Showing papers in "Journal of Applied Statistics in 2016"

Collinearity diagnostic applied in ridge estimation through the variance inflation factor

Abstract: The variance inflation factor (VIF) is used to detect the presence of linear relationships between two or more independent variables (i.e. collinearity) in the multiple linear regression model. However, the traditionally used VIF definitions encounter some problems when extended to the case of the ridge estimation (RE). This paper presents an extension of the VIF in RE by providing two alternative VIF expressions that overcome these problems in the general case. Some characteristics of these expressions are also presented and compared with the traditional expression. The results are illustrated with an economic example in the case of three independent variables and with a Monte Carlo simulation for the general case.

The Weibull Fréchet distribution and its applications

Abstract: A new four-parameter lifetime model called the Weibull Frechet distribution is defined and studied. Various of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Renyi and δ-entropies and order statistics are investigated. The new density function can be expressed as a linear mixture of Frechet densities. The maximum likelihood method is used to estimate the model parameters. The new distribution is applied to two real data sets to prove empirically its flexibility. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in many areas.

Diagnostics in multivariate generalized Birnbaum-Saunders regression models

Abstract: Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.

Systematic handling of missing data in complex study designs - experiences from the Health 2000 and 2011 Surveys

Abstract: We present a systematic approach to the practical and comprehensive handling of missing data motivated by our experiences of analyzing longitudinal survey data. We consider the Health 2000 and 2011 Surveys (BRIF8901) where increased non-response and non-participation from 2000 to 2011 was a major issue. The model assumptions involved in the complex sampling design, repeated measurements design, non-participation mechanisms and associations are presented graphically using methodology previously defined as a causal model with design, i.e. a functional causal model extended with the study design. This tool forces the statistician to make the study design and the missing-data mechanism explicit. Using the systematic approach, the sampling probabilities and the participation probabilities can be considered separately. This is beneficial when the performance of missing-data methods are to be compared. Using data from Health 2000 and 2011 Surveys and from national registries, it was found that multiple i...

Difference-in-difference estimation by FE and OLS when there is panel non-response

Abstract: We show that the ordinary least squares (OLS) and fixed-effects (FE) estimators of the popular difference-in-differences model may deviate when there is time-varying panel non-response. If such non-response does not affect the common-trend assumption, then OLS and FE are consistent, but OLS is more precise. However, if non-response is affecting the common-trend assumption, then FE estimation may still be consistent, while OLS will be inconsistent. We provide simulation as well as empirical evidence for this phenomenon to occur. We conclude that in case of unbalanced panels, deviating OLS and FE estimates should be considered as evidence that non-response is not ignorable for the differences-in-differences estimation.

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 pro...

Analysis of means: a generalized approach using R

Abstract: Papers on the analysis of means (ANOM) have been circulating in the quality control literature for decades, routinely describing it as a statistical stand-alone concept. Therefore, we clarify that ANOM should rather be regarded as a special case of a much more universal approach known as multiple contrast tests (MCTs). Perceiving ANOM as a grand-mean-type MCT paves the way for implementing it in the open-source software R. We give a brief tutorial on how to exploit R's versatility and introduce the R package ANOM for drawing the familiar decision charts. Beyond that, we illustrate two practical aspects of data analysis with ANOM: firstly, we compare merits and drawbacks of ANOM-type MCTs and ANOVA F-test and assess their respective statistical powers, and secondly, we show that the benefit of using critical values from multivariate t-distributions for ANOM instead of simple Bonferroni quantiles is oftentimes negligible.

On increasing the sensitivity of mixed EWMA–CUSUM control charts for location parameter

Abstract: Control chart is an important statistical technique that is used to monitor the quality of a process. Shewhart control charts are used to detect larger disturbances in the process parameters, whereas cumulative sum (CUSUM) and exponential weighted moving average (EWMA) are meant for smaller and moderate changes. In this study, we enhanced mixed EWMA–CUSUM control charts with varying fast initial response (FIR) features and also with a runs rule of two out of three successive points that fall above the upper control limit. We investigate their run-length properties. The proposed control charting schemes are compared with the existing counterparts including classical CUSUM, classical EWMA, FIR CUSUM, FIR EWMA, mixed EWMA–CUSUM, 2/3 modified EWMA, and 2/3 CUSUM control charting schemes. A case study is presented for practical considerations using a real data set.

Box–Cox realized asymmetric stochastic volatility models with generalized Student's t-error distributions

Abstract: This study proposes a class of non-linear realized stochastic volatility (SV) model by applying the Box–Cox (BC) transformation, instead of the logarithmic transformation, to the realized estimator. The non-Gaussian distributions such as Student's t, non-central Student's t, and generalized hyperbolic skew Student's t-distributions are applied to accommodate heavy-tailedness and skewness in returns. The proposed models are fitted to daily returns and realized kernel of six stocks: SP500, FTSE100, Nikkei225, Nasdaq100, DAX, and DJIA using an Markov chain Monte Carlo Bayesian method, in which the Hamiltonian Monte Carlo (HMC) algorithm updates BC parameter and the Riemann manifold HMC algorithm updates latent variables and other parameters that are unable to be sampled directly. Empirical studies provide evidence against both the logarithmic transformation and raw versions of realized SV model.

Examining the effect of social influence on student performance through network autocorrelation models

Abstract: The paper investigates the link between student relations and their performances at university. A social influence mechanism is hypothesized as individuals adjusting their own behaviors to those of others with whom they are connected. This contribution explores the effect of peers on a real network formed by a cohort of students enrolled at a graduate level in an Italian University. Specifically, by adopting a network effects model, the relation between interpersonal networks and university performance is evaluated assuming that student performance is related to the performance of the other students belonging to the same group. By controlling for individual covariates, the network results show informal contacts, based on mutual interests and goals, are related to performance, while formal groups formed temporarily by the instructor have no such effect.

Economic-statistical design of simple linear profiles with variable sampling interval

Abstract: Control charts are statistical tools to monitor a process or a product. However, some processes cannot be controlled by monitoring a characteristic; instead, they need to be monitored using profiles. Economic-statistical design of profile monitoring means determining the parameters of a profile monitoring scheme such that total costs are minimized while statistical measures maintain proper values. While varying sampling interval usually increases the effectiveness of profile monitoring, economic-statistical design of variable sampling interval (VSI) profile monitoring is investigated in this paper. An extended Lorenzen–Vance function is used for modeling total costs in VSI model where the average time to signal is employed for depicting the statistical measure of the obtained profile monitoring scheme. Two sampling intervals; number of set points and the parameters of control charts that are used in profile monitoring are the variables that are obtained thorough the economic-statistical model. A genetic a...

Preprocessing of centred logratio transformed density functions using smoothing splines

Abstract: With large-scale database systems, statistical analysis of data, occurring in the form of probability distributions, becomes an important task in explorative data analysis. Nevertheless, due to specific properties of density functions, their proper statistical treatment of these data still represents a challenging task in functional data analysis. Namely, the usual L2 metric does not fully accounts for the relative character of information, carried by density functions; instead, their geometrical features are captured by Bayes spaces of measures. The easiest possibility of expressing density functions in an L2 space is to use centred logratio transformation, even though this results in functional data with a constant integral constraint that needs to be taken into account in further analysis. While theoretical background for reasonable analysis of density functions is already provided comprehensively by Bayes spaces themselves, preprocessing issues still need to be developed. The aim of this paper is to i...

An improved fuzzy time-series method of forecasting based on L–R fuzzy sets and its application

Abstract: Classical time-series theory assumes values of the response variable to be ‘crisp’ or ‘precise’, which is quite often violated in reality. However, forecasting of such data can be carried out through fuzzy time-series analysis. This article presents an improved method of forecasting based on L–R fuzzy sets as membership functions. As an illustration, the methodology is employed for forecasting India's total foodgrain production. For the data under consideration, superiority of proposed method over other competing methods is demonstrated in respect of modelling and forecasting on the basis of mean square error and average relative error criteria. Finally, out-of-sample forecasts are also obtained.

Alternative mean-squared error estimators for synthetic estimators of domain means

Abstract: In forest management surveys, the mean of a variable of interest (Y) in a population composed of N equal area spatial compact elements is increasingly estimated from a model linking Y to an auxiliary vector X known for all elements in the population It is also desired to have synthetic estimates of the mean of Y in spatially compact domains (forest stands) with no or at most one sample-based observation of Y We develop three alternative estimators of mean-squared errors (MSE) that reduce the risk of a serious underestimation of the uncertainty in a synthetic estimate of a domain mean in cases where the employed model does not accounts for domain effects nor spatial autocorrelation in unobserved residual errors Expansions of the estimators including anticipated effects of a spatial autocorrelation in residual errors are also provided Simulation results indicate that the conventional model-dependent (MD) population-level estimator of variance in a synthetic estimate of a domain mean underestimat

A multivariate finite mixture latent trajectory model with application to dementia studies

Abstract: Dementia patients exhibit considerable heterogeneity in individual trajectories of cognitive decline, with some patients showing rapid decline following diagnoses while others exhibiting slower decline or remaining stable for several years. Dementia studies often collect longitudinal measures of multiple neuropsychological tests aimed to measure patients’ decline across a number of cognitive domains. We propose a multivariate finite mixture latent trajectory model to identify distinct longitudinal patterns of cognitive decline simultaneously in multiple cognitive domains, each of which is measured by multiple neuropsychological tests. EM algorithm is used for parameter estimation and posterior probabilities are used to predict latent class membership. We present results of a simulation study demonstrating adequate performance of our proposed approach and apply our model to the Uniform Data Set from the National Alzheimer's Coordinating Center to identify cognitive decline patterns among dementia p...

Childhood mortality spatial distribution in Ethiopia

Abstract: The risk of a child dying before completing five years of age is highest in Sub-Saharan African countries. But Child mortality rates have shown substantial decline in Ethiopia. For this study, the 2000, 2005 and 2011 Ethiopian Demographic Survey (EDHS) was used. Generalized linear mixed model with spatial covariance structure was adapted. The model allowed for spatial correlation, and leads to the more realistic estimate for under-five mortality risk factors. The analysis showed that the risk of under-five mortality shows decline in years. But, some regions showed increase in years. The study highlights the need to implement better education for family planning and child care to improve the under-five mortality situation in some administrative areas.

Survival and lifetime data analysis with a flexible class of distributions

Abstract: We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and contains members that can capture different tail behaviours and shapes, producing also a variety of hazard functions. The proposed distributions represent a flexible alternative to the classical choices such as the log-normal, Gamma, and Weibull distributions. We investigate empirically the inferential properties of the proposed models through an extensive simulation study. We present some applications using real data in the contexts of time-to-event and accelerated failure time models. In the second kind of applications, we explore the use of these models in the estimation of the distribution of the individual remaining life.

Aranda-Ordaz quantile regression for student performance assessment

Abstract: In education research, normal regression models may not be appropriate due to the presence of bounded variables, which may exhibit a large variety of distributional shapes and present floor and ceiling effects. In this article a class of quantile regression models for bounded response variables is developed. The one-parameter Aranda-Ordaz symmetric and asymmetric families of transformations are applied to address modelling issues that arise when estimating conditional quantiles of a bounded response variable whose relationship with the covariates is possibly nonlinear. This approach exploits the equivariance property of quantiles and aims at achieving linearity of the predictor. This offers a flexible model-based alternative to nonparametric estimation of the quantile function. Since the transformation is quantile-specific, the modelling takes into account the local features of the conditional distribution of the response variable. Our study is motivated by the analysis of reading performance in seven-yea...

Application of multinomial logistic regression to educational factors of the 2009 General Household Survey in South Africa

Abstract: This paper combines factor analysis and multinomial logistic regression (MLR) in understanding the relationship between extracted factors of quality of life pertaining to education and variables of five key areas of the levels of development in the context of the South African 2009 General Household Survey. MLR was used to analyse the identified educational factors from factor analysis. It was also used to determine the extent to which these factors impact on educational level outcomes across South Africa. The overall classification accuracy rate displayed was 73.0% which is greater than the proportion by chance accuracy criteria of 57.0%. This means that the model improves on the proportion by chance accuracy rate of 25.0% or more so that the criterion for classification accuracy is satisfied and the model is adequate. Evidence is that being historically disadvantaged, absence of parental care, violence in schools and the perception that fees were too high generally have a negative influence on education...

A beta inflated mean regression model for fractional response variables

Abstract: This article proposes a new regression model for a dependent fractional random variable on the interval [0,1] that takes with positive probability the extreme values 0 or 1. Our model relates the expected value of this variable with a linear predictor through a special parametrization that let the parameters free in the parameter space. A simulation-based study and an application to capital structure choices were conducted to analyze the performance of the likelihood estimators in the model. The results show not only accurate estimations and a better fit than other traditional models but also a more straightforward and clear way to estimate the effects of a set of covariates over the mean of a fractional response.

Clustering ranking data in market segmentation: a case study on the Italian McDonald's customers’ preferences†

Abstract: Cluster analysis is often used for market segmentation. When the inputs in the clustering algorithm are ranking data, the intersubject (dis)similarities must be measured by matching-type measures, able to take account of the ordinal nature of the data. Among them, we used a Weighted Spearman's rho, suitably transformed into a (dis)similarity measure, in order to emphasize the concordance on the top ranks. This allows creating clusters grouping customers that place the same items (products, services, etc.) higher in their rankings. Also the statistical instruments used to interpret the clusters must be conceived to deal with ordinal data. The median and other location measures are appropriate but not always able to clearly differentiate groups. The so-called bipolar mean, with its related variability measure, may reveal some additional features. A case study on real data from a survey carried out in the Italian McDonald's restaurants is presented.

Performance and decisions: immigrant–native gaps in educational transitions in Italy

Abstract: Following the seminal work of Boudon [5], sociological research has conceptualized immigrant–native gaps in educational transitions as deriving from children of immigrants' poorer academic performance (primary effects) and from different decision models existing between native and immigrant families (secondary effects). The limited evidence on immigrant–native gaps in Europe indicates that secondary effects are generally positive: children of immigrants tend to make more ambitious educational choices than natives with the same prior performance. In this paper we review the different decomposition methods employed so far in the literature to tackle similar research questions, and extend the existing methodology to allow including interaction effects and taking explanatory variables under control. We apply this method to data coming from a unique Italian administrative data set. We find that children of immigrants exhibit higher likelihood to opt for vocational training over more generalist and academic pro...

Asymmetric uniform designs based on mixture discrepancy

Abstract: Efficient experimental design is crucial in the study of scientific problems. The uniform design is one of the most widely used approaches. The discrepancies have played an important role in quasi-Monte Carlo methods and uniform design. Zhou et al. [17] proposed a new type of discrepancy, mixture discrepancy (MD), and showed that MD may be a better uniformity measure than other discrepancies. In this paper, we discuss in depth the MD as the uniformity measure for asymmetric mixed two and three levels U-type designs. New analytical expression based on row distance and new lower bound of the MD are given for asymmetric levels designs. Using the new formulation and the new lower bound as the benchmark, we can implement a new version of the fast local search heuristic threshold accepting. By this search heuristic, we can obtain mixed two and three levels U-type designs with low discrepancy.

On regression modelling with dummy variables versus separate regressions per group: Comment on Holgersson et al.

Abstract: In a recent issue of this journal, Holgersson et al. [Dummy variables vs. category-wise models, J. Appl. Stat. 41(2) (2014), pp. 233–241, doi:10.1080/02664763.2013.838665] compared the use of dummy coding in regression analysis to the use of category-wise models (i.e. estimating separate regression models for each group) with respect to estimating and testing group differences in intercept and in slope. They presented three objections against the use of dummy variables in a single regression equation, which could be overcome by the category-wise approach. In this note, I first comment on each of these three objections and next draw attention to some other issues in comparing these two approaches. This commentary further clarifies the differences and similarities between dummy variable and category-wise approaches.

Investigating the determinants of job satisfaction of Italian graduates: a model-based approach

Abstract: The paper explores the relationship between personal, economic and time-dependent covariates as determinants of the job satisfaction expressed by graduate workers. After discussing the main results of the literature, the work emphasizes a statistical modelling approach able to effectively estimate and visualize those determinants and their interactions with subjects' covariates. Interpretation and visualization of graduates' profiles are shown on the basis of a survey conducted in Italy; more specifically, the determinants of both satisfaction and uncertainty of the respondents are explicitly discussed.

Corporate Social Responsibility perception versus human values: a structural equation modeling approach

Abstract: In the business world, increasing importance is being given to Corporate Social Responsibility (CSR). Consumer perception of CSR is determinant on the success of CSR practices and this perception is directly influenced by individual value structures. Despite research efforts and the continued preoccupation of CSR role in business and Society, few studies to date have analyzed jointly CSR perception and the value structure. As a result, the paper brings new knowledge of the relationship between basic human values and CSR's perception under a particular social initiative carried out by a company. To reach our purpose a Hierarchical Component Model which includes the variable gender to control for heterogeneity is adopted. The model focuses on not only by analyzing the effects of human values on CSR but also analyzes the influence of values by gender on CSR perception. This approach to study the relationship of CSR versus values considering the Schwartz's higher-order values and the moderating role o...

A biclustering approach to university performances: an Italian case study

Abstract: University evaluation is a topic of increasing concern in Italy as well as in other countries. In empirical analysis, university activities and performances are often measured by means of indicator variables. The available information are then summarized to respond to different aims. We argue that the evaluation process is a complex phenomenon that cannot be addressed by a simple descriptive approach. In this paper, we used a model-based approach to account for association between indicators and similarities among the observed universities. We examine faculty-level data collected from different sources, covering 55 Italian Economics faculties in the academic year 2009/2010. Making use of a clustering methodology, we introduce a biclustering model that accounts for both homogeneity/heterogeneity among faculties and correlations between indicators. Our results show that there are two substantial different performances between universities which can be strictly related to the nature of the institutions, name...

Modified inference function for margins for the bivariate clayton copula-based SUN Tobit Model

Abstract: This paper extends the analysis of the bivariate Seemingly Unrelated Regression (SUN) Tobit model by modeling its nonlinear dependence structure through the Clayton copula. The ability to capture/model the lower tail dependence of the SUN Tobit model where some data are censored (generally, left-censored at zero) is an useful feature of the Clayton copula. We propose a modified version of the (classical) Inference Function for Margins (IFS) method by Joe and XP [H. Joe and J.J. XP, The estimation method of inference functions for margins for multivariate models, Tech. Rep. 166, Department of Statistics, University of British Columbia, 1996], which we refer to as Modified Inference Function for Margins (MIFF) method, to obtain the (point) estimates of the marginal and Clayton copula parameters. More specifically, we employ the (frequenting) data augmentation technique at the second stage of the IFS method (the first stage of the MIFF method is equivalent to the first stage of the IFS method) to gen...

Statistics in Education

Abstract: During the last few decades, educational systems have attracted a great deal of interest because they are closely related to economic and social systems. For example, ‘higher education has been aff...

Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models

Abstract: This paper considers the estimation of the stress–strength reliability of a multi-state component or of a multi-state system where its states depend on the ratio of the strength and stress variables through a kernel function. The article presents a Bayesian approach assuming the stress and strength as exponentially distributed with a common location parameter but different scale parameters. We show that the limits of the Bayes estimators of both location and scale parameters under suitable priors are the maximum likelihood estimators as given by Ghosh and Razmpour [15]. We use the Bayes estimators to determine the multi-state stress–strength reliability of a system having states between 0 and 1. We derive the uniformly minimum variance unbiased estimators of the reliability function. Interval estimation using the bootstrap method is also considered. Under the squared error loss function and linex loss function, risk comparison of the reliability estimators is carried out using extensive simulations.