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A Comparative Study of Fixed Effects Models and Random Intercept/Slope Models as a Special Case of Linear Mixed Models for Repeated Measurements
Neslihan ?yit,A??r Gen
Sel?uk Journal of Applied Mathematics , 2007,
Abstract: Any dataset in which subjects are measured repeatedly over time or space can be described as repeated measurements data. A linear mixed model (LMM) is a powerful method for analyzing repeated measurements data. It is made up of two components. The first component consists of a regression model for the average response over time and the effects of covariates on this average response. The second component provides a model for the pattern of covariances or correlations between the repeated measurements. In this study, a comparative evaluation of fixed effects models with random intercept models and random intercept and slope models as a special case of random effects models from linear mixed models are taken into consideration and the superiority of random intercept and slope models allow to modeling possible heterogeneity in intercepts and in slopes of the individual's own regression line for repeated measurements data is emphasized.
On Some New Modifications of Ridge Estimators
Yasin Asar,A??r Gen
Statistics , 2015,
Abstract: Ridge estimator is an alternative to ordinary least square estimator when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose new estimators which are modifications of the estimator suggested by Lawless and Wang (1976). A Monte Carlo experiment has been conducted for the comparison of the performances of the estimators. Mean squared error (MSE) is used as a performance criterion. The benefits of new estimators are illustrated using two real datasets. According to both simulation results and applications, our new estimators have better performances in the sense of MSE in most of the situations.
The Determination of Outlier Values by M Estimator in Nonlinear Regression and a Simulation Study
Ahmet Pekg?r,A??r Gen
Sel?uk Journal of Applied Mathematics , 2011,
Abstract: The existence of a few outlier values in the sampling would prevent the information given by the majority of the sampling and all of the statistics would turn to be insignificant. Therefore it is essential to determine the outliers in the sampling. In the literature, there are studies regarding the determination of the outliers in the linear regression. In this study, under the light of the studies of Rousseeuw ve Zomeren (1990) and Wu and Lee (2006), it is aimed to determination of outlier values by M estimator in nonlinear regression, one of the robust location estimators. In the application, the height of a corn plant has been analyzed as the sample data set per weeks in the period of 2008 in the Konya region using the Sel uk STAT statistics package program.
Selcuk Stat with Statistical Calculations and Performance Evaluation
Ahmet Pekg?r,A??r Gen
Sel?uk Journal of Applied Mathematics , 2012,
Abstract: Mining, analysing and presenting data by statistical packages provide their users the capability of modelling and foresight. Nowadays, by the virtue of technological improvement, users are empowered by various statistical packages against even most complicated statistical problems. But in current circumstances, to benefit completely from these packages, one must face various challenges. Two important criteria to choose one among competing packages may probably be the prices and the languages in which the packages are written. In this study, a free Turkish statistical package Sel uk STAT encoded with Delphi is compared with some other common statistical packages SPSS v17 and Minitab v15 in terms of their performance and speed.
LS-SVM Method for Fuzzy Nonlinear Regression
ümran M. Tek?en,A??r Gen
Sel?uk Journal of Applied Mathematics , 2011,
Abstract: In this study LS-SVM method is applied for fuzzy nonlinear regression whose input and output are fuzzy numbers. The method solves any problem of classification or regression via transforming to a quadratic problem without running into local solutions. This method is favourable owing to independent from a model. In this study, two practises are applied to linear and nonlinear data.
An Application of Structural Change Tests on Linear Regression Models
Ayd?n Karakoca,A??r Gen
Sel?uk Journal of Applied Mathematics , 2011,
Abstract: In this study, we introduced structural change tests on linear regression models. Properties of structural tests are decribed and an application of tests done on a data sets on deposit interest rate for Latvia, Holland and Turkey which gets from unistat and Tuik.
Nonlinear Time Series Analysis of Daily Gold Sale Price in Turkey
?smail K?nac?,A??r Gen
Sel?uk Journal of Applied Mathematics , 2006,
Abstract: A time series is a sequence of observations made periodically within time. For time series that are met in real situations, generally first of all linear time series models are conserned. This depends on the fact that by linear models it is easier to make statistical inferences and forecasts. However, in some cases, linear time series models can be insufficient to explain the series and in this condition it is inevitable to usage of nonlinear time series models. In this study, the series of daily gold sale price (TL/gr) in Turkey between the dates 23.02.2001 and 07.07.2004 are used. Then, a suitable nonlinear model among the nonlinear time series models are chosen fort his series. Finally, the results obtained from these two models are discussed comparatively.
Application of a New Mathematical Model for Estimating Maize Yield
Ufuk Karadavut,A??r Gen,?etin Palta,?eref Aksoyak
Sel?uk Journal of Applied Mathematics , 2005,
Abstract: This research was carried out International Agricultural Research Institute’s experimental areas in Konya province in the Central Anatolian Region of Turkey. In the research, three corn cultivars (P 3394, DK 585 and NS 640) were tested in randomized complete block design with four replications. The interelation between the productivity of Zea mays and the increasing of it’s generative organs during the phenological phase ‘tasseling-milky ripeness’, as far as the dependence of this relation on some factors influencing crop grow, provide a basis for a quantity analysis left to this work. The potantial yield of the used hybrid was the only parametric index from the stock of the growth limiting factors, which take part in the analysis. Environmental factors, especially sum of effective temperatures, precipitation and nitorgen supply, were strongly effected yield formation. The interrelation between these factors gave us a real possibility to determine the function of the growth and yield.
Comparison of Some Estimation Methods in Linear Regression
A??r Gen,ümran M. Tek?en,?lkay Alt?nda?
Sel?uk Journal of Applied Mathematics , 2010,
Abstract: In this study, we are informed about some methods as alternatives to the classical least squares methods which are used for simple linear and multiple linear regression analysis. In short, linear regression model is shown via matrix as;Y=Xβ+ε where Y is the vector belonging to dependent variable, X is the design matrix of independent variables, β is the parameter vector, εis the vector belonging to error terms, so the least squares estimator of the linear regression is shown byβ=(X^{′-1}X′Y) Alternative methods have emerged on the purpose of outliers' existing in observations unlike the least squares estimation, data's not providing the regression assumptions or using of the previous information about parameters as well. In the study, we are informed about the least absolute deviations regression apart from the least squares method, artificial neural networks, M-regression, the nonparametric regression and Bayesian regression. On the purpose of comparison of the methods' results, numerical results are derived by using the temperature variation data in Antalya and Fethiye regions for simple regression analysis and variables affecting the fuel percentage in crude oil for multiple regression analysis.
Filtering Data of High-Resolution Terrestrial Laser Scanner and Effects of Filtrations on the Landslide Monitoring
Mustafa Zeybek, ?smail ?anl?o?lu, A??r Gen
Dogal Afetler ve Cevre Dergisi , 2015, DOI: 10.21324/dacd.22635
Abstract: Monitoring and investigating natural disasters is one of the most important works for decreasing damages and preventing losses. In this study, using Terrestrial Laser Scanning (TLS) techniques for landslide monitoring studies, processing data obtained from these techniques and evaluating the results were performed. Research was carried out on a landslide zone which occurred in the Middle Taurus Mountains. When previous studies were examined, deformations reaching up to 5m were formed in the region. In this article, automatic filtering of terrestrial laser scanning data, filtering of trees and other objects on the earth and acquiring digital elevation model (DEM) and by means of this model, assessing changes occurring in the elevation components on the land surface and the effect of filtering algorithms on analysis were investigated. Progressive Morphological Filtering (PMF) algorithm was used for this research. Point cloud filtering algorithm has automatically obtained two filtered data as the ground and the non-ground. Using the real surface ground models of the earth to obtain DEM model’s reflection of real earth surface has a direct impact on determining the true surface deformation. In conclusion, things such as trees, objects, vehicles, houses, man-made structures and vegetation must be filtered out of data because analysis in a regional base may cause misinterpretation without filtered point cloud data. The results revealed that the filtered comparison analyzes were evaluated easier. In addition, changes in plant cover in different periods for the comparison of models has been automatically filtered and the landslide movements have been interpreted with purifying from artificial distortion.
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