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.
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.
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.
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.
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.
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.
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.