduce new methods and evaluate them based on various aspects of data. However, studies on the impact of/on a model with multiple response variables are limited. This study compares some newly-developed (envelope) and well-established (PLS, PCR) prediction methods based on real data and simulated data specifically designed by varying properties such as multicollinearity, the correlation between multiple responses and position of relevant principal components of predictors. This study aims to give some insight into these methods and help the researcher to understand and use them in further studies.

• Helland, Inge Svein; Sæbø, Solve; Almøy, Trygve & Rimal, Raju (2018). Model and estimators for partial least squares regression. Journal of Chemometrics.  ISSN 0886-9383.  32(9) . doi: 10.1002/cem.3044 Show summary

  Partial least squares (PLS) regression has been a very popular method for prediction. The method can in a natural way be connected to a statistical model, which now has been extended and further developed in terms of an envelope model. Concentrating on the univariate case, several estimators of the regression vector in this model are defined, including the ordinary PLS estimator, the maximum likelihood envelope estimator, and a recently proposed Bayes PLS estimator. These are compared with respect to prediction error by systematic simulations. The simulations indicate that Bayes PLS performs well compared with the other methods.

• Rimal, Raju; Almøy, Trygve & Sæbø, Solve (2018). A tool for simulating multi-response linear model data. Chemometrics and Intelligent Laboratory Systems.  ISSN 0169-7439.  176, s 1- 10 . doi: 10.1016/j.chemolab.2018.02.009 Full text in Research Archive. Show summary

  Data science is generating enormous amounts of data, and new and advanced analytical methods are constantly being developed to cope with the challenge of extracting information from such “big-data”. Researchers often use simulated data to assess and document the properties of these new methods, and in this paper we present an extension to the R-package simrel, which is a versatile and transparent tool for simulating linear model data with an extensive range of adjustable properties. The method is based on the concept of relevant components, and is equivalent to the newly developed envelope model. It is a multi-response extension of R-package simrel which is available in R-package repository CRAN, and as simrel the new approach is essentially based on random rotations of latent relevant components to obtain a predictor matrix X, but in addition we introduce random rotations of latent components spanning a response space in order to obtain a multivariate response matrix Y. The properties of the linear relation between X and Y are defined by a small set of input parameters which allow versatile and adjustable simulations. Sub-space rotations also allow for generating data suitable for testing variable selection methods in multi-response settings. The method is implemented as an update to the R-package simrel.

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• Rimal, Raju (2019). Exploration of Multi-response Multivariate Methods. Show summary

  A linear regression model defines a linear relationship between two or more random variables. The random variables that depend on other random variables are often called response variables and the independent random variables are called predictor variables. In most cases not all variation is relevant for regression, i.e. only a certain amount of the variation in the predictors is relevant and only so for a part of the variation in the response. This leads to a reduction of the linear regression model where one can imagine a subspace of the space spanned by the predictor variables that contains all the relevant information for a subspace of the space spanned by the response variables. In this thesis we attempt to compare some new methods which are based on the envelope model and some established methods such as principal components regression (PCR) and partial least squares regression (PLS). The comparison tests these methods on their performance of producing minimum prediction and estimation error while modelling data simulated with specifically designed properties. For the simulation we have also created an R-package called simrel with a web interface. A simulation model for a multi-response multivariate linear model, on which the simulation tool is based, is discussed in the first paper. This paper prepares a basic foundation for the simulations with the concept of reduction of regression models. The second paper discusses the similarities of the envelope, PCR and PLS population models. This paper compares the prediction performance of several multivariate methods using a model with a single response. The final two papers make an extensive investigation evaluating the pre- diction and estimation performance of established (PCR, PLS1 and PLS2) and newly developed envelope based (Xenv and Senv) methods. Unsurpris- ingly the study found that not one method dominates in all situations, but their performance depend on the properties of the data they model. How- ever, the envelope based methods have shown remarkable performance in many cases, both in prediction and estimation. The study also recommend researchers to use and evaluate the envelope methods.

• Rimal, Raju; Almøy, Trygve & Sæbø, Solve (2019). A prediction comparison of some multivariate methods. Show summary

  A linear model is a widely used relationship structure which we encounter. A versatile tool to simulate linear model data controlling various aspects of it can be useful not only for comp aring methods, algorithms and models but also accessing and understanding their properties. Here we will present an R-package `simrel` that can control properties such as collinearity bet ween the variables, information content in predictors that is relevant for responses and position of the predictor components that contain this information. With few parameters, the packa ge can simulate data with a wide range of properties. Various multivariate prediction methods are developed over time to address the problem related to such properties. In the second part of the talk, we will compare relatively established methods such as Principal Component Regression, Partial Least Squares Regression together with newly developed envelope methods using the multi-response data simulated with varying properties. These methods deal with the relevant and irrelevant regression structure in a different way. This part will pr esent these differences and make some comparisons on these methods.

• Rimal, Raju; Almøy, Trygve & Sæbø, Solve (2018). A versatile tool for simulating linear model data. Show summary

  Data science is generating enormous amounts of data, and new and advanced analytical methods are constantly being developed to cope with the challenge of extracting information from such “big-data”. Researchers often use simulated data to assess and document the properties of these new methods, and in this paper, we present an extension to the R-package simrel, which is a versatile and transparent tool for simulating linear model data with an extensive range of adjustable properties. The method is based on the concept of relevant components and is equivalent to the newly developed envelope model. It is a multi-response extension of R-package simrel which is available in R-package repository CRAN, and as simrel the new approach is essentially based on random rotations of latent relevant components to obtain a predictor matrix X, but in addition we introduce random rotations of latent components spanning a response space in order to obtain a multivariate response matrix Y. The properties of the linear relation between X and Y are defined by a small set of input parameters which allow versatile and adjustable simulations. The method is implemented as an update to the R-package simrel.

• Rimal, Raju (2016). A comparetive study on PCR, PLS, Envelope and BayesPLS models.
• Rimal, Raju (2015). Multimatrix Extension of Partial Least Square.

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