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Öğe Accounting for Zero Inflation of Mussel Parasite Counts Using Discrete Regression Models(2017) Cankaya, Emel; Alpay, Olcay; Ozer, AhmetIn many ecological applications, the absences of species are inevitable due to either detection faults in samples oruninhabitable conditions for their existence, resulting in high number of zero counts or abundance. Usual practice formodelling such data is regression modelling of log(abundance+1) and it is well know that resulting model isinadequate for prediction purposes. New discrete models accounting for zero abundances, namely zero-inflatedregression (ZIP and ZINB), Hurdle-Poisson (HP) and Hurdle-Negative Binomial (HNB) amongst others are widelypreferred to the classical regression models. Due to the fact that mussels are one of the economically most importantaquatic products of Turkey, the purpose of this study is therefore to examine the performances of these four modelsin determination of the significant biotic and abiotic factors on the occurrences of Nematopsis legeri parasiteharming the existence of Mediterranean mussels (Mytilus galloprovincialis L.). The data collected from the threecoastal regions of Sinop city in Turkey showed more than 50% of parasite counts on the average are zero-valued andmodel comparisons were based on information criterion. The results showed that the probability of the occurrence ofthis parasite is here best formulated by ZINB or HNB models and influential factors of models were found to becorrespondent with ecological differences of the regions.Öğe ALTERNATIVE ROBUST ESTIMATORS FOR PARAMETERS OF THE LINEAR REGRESSION MODEL(2022) Altuntaş, Mutlu; Cankaya, Emel; Arslan, OlcayThis paper considers parameter estimation of the linear regression model with Ramsay-Novick (RN) distributed errors, focusing on its use to aid robustness. Positioning within the class of heavy-tailed distributions, RN distribution can be defined as the modification of unbounded influence function of a non-robust density so that it has more resistance to outliers. \rPotential use of this robust density has been assessed in Bayesian settings on real data examples and there is a lack of performance assessment for finite samples in the classical approach. Therefore, this study explores its robustness properties when used as error distribution compared to normal and other alternating heavy-tailed distributions like Laplace and Studentt. An extensive simulation study was conducted for this purpose under different settings of sample size, model parameters and outlier percentages. An efficient data generation of RN distribution through random-walk Metropolis algorithm is here also suggested. The results were supported by a real world application on famously known as Brownlee’s stack loss plant data.Öğe Evaluation of diffuse lymphadenopathy via various quantitative PET/CT parameters(Hellenic Soc Nuclear Medicine, 2023) Silov, Guler; Cankaya, Emel; Karacavus, SeyhanObjective: Discovery of diffuse lymphadenopathy (DLAP) in fluorine-18-fluorodeoxyglucose ( F-18-FDG) positron emission tomography/computed tomography (PET/CT) imaging alerts for the existence of many pathologic conditions with severity ranging from benign to malignancy. This study examines the role of various metabolic parameters reflecting F-18-FDG characteristics of organs/tissues to reach an accurate differential diagnosis for further clinical assessment. Materials and Methods: Positron emission tomography/CT images of 78 patients with DLAP were reviewed retrospectively. The diameter of the largest lymph node (DLlyn), maxi- mum standardized uptake value (SUVmax) of the liver (L), the largest lymph node (Llyn), spleen (S), and bone marrow (BM) were measured. Ratios to liver SUVmax were calculated for all, resulting LLRmax, SLRmax, and BMLRmax respectively. Results: The diameter of the largest lymph node, Llyn. SUVmax, LLRmax, and SLRmax produced cut-off values as 25.5, 8.86, 2.80, and 0.82 with corresponding sensitivity: specificity values as 65%:83%, 74%:77%, 74%:71%, and 79%:63% respectively for risk stratification of malignant causes. To differentiate lymphoma from sarcoidosis, DLlyn, SLRmax, and BMLRmax were found valuable with cut-off values obtained as 28.5, 0.84, and 1.19 with corresponding sensitivity: specificity values as 79%:91%, 79%:82%, and 54%:91%, respectively. Interdependency between parameters was also evaluated. Conclusion: High values of Llyn. Maximum SUV and LLRmax are the main characteristics of lymphoma, metastasis, and sarcoidosis. The diameter of the largest lymph node, SLRmax, and BMLRmax are determined as distinct parameters for distinguishing lymphoma from sarcoidosis. Besides, observed correlation structures amongst some PET/CT parameters were identified as nodal, extranodal, and diffuse patterns for three disease groups except sarcoidosis. These findings extend the knowledge about diagnostic factors based on F-18-FDG PET/CT patterns for DLAP.Öğe EXPONENTIATED GENERALIZED RAMOS-LOUZADA DISTRIBUTION WITH PROPERTIES AND APPLICATIONS(Ankara Univ, Fac Sci, 2024) Altinisik, Yasin; Cankaya, EmelIn this paper, we propose a new generalization of Ramos-Louzada (RL) distribution based on two additional shape parameters. Along with the genesis of its distributional form, the derivation of cumulative density function (cdf), survival and hazard rate functions, the quantile function (qf), moments, moment generating function (mgf), Shannon and Renyi entropies, order statistics and a linear representation of the proposed distribution are inspected. Several estimation methods of the model parameters are discussed throughout two comprehensive simulation studies conducted to compare its performance against some lifetime distributions. Application of a real dataset is presented to illustrate the potentiality of this distribution in line with the simulation studies.Öğe Modelling of Factors Influencing the Citation Counts in Statistics(2022) Alpay, Olcay; Danacioglu, Nazan; Cankaya, EmelCitation is considered as the most popular quality assessment metric for scientific papers, and it is thus important to determine what factors promote the citation count of a paper in comparison to the others in the same field. The main aim of this study is to model the citation counts of the research published in SCI or SCI-Expanded journals of Statistics field with the growing number of scientific works in Turkey. It is well known that the right-skewed nature of the counts makes the classical regression modelling inappropriate, even if the log transformation of counts is applied [1]. Due to the fact that distribution of citation counts involves a great number of zeros, this study serves for an additional aim that is to model the counts with advanced discrete regression models for a more precise prediction [2]. Data collected for this study consist of the citation counts of all scientific papers produced by 261 Statisticians in between 2005-2017. Discrete models varying from Poisson to Zero-Inflated or Hurdle were constructed by possible influential factors, such as the publication age, the number of references, the journal category etc. Predictive performances of alternative discrete models were compared via AIC and Vuong test [3]. Results suggested that Zero Inflated Negative Binomial and Hurdle Negative Binomial mixture models are the best forms to predict the zero inflation of citation counts [4]. In addition, the influential factors of the final model were interpreted to make some suggestions to Statisticians to increase the citation counts of their work.Öğe New zero-inflated regression models with a variant of censoring(Brazilian Statistical Association, 2022) Altinisik, Yasin; Cankaya, EmelThere is ever growing demand of modeling overdispersed count data generated by various disiplines. Excessive number of zeros and hetero-geneity in the population are two main sources of the overdispersion problem. Development of new count models that are more flexible than conventional Poisson model is thus necessary in order to address such sources. This study fullfils this need by proposing a new heterogeneous Poisson model with a cap-ture of excess zeros, namely zero-inflated Poisson-Ailamujia (ZIPA) model. In line with the aim of curing overdispersion, a censored variant of this newly suggested model is also here developed. An extensive simulation study is conducted to assess the performances of both forms of new models in terms of bias, precision and accuracy measures. Additionally, two real world ap-plications are presented to illustrate practical implications of zero-inflated (censored) Poisson-Ailamujia models in comparison to some alternatives.Öğe Performance of prior and weighting bias correction methods for rare event logistic regression under the influence of sampling bias(Taylor & Francis Inc, 2023) Alpay, Olcay; Cankaya, EmelThe problem of classifying events to binary classes has been popularly addressed by Logistic Regression Analysis. However, there may be situations where the most interested class of event is rare such as an infectious disease, earthquake, financial crisis etc. The model of such events tends to focus on the majority class, resulting in the underestimation of probabilities for the rare class. Additionally, the model may incorporate sampling bias if the rare class of the sample is not representative of its population. It is therefore important to investigate whether such rareness is genuine or caused by an improperly drawn sample. We conducted a simulation study by creating three populations with different rarity levels and drawing samples from each of those which are either compatible or incompatible with the actual rare classes of the population. Then, the effect of sampling bias is discussed under the two correction methods of bias due to rareness as suggested by King and Zeng.Öğe Relative variation of ionic composition in a karstic lake under the theory of unweighted vs weighted logratio analysis(Iwa Publishing, 2008) Cankaya, Emel; Sivaci, E. Ridvan; Kilinc, Sabri; Dere, SueranThe use of logratio analysis in limnological studies has proved to be effective for solving the problems of the constrained nature of compositional data. The method offers a graphical tool, the relative variation biplot, to explore relative changes of the ions. However, recent methodological developments have shown that the results can be perturbed by low-valued ions with high variances and proposed downweighting their influences as in correspondence analysis. Additional to all properties of the unweighted version, this weighted logratio analysis extends the previous work and has the advantage of the principle of distributional equivalence. As a motivating application, we chose a karstic lake with dominating ions calcium and sulphate causing other ions to be present relatively in low absolute levels. Besides, one of the collected compositional samples was suspected to be unusual which, in part, contributes to high relative variances. This paper is therefore concerned with the choice of the best method for the analysis of such extremely saline water systems by comparing performances of both unweighted and weighted logratio analyses. We concluded that introducing weights captured more features of ionic relationships with almost all compositional variability explained. We observed that the ratio of calcium to sulphate, ammonium or phosphorus (to a lesser extent) was particularly valuable in understanding the natural chemical process of the lake. A constant log-contrast model based on calcium, ammonium, nitrate and total soluble phosphorus appeared as an equilibrium equation.Öğe ROBUST BAYESIAN REGRESSION ANALYSIS USING RAMSAY-NOVICK DISTRIBUTED ERRORS WITH STUDENT-T PRIOR(Ankara Univ, Fac Sci, 2019) Kaya, Mutlu; Cankaya, Emel; Arslan, OlcayThis paper investigates bayesian treatment of regression modelling with Ramsay-Novick (RN) distribution specifically developed for robust inferential procedures. It falls into the category of the so-called heavy-tailed distributions generally accepted as outlier resistant densities. RN is obtained by coverting the usual form of a non-robust density to a robust likelihood through the modification of its unbounded influence function. The resulting distributional form is quite complicated which is the reason for its limited applications in bayesian analyses of real problems. With the help of innovative Markov Chain Monte Carlo (MCMC) methods and softwares currently available, here we first suggested a random number generator for RN distribution. Then, we developed a robust bayesian modelling with RN distributed errors and Student-t prior. The prior with heavy-tailed properties is here chosen to provide a built-in protection against the misspecification of conflicting expert knowledge (i.e. prior robustness). This is particularly useful to avoid accusations of too much subjective bias in the prior specification. A simulation study conducted for performance assessment and a real-data application on the famously known stack loss data demonstrated that robust bayesian estimates with RN likelihood and heavy-tailed prior are robust against outliers in all directions and inaccurately specified priors.Öğe Seasonal assessment of epiphytic diatom distribution and diversity in relation to environmental factors in a karstic lake (Central Turkey)(Gebruder Borntraeger, 2008) Sivaci, E. Ridvan; Cankaya, Emel; Kilinc, Sabri; Dere, SuekranSeasonal variation in the composition and concentration of epiphytic diatoms from a Karstic Lake, Great Lota, in Anatolia which has a distinctive ionic character was investigated during October 2000 and October 2001. A total of 66 diatom taxa belonging to 24 genera were identified. Mastogloia was the most dominant genus in all sampling periods. Gomphonema, Cymbella and Nitzschia were the subdominant epiphytic diatom genera. Relationships between epiphytic diatom assemblages and measured limnological variables were extracted by means of Redundancy Analysis (RDA). It was revealed that temperature, calcium (Ca2+), sulphate (SO42-) and total soluble phosphate (TSP) parameters accounted for a significant amount of the variation in the distribution of the diatom assemblages. While some dominant taxa (e.g. Mastogloia smithii and Nitzschia amphibia) appeared relatively abundant in the cold waters with high calcium concentration, other taxa (e.g. Rhopalodia gibberula and Cymbella affinis) showed affinities towards warmer water with low calcium level. Cluster analysis produced four major groups reflecting the importance of seasonal influence on the epiphytic taxa. Formation of these seasonal clusters was controlled mainly by the increase and decrease of Mastogloia species. Influence of seasons on species compositions was also assessed in terms of Diversity index (H') and evenness (J) values.Öğe The Proposal of Gamma Folded-Normal Distribution(2022) Altinisik, Yasin; Ceylan, Tahir; Cankaya, EmelDevelopment of new flexible distributions for modeling non-negative measurements occuring in lifetime or reliability studies is a prominent research area in Statistics. As being the most favoured positive definite form, the Gamma distribution poses a basis for such improvements. It is well known that transforming a Gamma variable with another continuous random variable (X) creates Gamma-X family of distributions. Following this principle, we here attempted to define the X variable as Folded-Normal distributed which is also positive definite so as to propose a new family of distributions. Named as Gamma Folded-Normal distribution (GFN), our proposal is a generalization of Gamma Half-Normal distribution and contains more freely estimated parameters. This study evaluates some mathematical properties of GFN distribution such as moments and illustrates the estimation procedure for unknown parameters through a simulation study. A separate simulation is also conducted to compare the performance of this new distribution with the Folded-Normal, Half-Normal and Gamma Half-Normal distributions. Besides, the practical importance of our new proposal is illustrated by analyzing a real world data set.
