Semra Türkan

A new modified Jackknifed estimator for the Poisson regression model

ABSTRACT The Poisson regression is very popular in applied researches when analyzing the count data. However, multicollinearity problem arises for the Poisson regression model when the independent variables are highly intercorrelated. Shrinkage estimator is a commonly applied solution to the general problem caused by multicollinearity. Recently, the ridge regression (RR) estimators and some methods for estimating the ridge parameter k in the Poisson regression have been proposed. It has been found that some estimators are better than the commonly used maximum-likelihood (ML) estimator and some other RR estimators. In this study, the modified Jackknifed Poisson ridge regression (MJPR) estimator is proposed to remedy the multicollinearity. A simulation study and a real data example are provided to evaluate the performance of estimators. Both mean-squared error and the percentage relative error are considered as the performance criteria. The simulation study and the real data example results show that the proposed MJPR method outperforms the Poisson ridge regression, Jackknifed Poisson ridge regression and the ML in all of the different situations evaluated in this paper.

Modeling destructive earthquake casualties based on a comparative study for Turkey

The statistical modeling of destructive earthquakes is an indispensable tool for extracting information for prevention and risk reduction casualties after destructive earthquakes in a seismic region. The linear regression (LR) model can reveal the relation between casualty rate and related covariates based on earthquake catalog. However, if some covariates affect the casualty rate parametrically and some of them nonparametrically, the LR model may entail serious bias and loss of power when estimating or making inference about the effect of parameters. We suggest that semi-parametric beta regression (SBR), semi-parametric additive regression (SAR), and beta regression (BR) models could provide a more suitable description than the LR model to analyze the observed casualties after destructive earthquakes. We support this argument using destructive earthquakes occurred in Turkey between 1900 and 2012 having surface wave magnitudes five or more. The LR, SAR, BR, and SBR models are compared within the context of this data. The data strongly support that the SBR and SAR models can lead to more precise results than the BR and LR models. Furthermore, the SBR is the best model for the earthquake data since the beta distribution provides a flexible model that can be used to analyze the data involving proportions or rates. The results from this model suggest that the casualty rate depends on energy, damaged buildings, and the number of aftershocks of a destructive earthquake.

Detection of influential observations in ridge regression and modified ridge regression

The detection of influential observations is important because of their unduly large influence on the regression analysis results. Numerous diagnostics on identifying these observations are developed in the regression analysis. Penas statistic is one of the proposed diagnostics. In this study, Penas approach is formulated to ridge regression (RR) and modified ridge regression (MRR). The real data and artificial data are used to see performance of proposed diagnostic for the RR and MRR on detecting influential observations.

Effects of nutrient and water level changes on the composition and size structure of zooplankton communities in shallow lakes under different climatic conditions: a pan-European mesocosm experiment

Lentic ecosystems act as sentinels of climate change, and evidence exists that their sensitivity to warming varies along a latitudinal gradient. We assessed the effects of nutrient and water level variability on zooplankton community composition, taxonomic diversity and size structure in different climate zones by running a standardised controlled 6-months (May to November) experiment in six countries along a European north–south latitudinal temperature gradient. The mesocosms were established with two different depths and nutrient levels. We took monthly zooplankton samples during the study period and pooled a subsample from each sampling to obtain one composite sample per mesocosm. We found a significant effect of temperature on the community composition and size structure of the zooplankton, whereas no effects of water depth or nutrient availability could be traced. The normalised size spectrum became flatter with increasing temperature reflecting higher zooplankton size diversity due to higher abundance of calanoid copepods, but did not differ among depths or nutrient levels. Large-bodied cladocerans such as Daphnia decreased with temperature. Taxonomic diversity was positively related to size diversity, but neither of the two diversity measures demonstrated a clear pattern along the temperature gradient nor with nutrient and water levels. However, genus richness decreased at the warm side of the temperature gradient. Our experiment generally supports recent empirically based findings that a continuing temperature increase may result in lower genus richness and lower abundance of large-sized zooplankton grazers, the latter likely resulting in reduced control of phytoplankton.

A Jackknifed estimators for the negative binomial regression model

ABSTRACT Shrinkage estimator is a commonly applied solution to the general problem caused by multicollinearity. Recently, the ridge regression (RR) estimators for estimating the ridge parameter k in the negative binomial (NB) regression have been proposed. The Jackknifed estimators are obtained to remedy the multicollinearity and reduce the bias. A simulation study is provided to evaluate the performance of estimators. Both mean squared error (MSE) and the percentage relative error (PRE) are considered as the performance criteria. The simulated result indicated that some of proposed Jackknifed estimators should be preferred to the ML method and ridge estimators to reduce MSE and bias.

2014-2015 Öğretim Yılında Türkiye’de Devlet Üniversitelerinin Etkinlikleri ve Etkinliğe Etki Eden Faktörlerin Belirlenmesi

The concepts of efficiency and productivity are of vital importance in a world of limited resources. In this study, the productivity of state universities in Turkey is determined through data envelopment analysis, and the universities are ordered according to efficiency using a super efficiency model. Then, factors affecting efficiency are examined by Tobit and beta regression analysis; the results obtained from the two different methods are analyzed on a comparative basis. In the study, data from the 2014–2015 academic year are utilized to measure the training efficiency of 43 state universities in Turkey. As a result of data envelopment analysis, Gebze Technical University, Anadolu University, Middle East Technical University, Istanbul Technical University, Istanbul University, Marmara University, Hacettepe University, Gazi University, Ankara University, and Ege University are found to be effective universities. Generally, 22% of state universities are found to be effective. In terms of the criteria discussed in this study, Cumhuriyet University has the lowest efficiency value. According to the results of the Tobit and beta regression and h-index, the number of graduated students improves the efficiency value of state universities, while the presence of medical schools decreases the efficiency value.