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Advances in Methodology and Statistics

An Empirical Likelihood Ratio Based Comparative Study on Tests for Normality of Residuals in Linear Models

2019    Chioneso Show Marange and Yongsong Qin; 16(1):1-16

The application of goodness-of-fit (GoF) tests in linear regression modeling is a common practice in applied statistical sciences. For instance, in simple linear regression the assumption of normality of residuals is always necessary to test before making any further inferences. The growing popularity of the use of powerful and efficient empirical likelihood ratio (ELR) based GoF tests in checking for departures from normality in various continuous distributions can be of great use in checking for distributional assumptions of residuals in linear models. Motivated by the attractive properties of the ELR based GoF tests the researchers conducted an extensive Type I error rate assessment as well as a Monte Carlo power comparison of selected ELR GoF tests with well-known existing tests against symmetric and asymmetric alternative OLS and BLUS residuals. Under the simulated scenarios, all the studied tests have good control of Type I error rates. The Monte Carlo experiments revealed the superiority of the ELR GoF tests under certain alternatives of both the OLS and BLUS residuals. Our findings also demonstrated the superiority of OLS over BLUS residuals when one is testing for normality in simple linear regression models. A real data study further revealed the applicability of the ELR based GoF tests in testing normality of residuals in linear regression models.

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Mechanisms Generating Asymmetric Core-Cohesive Blockmodels

2019    Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj; 16(1):17-41

The paper addresses the relationship between different local network mechanisms and different global network structures, described by blockmodels. The research question is narrowed to the context of preschool children networks. Based on the studies regarding friendship, liking and interactional networks among preschool children, the popularity, transitivity, mutuality and assortativity mechanisms are assumed to be important for the evolution of such networks. It is assumed that the global network structure is defined by an asymmetric core-cohesive blockmodel consisting of one core group of units and two or more cohesive groups of units. Therefore, the main research question is whether the emergence of an asymmetric core-cohesive blockmodel can be a result of the influence of the listed mechanisms. Different initial global network structures are considered. Monte Carlo simulations were used. The relative fit measure is proposed and used to compare different blockmodel types on generated networks. The results show that the listed mechanisms indeed lead to the assumed global network structure.

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Two Stage Adaptive Cluster Sampling based on Ordered Statistics

2019 Girish Chandra, Neeraj Tiwari and Raman Nautiyal; 16(1): 43-60

The estimation problem on sparsely distributed populations using adaptive cluster sampling (ACS) is discussed. In the first phase of ACS, two stage sampling is used in which primary and secondary sampling units are selected using simple random sampling without replacement. The idea of Thompson (1996) is introduced in order to choose an appropriate fixed value of pre-specified condition, which might represent the number of rare species, before conducting the survey by the use of order statistics. Different estimators of the population mean under the two possible schemes (open and closed boundaries of primary sampling units) are studied and the Rao-Blackwell theorem for improving these estimators is also used. Numerical illustrations, one on real life data and the other based on simulation study, are discussed for these two schemes. This design may be quite useful in environmental, forestry and other areas of research dealing with rare, endangered or threatened species.

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Effects of the Same-Gender vs. Cross-Gender Mentoring on a Protégé Outcome in Academia: An Exploratory Study

2019 Metka Kogovšek and Irena Ograjenšek; 16(1): 61-78

Mentoring seems to be an important way to start and advance individual researcher’s career in science. Therefore, it is essential to examine the factors related to successful mentoring in order to find ways of efficiently supporting young academics on their career development path. Building on the similarity-attraction and social identity theories, our research indicates that gender similarity in academic mentoring might be related to the protégés’ postdoctoral publication scores that lead to career advancement. The scores in a typical five-year publication cycle are higher for the protégés situated within same-gender mentoring dyads. Furthermore, the mentors’ research performance importantly adds to the protégés’ postdoctoral research performance.

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Wellbeing Assessment Yardstick: Evidence from the Elderly Wellbeing across Russian Subnational Macro-Regions

2019 Irina Pavlova, Ilya Gumennikov, Evgeny Monastyrny, and Elena Golubeva; 16(2): 21-40

Although Russia manifests some dynamics in its national policy on ageing, it still lacks comprehensive tools for the older generation wellbeing assessment both on national and regional levels. This research work is an ongoing project aimed at the development of the composite index (composite indicator) to assess the elderly population wellbeing in Russia for cross-regional comparison to equip Russian policy-makers with an essential tool and relevant reliable data to facilitate the decision-making and policy design at national, regional and local levels. The paper discusses the possibility of selecting relevant data from the pool of the official state statistics indicators to assess the elderly generation’s wellbeing in 85 regions of the Russian Federation by four index domains (economic, social, health and regional environment dimensions). Due to a high geographical and territorial heterogeneity, this index can be advised to be adopted as a potential tool to monitor wellbeing across Russian regions with the focus on policy development for macro-regions. This grouping of regions can minimize transaction costs of bargaining on behalf of the 85 regions while developing national policies and strategies. The paper employs the Russian Elderly Wellbeing Index (REWI) to compare calculation results for 2014 and 2016 as well as addresses the issue of elderly population wellbeing analysis on the meso level in the context of federal districts. The authors run cluster analysis for the REWI indicators to compare clusters of Russian regions and federal districts.

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Measuring Personal Networks with Surveys

2019 Tina Kogovšek and Valentina Hlebec; 6(2): 41-55

Like in other fields of inquiry in the social sciences, in social network research the most frequently used measurement method is the survey. Compared with other measurement objects such as networks of opinions, attitudes or values, measurement is more complex and thus often more challenging. Measurement typically occurs in two main phases. First, network units are measured (generated). Second, the relationships among the units and other unit characteristics (e.g. demographic properties) are determined, while some specific questions arise as to whether whole or egocentric (personal) networks are to be measured. In this paper, we limit ourselves to measuring personal networks, especially when compared with different methods for generating networks. There are five basic approaches to generating a personal network: name generator, role generator, event generator, positional generator, and contextual generator. Each is associated with particular research goals, costs (financial, time, respondent burden), advantages, and limitations. Moreover, the complexity and specifics of generating networks mean one must consider the characteristics of data collection modes (e.g. face-to-face, telephone, web). In this sense, we will present the advantages and limits of various methods of generating personal networks, evaluate them critically and comparatively, and illustrate them with often used examples.

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The Bad Mathematics of the Bad Luck Theory

2019 Mariia Beliaeva; 6(2): 58-69

The mathematics of the Bad Luck theory of carcinogenesis by Tomasetti and Vogelstein generated a great deal of controversy among cancer specialists but did not draw the mathematicians’ attention. Thus the gross mathematical mistakes of the theory foundation did not get a proper critique and remained unnoticed. As a result, the sensational quantitative estimates of the role of Bad Luck in cancer occurrence, though being erroneous, have spread widely among researchers and the general public and got the unfair popularity. The present paper reviews the actual mathematical mistakes of Bad Luck theory.

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Advances in Methodology and Statistics

Comparing Two Partitions of Non-Equal Sets of Units                                       

2018    Marjan Cugmas and Anuška Ferligoj; 15(1):1-21

Rand (1971) proposed what has since become a well-known index for comparing two partitions obtained on the same set of units. The index takes a value on the interval between 0 and 1, where a higher value indicates more similar partitions. Sometimes, e.g. when the units are observed in two time periods, the splitting and merging of clusters should be considered differently, according to the operationalization of the stability of clusters. The Rand Index is symmetric in the sense that both the splitting and merging of clusters lower the value of the index. In such a non-symmetric case, one of the Wallace indexes (Wallace, 1983) can be used. Further, there are several cases when one wants to compare two partitions obtained on different sets of units, where the intersection of these sets of units is a non-empty set of units. In this instance, the new units and units which leave the clusters from the first partition can be considered as a factor lowering the value of the index. Therefore, a modified Rand index is presented. Because the splitting and merging of clusters have to be considered differently in some situations, an asymmetric modified Wallace Index is also proposed. For all presented indices, the correction for chance is described, which allows different values of a selected index to be compared.

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Web Survey Paradata on Response Time Outliers: A Systematic Literature Review                                                             

2018    Miha Matjašič, Vasja Vehovar and Katja Lozar Manfreda; 15(1):23-41         

In the last two decades, survey researchers have intensively used computerised methods for the collection of different types of paradata, such as keystrokes, mouse clicks and response times, to evaluate and improve survey instruments as well as to understand the survey response process. With the growing popularity of web surveys, the importance of paradata has further increased. Within this context, response time measurement is the prevailing paradata approach. Papers typically analyse the time (measured in milliseconds or seconds) a respondent needs to answer a certain item, question, page or questionnaire. One of the key challenges when analysing the response time is to identify and separate units that are answering too quickly or too slowly. These units can have a poor response quality and are typically labelled as response time outliers. This paper focuses on approaches for identifying and processing response time outliers. It presents a systematic overview of scientific papers on response time outliers in web surveys. The key observed characteristics of the papers are the approaches used, the level of time measurement, the processing of response time outliers and the relationship between response time and response quality. The results show that knowledge on response time outliers is scattered, inconsistent and lacking systematic comparisons of approaches. Consequently, there is a need to improve and upgrade the knowledge on this issue and to develop new approaches that will overcome existing deficiencies and inconsistencies in identifying and dealing with response time outliers.

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Behind the Curve and Beyond: Calculating Representative Predicted Probability Changes and Treatment Effects for Non-Linear Models                                       

2018    Bastian Becker; p. 15(1):43-58         

Parameter coefficients from non-linear models are inherently difficult to interpret, and scholars frequently opt for computing and comparing predicted probabilities for variables of interest. In an influential article, Hanmer and Ozan Kalkan (2013) discuss the two most common approaches, the average case respectively observed values approach, and make a strong case for the latter. In this paper, I propose a further refinement of the observed values approach for the purpose of computing predicted probability changes. This refinement concerns the use of counterfactual values for the independent variable of interest. I demonstrate that accounting for non-linearities with regards to the variable of interest is important to avoid estimation biases. I also discuss the implications of this insight for estimating average treatment effects from observational data.

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Gumbel GARCH Model with Stock Application                                           

2018    Mehrnaz Mohammadpour and Fatemeh Ziaeenejad; p. 15(1):59-72                                                                               

The paper proposes a new GARCH model with Gumbel conditional distribution. Several statistical properties of the model are established, like autocorrelation function and stationarity. We consider two methods for estimating the unknown parameters of the model and investigate properties of the estimators. The performances of the estimators are checked by a simulation study. We investigate the application of the process using a real stock data.

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Internal Evaluation Criteria for Categorical Data in Hierarchical Clustering: Optimal Number of Clusters Determination                   

2018    Zdeněk Šulc, Jana Cibulková, Jiřı́ Procházka and Hana Řezanková ; p. 15(2):1-20                        

The paper compares 11 internal evaluation criteria for hierarchical clustering of categorical data regarding a correct number of clusters determination. The criteria are divided into three groups based on a way of treating the cluster quality. The variability-based criteria use the within-cluster variability, the likelihood-based criteria maximize the likelihood function, and the distance-based criteria use distances within and between clusters. The aim is to determine which evaluation criteria perform well and under what conditions. Different analysis settings, such as the used method of hierarchical clustering, and various dataset properties, such as the number of variables or the minimal between-cluster distances, are examined. The experiment is conducted on 810 generated datasets, where the evaluation criteria are assessed regarding the optimal number of clusters determination and mean absolute errors. The results indicate that the likelihood-based BIC1 and variability-based BK criteria perform relatively well in determining the optimal number of clusters and that some criteria, usually the distance-based ones, should be avoided.

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Mode Effects on Socially Desirable Responding in Web Surveys Compared to Face-to-Face and Telephone Surveys

2018    Nejc Berzelak and Vasja Vehovar ; p. 15(2):21-43         

This paper elaborates upon differences in socially desirable responding as being the result of mode effects between web, telephone, and face-to-face survey modes. Social desirability is one of the main threats to comparability of data between different modes. The paper conceptualises socially desirable responding as a specific type of mode effect, which is not only a result of inherent characteristics of a survey mode, but is also mediated and moderated by complex interdependencies of specific survey implementations, contextual factors, and characteristics and behaviours of respondents. While web surveys are generally less prone to socially desirable responding, it is essential to be wary of circumstances that may reduce the perceived privacy of the survey situation and lead to biased reporting. The presented empirical study analyses the answers to a large number of items used in a pilot implementation of the Generations and Gender Survey across the three modes to gain insights into the incidence of socially desirable responding and its role in the observed differences in estimates. The comparison of means, distributions, and proportions of extreme responses to scale questions is performed across 89 survey items. The results are inline with the previous findings on lower susceptibility of web surveys to social desirability bias. More importantly, the findings suggest that the problem of socially desirable responding is likely to be a major contributor to the differences in mean estimates, response distributions, and the level of extreme responding between the studied modes.

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Estimation of Power Function Distribution Based on Selective Order Statistic                                      

2018    Mohd T. Alodat, Mohammad Y. Al-Rawwash and Sameer A. Al-Subh; p. 15(2):45-56         

In this article, we present the selective order statistic sampling scheme as a promising approach to estimate the parameter of the univariate power function distribution. We derive the maximum likelihood estimator and the method of moments estimator of the power function distribution parameter as well as the reliability parameter and the ratio of two means. Moreover, we derive the asymptotic properties of the proposed estimators. Finally, we conduct simulation studies to investigate the performance of the selective order statistic scheme and concluded that it suits the power function distribution and we found that the maximum likelihood estimator is better than the method of moments estimator under the selective order statistic sampling scheme.

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Advances in Methodology and Statistics