Hyperbolic Sine Transformation Research Articles

Licensing Scheme in the Green Industry Sector: The Case of Georgia Tree Care Service Providers

AbstractTree care license requirements are expected to improve service quality and provider competencies. The study elicits the licensing fee Georgia firms would pay using survey data from 153 tree care firms. An empirical relationship identifies firm characteristics that influence the fee size using the inverse hyperbolic sine transformation function. Results show that respondents who propose higher annual licensing fees are on average younger, more educated, male, and likely to agree that mandatory licensing is necessary to establish professionalism in the tree care industry. Also, those often engaged in tree trimming services and firms with higher annual revenues contemplate paying higher licensing fees.

Why Transform Y? The Pitfalls of Transformed Regressions with a Mass at Zero*

AbstractApplied economists often transform a dependent variable that is non‐negative and skewed with the natural log transformation, the inverse hyperbolic sine transformation, or power function. We show that these transformations separate the zeros from the positives such that the estimated parameters are related to those from a scaled linear probability model. The retransformed marginal effects and elasticities are sensitive to changes in a shape parameter, ranging in magnitude between those of an untransformed least squares regression and those of a scaled linear probability model. Instead of transforming the dependent variable with non‐negative outcomes that includes zeros, we recommend using a non‐transformed dependent variable, such as a two‐part model, untransformed linear regression, or Poisson.

Estimating COVID-19 under-reporting through stochastic frontier analysis and official statistics: A case study of São Paulo State, Brazil

During outbreaks, natural disasters, and any unexpected event, it is usual that public authorities face issues tracking the outcomes, and the available reports of casualties tend to be lower than actual numbers. Using weekly data at the municipality level in São Paulo State (the most densely populated region in Brazil), we employ stochastic frontier methods to fit the dynamics of the COVID-19 outbreak spanning from March 2020 to December 2021. The empirical model incorporates the inverse hyperbolic sine transformation to address the issue of zero reporting of COVID-19 deaths. Furthermore, we utilize a flexible frontier method to capture the S-shaped epidemic curve in two distinct waves of infections/deaths. Our results reveal that the actual death toll resulting from COVID-19 is, on average, 1.24 times higher than the officially reported figures. Consequently, these findings hold significant implications for public authorities in identifying regions characterized by substantial under-reporting of COVID-19 fatalities. Moreover, this study presents an empirical framework that can be used for other municipalities, states, or countries confronting outbreak scenarios.

The statistical challenge of analysing changes in dual energy computed tomography (DECT) urate volumes in people with gout

BackgroundDual energy computed tomography (DECT) allows direct visualization of monosodium urate crystal deposition in gout. However, DECT urate volume data are often highly skewed (mostly small volumes with the remainder considerably larger), making statistical analyses challenging in longitudinal research. The aim of this study was to explore the ability of various analysis methods to normalise DECT urate volume data and determine change in DECT urate volumes over time. MethodsSimulated datasets containing baseline and year 1 DECT urate volumes for 100 people with gout were created from two randomised controlled trials. Five methods were used to transform the DECT urate volume data prior to analysis: log-transformation, Box-Cox transformation, log(X-(min(X)-1)) transformation; inverse hyperbolic sine transformation, and rank order. Linear regression analyses were undertaken to determine the change in DECT urate volume between baseline and year 1. Cohen's d were calculated as a measure of effect size for each data treatment method. These analyses were then tested in a validation clinical trial dataset containing baseline and year 1 DECT urate volumes from 91 people with gout. ResultsNo data treatment method successfully normalised the distribution of DECT urate volumes. For both simulated and validation data sets, significant reductions in DECT urate volumes were observed between baseline and Year 1 across all data treatment methods and there were no significant differences in Cohen's d effect sizes. ConclusionsNormalising highly skewed DECT urate volume data is challenging. Adopting commonly used transformation techniques may not significantly improve the ability to determine differences in measures of central tendency when comparing the change in DECT urate volumes over time.

Income inequality and its association with COVID-19 cases and deaths: a cross-country analysis in the Eastern Mediterranean region

IntroductionThere is limited evidence on the associations between economic and social disparities in the Eastern Mediterranean region (EMR) with COVID-19 infections and deaths. This study aims to investigate the relationship...

Habitual behavior of household food expenditure by store type in the United States.

We examine how socio-demographic factors, spending habits, and characteristics of the retail food environment affect household expenditure across all food and beverage categories by store outlet in the United States. The six outlets considered are grocery stores, convenience stores, discount stores, club stores, drug stores, and dollar stores. The source of data for this analysis is the Nielsen Homescan Panel over the period between 2011 and 2015. We employ a dynamic correlated random effect Tobit model to incorporate habitual purchasing behavior as well as a novel method to deal with zero observations using the inverse hyperbolic sine transformation. The results suggest that habitual spending behavior undoubtedly is a key factor in affecting food and beverage expenditures across all store outlets. Additionally, household size, age, urbanization, education, race, ethnicity, and region are drivers of household food and beverage expenditures across the six store outlets.

Distributional properties of the book to market ratio and their implications for empirical analysis

Financial accounting standards, government regulatory requirements and the capital market assumptions on which received asset pricing theory is based are used to develop a linear-quadratic diffusion process under which the unconditional probability density of the book to market ratio of equity will be either Gaussian (that is, normal) or the Pearson Type IV. Empirical analysis based on book to market ratios drawn from the Compustat North America Standard & Poor’s Fundamentals Quarterly Database shows the Pearson Type IV probability density provides a superior fit to firm book to market ratio sample distributions when compared to the Gaussian density with around two-thirds of firm sample book to market ratio distributions failing standard Gaussian goodness of fit tests. Moreover, around one in eight of the firm book to market ratio sample distributions return parameter estimates for the Pearson Type IV which are compatible with a non-convergent (that is, undefined) variance and higher moments. It is also shown how the inverse hyperbolic sine transformation can be used to mitigate the adverse consequences of heteroscedasticity and non-convergent moments in empirical work involving the book to market ratio.

The inverse hyperbolic sine transformation and retransformed marginal effects

In this article, I show how to calculate consistent marginal effects on the original scale of the outcome variable in Stata after estimating a linear regression with a dependent variable that has been transformed by the inverse hyperbolic sine function. The method uses a nonparametric retransformation of the error term and accounts for any scaling of the dependent variable. The inverse hyperbolic sine function is not invariant to scaling, which is known to shift marginal effects between those from an untransformed dependent variable to those of a logtransformed dependent variable, when all observations are positive.

Is visitors’ expenditure at destination influenced by weather conditions?

ABSTRACT Weather has been shown to affect consumption patterns by altering people’s moods. This paper examines the impact of atmospheric conditions on destination expenditure considering cruise passengers’ onshore expenditure as the case study. We exploit quasi-random variation in a set of hourly real-time weather indicators in a port of call, through the Tourism Climate Index (TCI) and the Physiologically Equivalent Temperature (PET), to draw inference about their effect on destination expenditure. Therefore, we capture the specific atmospheric conditions encountered by tourists, alleviating the usual aggregation bias in related studies. In particular, information about mean and maximum air temperature, wind speed, rainfall, sunshine duration and mean and minimum relative humidity is considered. We estimate a heteroskedastic Tobit model with an inverse hyperbolic sine transformation of the dependent variable that deals with problems of non-normality and extreme values. Controlling for several sociodemographic characteristics and cruise size, we find consistent evidence that pleasant weather (either using TCI or PET indexes) increases onshore expenditure. Our findings have important implications for destination management.

Impact of ICT diffusion on the interaction of growth and its volatility: Evidence from cross-country analysis

There is a large body of research investigating the impact of information and communication technologies (ICT) on economic growth; however, the empirical evidence on growth and its volatility simultaneously driven by ICT diffusion has still remained scarce so far. To fill this void, system two-step generalized method of moments (S-GMM) estimator and a new proxy capturing the product of growth and its fluctuation is employed to determine the nexus between ICT penetration and the interaction of growth and its volatility. Using a comprehensive panel of 122 economies covering the period 2000–2019, we find that all proxies for the ICT revolution show positive impacts on the product of growth and its volatility. This means that an increase in ICT diffusion could lead to both higher growth and lower growth volatility. To offer robust and consistent results, ICT growth and its volatility nexus are confirmed through several econometric techniques such as panel quantile regression, the control of fixed effects, alternative measure for the interaction between growth and its fluctuation, and across countries with different national incomes. The research could give rise to use of this proxy for the product of growth and its volatility with inverse hyperbolic sine transformation in the empirically econometric model for the future studies.

Modeling censored tourism expenditures in Turkey with non-normal and heteroscedastic errors: An application of the inverse hyperbolic sine double-hurdle model

Censoring, extreme values, and non-normal distribution are common features in microdata. These data features can compromise the statistical distributions of the estimators when an appropriate model is not used. We use an inverse hyperbolic sine (IHS) transformation in the double-hurdle (DH) model to accommodate extreme values and skewness in censored accommodation spending among Turkish households. The full-parameterized model nests many restricted specifications which do not accommodate dependence, heteroscedasticity, and non-normality in the error terms. Statistical test results support the use of the fully parameterized dependent IHS-DH specification. The statistically significant correlation between the binary and level decisions of accommodation precludes the use of a model with a two-step structure. Some of the findings in our study have a determining or driving force in expressing causality relationship in monthly accommodation probability and level decisions. The study made also prudent policy recommendations about what the results might mean to policymakers and stakeholders.

A zero-bounded model of operant demand.

Contemporary approaches for evaluating the demand for reinforcers use either the Exponential or the Exponentiated model of operant demand, both derived from the framework of Hursh and Silberberg (2008). This report summarizes the strengths and complications of this framework and proposes a novel implementation. This novel implementation incorporates earlier strengths and resolves existing shortcomings that are due to the use of a logarithmic scale for consumption. The Inverse Hyperbolic Sine (IHS) transformation is reviewed and evaluated as a replacement for the logarithmic scale in models of operant demand. Modeling consumption in the "log10 -like" IHS scale reflects relative changes in consumption (as with a log scale) and accommodates a true zero bound (i.e., zero consumption values). The presence of a zero bound obviates the need for a separate span parameter (i.e., k) and the span of the model may be more simply defined by maximum demand at zero price (i.e., Q0 ). Further, this reformulated model serves to decouple the exponential rate constant (i.e., α) from variations in span, thus normalizing the rate constant to the span of consumption in IHS units and permitting comparisons when spans vary. This model, called the Zero-bounded Exponential (ZBE), is evaluated using simulated and real-world data. The direct reinstatement ZBE model showed strong correspondence with empirical indicators of demand and with a normalization of α (ZBEn) across empirical data that varied in reinforcing efficacy (dose, time to onset of peak effects). Future directions in demand curve analysis are discussed with recommendations for additional replication and exploration of scales beyond the logarithm when accommodating zero consumption data.

European FDI in Ireland and Iceland: Before and after the Financial Crisis

This paper analyses Foreign Direct Investment (FDI) investment in Ireland and Iceland from other European countries during two periods, i.e., the pre-financial crisis period of 2000–2007 and the financial crisis period of 2008–2010. The aim of this research is to determine what made the countries interesting to foreign investors in both good and bad times; and, secondly, to examine whether European Union membership (and the Euro) made a difference in this respect. The results were obtained by using data from the OECD, the World bank, and other sources. The model constructed for the study applies the inverse hyperbolic sine transformation of the gravity model, which is a novel approach. The results demonstrate that before the financial crisis of 2008, European Union (EU) membership did not help Ireland attract more FDI from other EU countries. However, once it had been hit by the crisis, Ireland attracted more FDI from other EU countries. Iceland, on the other hand, which is not an EU country, attracted FDI from non-EU countries rather than from EU countries before the financial crisis. After the crisis, however, the origin within Europe, of FDI in Iceland had no significant effect on the flow of FDI into the country.

What drives citations of frontier application publications?

A large body of literature exists on analysis of citation and reviews of application of efficiency frontier. However, the reviews that assessed the determinants of citation counts did not focus on frontier applications. We contribute to the literature by identifying the drivers of citations of frontier application publications on Ghana. We employed two-part mixture modelling with inverse hyperbolic sine (IHS) transformation of the second part, which was found to be more appropriate than single equation IHS transformation modelling, for our data. Use of stochastic frontier analysis or data envelopment analysis did not drive citations counts. However, quality of journals in which frontier application studies were published and accessibility of the journals to readers, drive citation counts. Authors, institutions and funders of studies on frontier applications may consider these over collaborations, in seeking growth in citation counts.

Units of measurement and the inverse hyperbolic sine transformation

Summary The inverse hyperbolic sine (IHS) transformation is frequently applied in econometric studies to transform right-skewed variables that include zero or negative values. We show that regression results can heavily depend on the units of measurement of IHS-transformed variables. Hence, arbitrary choices regarding the units of measurement for these variables can have a considerable effect on recommendations for policies or business decisions. In order to address this problem, we suggest a procedure for choosing units of measurement for IHS-transformed variables. A Monte Carlo simulation assesses this procedure under various scenarios, and an empirical illustration shows the relevance and applicability of our suggested procedure.

Time Evolution of Hurst Exponent: Czech Wholesale Electricity Market Study

In this paper we analyse a temporal evolution of the Hurst exponent estimated on hourly returns of intraday electricity prices in the Czech Republic in 2017 and 2018. Firstly we used the log-returns with adjustments due to negative values, and secondly we employed the returns based on the area hyperbolic sine transformation. We implemented a sliding window technique in order to estimate the Hurst exponent using the Detrended Fluctuation Analysis method on subsamples with four distinct window sizes. According to the stylised facts of electricity, the spot prices and their corresponding logarithmic returns should be mean-reverting. Since the Czech intraday electricity market remains mostly unexplored, we examined this phenomenon on the intraday rather than on the spot market. Consequently, our analysis showed that the estimated values of Hurst exponent indicate a mean-reverting process for time scales greater than 24 hours and a weakly mean-reverting process for the shorter time scales. There were a few exceptions, though, since our calculations have revealed the presence of a nearly random or even weakly persistent behaviour on the shorter time scales.

Elasticities and the Inverse Hyperbolic Sine Transformation

AbstractApplied econometricians frequently apply the inverse hyperbolic sine (or arcsinh) transformation to a variable because it approximates the natural logarithm of that variable and allows retaining zero‐valued observations. We provide derivations of elasticities in common applications of the inverse hyperbolic sine transformation and show empirically that the difference in elasticities driven by ad hoc transformations can be substantial. We conclude by offering practical guidance for applied researchers.

Sovereign wealth funds’ cross-border investments: Assessing the role of country-level drivers and spatial competition

The aim of this paper is to identify the driving forces of cross-border investments emanating from Sovereign wealth funds and to test the existence of spatial competition among recipient countries. For this, we develop an original econometric framework that quantifies the role of spatial dependence in the location of investments, and that uses a modified version of the standard estimation procedure of spatial panel model, which accommodates the Inverse Hyperbolic Sine transformation of the dependent variable. This transformation copes with two critical features of net capital flows, namely an highly skewed distribution and the presence of zero and negative values. Using a large-scale database, we provide evidence of negative spatial dependence, investments in one country being on average at the expense of its neighbors.

FlowVS: channel-specific variance stabilization in flow cytometry

BackgroundComparing phenotypes of heterogeneous cell populations from multiple biological conditions is at the heart of scientific discovery based on flow cytometry (FC). When the biological signal is measured by the average expression of a biomarker, standard statistical methods require that variance be approximately stabilized in populations to be compared. Since the mean and variance of a cell population are often correlated in fluorescence-based FC measurements, a preprocessing step is needed to stabilize the within-population variances.ResultsWe present a variance-stabilization algorithm, called flowVS, that removes the mean-variance correlations from cell populations identified in each fluorescence channel. flowVS transforms each channel from all samples of a data set by the inverse hyperbolic sine (asinh) transformation. For each channel, the parameters of the transformation are optimally selected by Bartlett’s likelihood-ratio test so that the populations attain homogeneous variances. The optimum parameters are then used to transform the corresponding channels in every sample. flowVS is therefore an explicit variance-stabilization method that stabilizes within-population variances in each channel by evaluating the homoskedasticity of clusters with a likelihood-ratio test.With two publicly available datasets, we show that flowVS removes the mean-variance dependence from raw FC data and makes the within-population variance relatively homogeneous. We demonstrate that alternative transformation techniques such as flowTrans, flowScape, logicle, and FCSTrans might not stabilize variance. Besides flow cytometry, flowVS can also be applied to stabilize variance in microarray data. With a publicly available data set we demonstrate that flowVS performs as well as the VSN software, a state-of-the-art approach developed for microarrays.ConclusionsThe homogeneity of variance in cell populations across FC samples is desirable when extracting features uniformly and comparing cell populations with different levels of marker expressions. The newly developed flowVS algorithm solves the variance-stabilization problem in FC and microarrays by optimally transforming data with the help of Bartlett’s likelihood-ratio test. On two publicly available FC datasets, flowVS stabilizes within-population variances more evenly than the available transformation and normalization techniques. flowVS-based variance stabilization can help in performing comparison and alignment of phenotypically identical cell populations across different samples. flowVS and the datasets used in this paper are publicly available in Bioconductor.

Spatial Dependence in Sovereign Wealth Funds' Investments

The aim of this paper is to identify the driving forces of Sovereign wealth funds' investments. For this, we develop an original econometric framework that quantifies the role of spatial dependence in the location of investments, and uses the Inverse Hyperbolic Sine transformation of the dependent variable in a spatial panel model context. This transformation copes with two features of net flows, namely an highly skewed distribution and the presence of zero and negative values. Using a large-scale database, we provide evidence of negative spatial dependence, investments in one country being on average at the expense of its neighbors.