• Title/Summary/Keyword: General linear model

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Normal Mixture Model with General Linear Regressive Restriction: Applied to Microarray Gene Clustering

  • Kim, Seung-Gu
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.205-213
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    • 2007
  • In this paper, the normal mixture model subjected to general linear restriction for component-means based on linear regression is proposed, and its fitting method by EM algorithm and Lagrange multiplier is provided. This model is applied to gene clustering of microarray expression data, which demonstrates it has very good performances for real data set. This model also allows to obtain the clusters that an analyst wants to find out in the fashion that the hypothesis for component-means is represented by the design matrices and the linear restriction matrices.

Variable Selection Theorems in General Linear Model

  • Yoon, Sang-Hoo;Park, Jeong-Soo
    • Proceedings of the Korean Statistical Society Conference
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    • 2005.11a
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    • pp.187-192
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    • 2005
  • For the problem of variable selection in linear models, we consider the errors are correlated with V covariance matrix. Hocking's theorems on the effects of the overfitting and the undefitting in linear model are extended to the less than full rank and correlated error model, and to the ANCOVA model

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Variable Selection Theorems in General Linear Model

  • Park, Jeong-Soo;Yoon, Sang-Hoo
    • 한국데이터정보과학회:학술대회논문집
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    • 2006.04a
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    • pp.171-179
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    • 2006
  • For the problem of variable selection in linear models, we consider the errors are correlated with V covariance matrix. Hocking's theorems on the effects of the overfitting and the underfitting in linear model are extended to the less than full rank and correlated error model, and to the ANCOVA model.

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A Statistical Model for Marker Position in Biomechanics

  • Kim, Jinuk
    • Korean Journal of Applied Biomechanics
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    • v.27 no.1
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    • pp.67-74
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    • 2017
  • Objective: The purpose of this study was to apply a general linear model in statistics to marker position vectors used to study human joint rotational motion in biomechanics. Method: For this purpose, a linear model that represents the effect of the center of hip joint rotation and the rotation of the marker position on the response was formulated. Five male subjects performed hip joint functional motions, and the positions of nine markers attached on the thigh with respect to the pelvic coordinate system were acquired at the same time. With the nine marker positions, the center of hip joint rotation and marker positions on the thigh were estimated as parameters in the general linear model. Results: After examining the fitted model, this model did not fit the data appropriately. Conclusion: A refined model is required to take into account specific characteristics of longitudinal data and other covariates such as soft tissue artefacts.

Analysis of Field Test Data using Robust Linear Mixed-Effects Model (로버스트 선형혼합모형을 이용한 필드시험 데이터 분석)

  • Hong, Eun Hee;Lee, Youngjo;Ok, You Jin;Na, Myung Hwan;Noh, Maengseok;Ha, Il Do
    • The Korean Journal of Applied Statistics
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    • v.28 no.2
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    • pp.361-369
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    • 2015
  • A general linear mixed-effects model is often used to analyze repeated measurement experiment data of a continuous response variable. However, a general linear mixed-effects model can give improper analysis results when simultaneously detecting heteroscedasticity and the non-normality of population distribution. To achieve a more robust estimation, we used a heavy-tailed linear mixed-effects model for a more exact and reliable analysis conclusion than a general linear mixed-effects model. We also provide reliability analysis results for further research.

Finite-Sample, Small-Dispersion Asymptotic Optimality of the Non-Linear Least Squares Estimator

  • So, Beong-Soo
    • Journal of the Korean Statistical Society
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    • v.24 no.2
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    • pp.303-312
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    • 1995
  • We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

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IPMN-LEARN: A linear support vector machine learning model for predicting low-grade intraductal papillary mucinous neoplasms

  • Yasmin Genevieve Hernandez-Barco;Dania Daye;Carlos F. Fernandez-del Castillo;Regina F. Parker;Brenna W. Casey;Andrew L. Warshaw;Cristina R. Ferrone;Keith D. Lillemoe;Motaz Qadan
    • Annals of Hepato-Biliary-Pancreatic Surgery
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    • v.27 no.2
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    • pp.195-200
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    • 2023
  • Backgrounds/Aims: We aimed to build a machine learning tool to help predict low-grade intraductal papillary mucinous neoplasms (IPMNs) in order to avoid unnecessary surgical resection. IPMNs are precursors to pancreatic cancer. Surgical resection remains the only recognized treatment for IPMNs yet carries some risks of morbidity and potential mortality. Existing clinical guidelines are imperfect in distinguishing low-risk cysts from high-risk cysts that warrant resection. Methods: We built a linear support vector machine (SVM) learning model using a prospectively maintained surgical database of patients with resected IPMNs. Input variables included 18 demographic, clinical, and imaging characteristics. The outcome variable was the presence of low-grade or high-grade IPMN based on post-operative pathology results. Data were divided into a training/validation set and a testing set at a ratio of 4:1. Receiver operating characteristics analysis was used to assess classification performance. Results: A total of 575 patients with resected IPMNs were identified. Of them, 53.4% had low-grade disease on final pathology. After classifier training and testing, a linear SVM-based model (IPMN-LEARN) was applied on the validation set. It achieved an accuracy of 77.4%, with a positive predictive value of 83%, a specificity of 72%, and a sensitivity of 83% in predicting low-grade disease in patients with IPMN. The model predicted low-grade lesions with an area under the curve of 0.82. Conclusions: A linear SVM learning model can identify low-grade IPMNs with good sensitivity and specificity. It may be used as a complement to existing guidelines to identify patients who could avoid unnecessary surgical resection.

Inference on the Joint Center of Rotation by Covariance Pattern Models

  • Kim, Jinuk
    • Korean Journal of Applied Biomechanics
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    • v.28 no.2
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    • pp.127-134
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    • 2018
  • Objective: In a statistical linear model estimating the center of rotation of a human hip joint, which is the parameter related to the mean of response vectors, assumptions of homoscedasticity and independence of position vectors measured repeatedly over time in the model result in an inefficient parameter. We, therefore, should take into account the variance-covariance structure of longitudinal responses. The purpose of this study was to estimate the efficient center of rotation vector of the hip joint by using covariance pattern models. Method: The covariance pattern models are used to model various kinds of covariance matrices of error vectors to take into account longitudinal data. The data acquired from functional motions to estimate hip joint center were applied to the models. Results: The results showed that the data were better fitted using various covariance pattern models than the general linear model assuming homoscedasticity and independence. Conclusion: The estimated joint centers of the covariance pattern models showed slight differences from those of the general linear model. The estimated standard errors of the joint center for covariance pattern models showed a large difference with those of the general linear model.

Testing General Linear Constraints on the Regression Coefficient Vector : A Note

  • Jeong, Ki-Jun
    • Journal of the Korean Statistical Society
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    • v.8 no.2
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    • pp.107-109
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    • 1979
  • Consider a linear model with n observations and k explanatory variables: (1)b $y=X\beta+u, u\simN(0,\sigma^2I_n)$. We assume that the model satisfies the ideal conditions. Consider the general linear constraints on regression coefficient vector: (2) $R\beta=r$, where R and r are known matrices of orders $q\timesk$ and q\times1$ respectively, and the rank of R is $qk+q$.

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Hypothesis Testing for New Scores in a Linear Model

  • Park, Young-Hun
    • Communications for Statistical Applications and Methods
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    • v.10 no.3
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    • pp.1007-1015
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    • 2003
  • In this paper we introduced a new score generating function for the rank dispersion function in a general linear model. Based on the new score function, we derived the null asymptotic theory of the rank-based hypothesis testing in a linear model. In essence we showed that several rank test statistics, which are primarily focused on our new score generating function and new dispersion function, are mainly distribution free and asymptotically converges to a chi-square distribution.