Search results for: logit function

Authors: Yungtai Lo

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Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a continuous right-skewed distribution for positive values. We review methods proposed in the literature for analyzing data with excess zeros. A two-part logit-log-normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.

Keywords: two-part model, semi-continuous variable, truncated normal, gamma regression, skew normal, Pearson residual, receiver operating characteristic curve

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Authors: A. J. Julius, E. Imoagene, O. A. Ganiyu

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The purpose of this study is to estimate the economic value of the services and functions rendered by the forest landscape using a conditional logit model. For this study, attributes and levels of forest landscape were chosen; specifically, attributes include topographical forest type, forest type, forest density, recreational factor (side trip, accessibility of valley), and willingness to participate (WTP). Based on these factors, 48 choices sets with balanced and orthogonal form using statistical analysis system (SAS) 9.1 was adopted. The efficiency of the questionnaire was 6.02 (D-Error. 0.1), and choice set and socio-economic variables were analyzed. To reduce the cognitive load of respondents, the 48 choice sets were divided into 4 types in the questionnaire, so that respondents could respond to 12 choice sets, respectively. The study populations were citizens from seven metropolitan cities including Ibadan, Ilorin, Osogbo, etc. and annual WTP per household was asked by using the interview questionnaire, a total of 267 copies were recovered. As a result, Oshogbo had 0.45, and the statistical similarities could not be found except for urban forests, forest density, recreational factor, and level of WTP. Average annual WTP per household for forest landscape was 104,758 Naira (Nigerian currency) based on the outcome from this model, total economic value of the services and functions enjoyed from Nigerian forest landscape has reached approximately 1.6 trillion Naira.

Keywords: economic valuation, urban cities, services, forest landscape, logit model, nigeria

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Authors: Georgios Charizanos, Haydar Demirhan, Duygu Icen

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Two of the most impactful issues in classical logistic regression are class imbalance and complete separation. These can result in model predictions heavily leaning towards the imbalanced class on the binary response variable or over-fitting issues. Fuzzy methodology offers key solutions for handling these problems. However, most studies propose the transformation of the binary responses into a continuous format limited within [0,1]. This is called the possibilistic approach within fuzzy logistic regression. Following this approach is more aligned with straightforward regression since a logit-link function is not utilized, and fuzzy probabilities are not generated. In contrast, we propose a method of fuzzifying binary response variables that allows for the use of the logit-link function; hence, a probabilistic fuzzy logistic regression model with the Monte Carlo method. The fuzzy probabilities are then classified by selecting a fuzzy threshold. Different combinations of fuzzy and crisp input, output, and coefficients are explored, aiming to understand which of these perform better under different conditions of imbalance and separation. We conduct numerical experiments using both synthetic and real datasets to demonstrate the performance of the fuzzy logistic regression framework against seven crisp machine learning methods. The proposed framework shows better performance irrespective of the degree of imbalance and presence of separation in the data, while the considered machine learning methods are significantly impacted.

Keywords: fuzzy logistic regression, fuzzy, logistic, machine learning

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Authors: A. Bere, H. G. Sithuba, K. Kyei, C. Sigauke

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We employ a discrete logit survival model to investigate the risk factors for early alcohol intake among students at two tertiary institutions in Thohoyandou, South Africa. Data were collected from a sample of 744 students using a self-administered questionnaire. Significant covariates were arrived at through a regularization algorithm implemented using the glmmLasso package. The tuning parameter was determined using a five-fold cross-validation algorithm. The baseline hazard was modelled as a smooth function of time through the use of spline functions. The results show that the hazard of initial alcohol intake peaks at the age of about 16 years and that at any given time, being of a male gender, prior use of other drugs, having drinking peers, having experienced negative life events and physical abuse are associated with a higher risk of alcohol intake debut.

Keywords: cross-validation, discrete hazard model, LASSO, smooth baseline hazard

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Authors: Nattabhorn Leamcharaskul

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This study aims to examine determining factors of the dynamics of poverty in Thailand by using panel data of 3,567 households in 2007-2017. Four techniques of estimation are employed to analyze the situation of poverty across households and time periods: the multinomial logit model, the sequential logit model, the quantile regression model, and the difference in difference model. Households are categorized based on their experiences into 5 groups, namely chronically poor, falling into poverty, re-entering into poverty, exiting from poverty and never poor households. Estimation results emphasize the effects of demographic and socioeconomic factors as well as unexpected events on the economic status of a household. It is found that remittances have positive impact on household’s economic status in that they are likely to lower the probability of falling into poverty or trapping in poverty while they tend to increase the probability of exiting from poverty. In addition, not only receiving a secondary source of household income can raise the probability of being a never poor household, but it also significantly increases household income per capita of the chronically poor and falling into poverty households. Public work programs are recommended as an important tool to relieve household financial burden and uncertainty and thus consequently increase a chance for households to escape from poverty.

Keywords: difference in difference, dynamic, multinomial logit model, panel data, poverty, quantile regression, remittance, sequential logit model, Thailand, transfer

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Authors: Babak Mirbaha, Mahmoud Saffarzadeh, Atieh Asgari Toorzani

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Pedestrians are the most vulnerable road users since they do not have a protective shell. One of the most common collisions for them is pedestrian-vehicle at intersections. In order to develop appropriate countermeasures to improve safety for them, researches have to be conducted to identify the factors that affect the risk of getting involved in such collisions. More specifically, this study investigates factors such as the influence of walking alone or having a baby while crossing the street, the observable age of pedestrian, the speed of pedestrians and the speed of approaching vehicles on risk perception of pedestrians. A nested logit model was used for modeling the behavioral structure of pedestrians. The results show that the presence of more lanes at intersections and not being alone especially having a baby while crossing, decrease the probability of taking a risk among pedestrians. Also, it seems that teenagers show more risky behaviors in crossing the street in comparison to other age groups. Also, the speed of approaching vehicles was considered significant. The probability of risk taking among pedestrians decreases by increasing the speed of approaching vehicle in both the first and the second lanes of crossings.

Keywords: pedestrians, intersection, nested logit, risk

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Authors: Festus M. Epetimehin

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This study was conducted to identify the effect of National Directorate of Employment (NDE) training on the profit of Agricultural-Small and Medium Enterprises (SMEs) and to evaluate the factors that influenced farmers' participation in NDE training, as well as the type and frequency of training farmers and other agro-allied entrepreneurs in Nigeria. Using a multi-stage sampling procedure, a total of 384 respondents were sampled, including 192 beneficiaries and 192 non-beneficiaries in Oyo and Lagos States, respectively. Data were analysed using Binary Logit regression and Propensity Score Matching techniques. According to the binary logit analysis, respondents’ gender, availability to extension services, and the location of respondent’s operation were determinant factors influencing NDE training enrolment. All identified factors are related to the probability of respondents’ involvement in a positive way. Propensity score matching revealed that Agricultural-SMEs who participated in the NDE program boosted their profit by N341,072.18. The positive outcome of the effect implies that NDE training enhances Agri-SME performance in Nigeria. The study concluded that greater funding should be provided for the NDE for performance-enhancing training of the Agri-SMEs.

Keywords: PSM, binary logit model, Agri-SME

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Authors: Kalandi Charan Pradhan

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In this study, we investigate does weather variation determine temporary labour migration using 210 sample households from six Semi-Arid Tropic (SAT) villages for the period of 2005-2014 in India. The study has made an attempt to examine how households use temporary labour migration as a coping mechanism to minimise the risk rather than maximize the utility of the households. The study employs panel Logit regression model to predict the probability of household having at least one temporary labour migrant. As per as econometrics result, it is found that along with demographic and socioeconomic factors; weather variation plays an important role to determine the decision of migration at household level. In order to capture the weather variation, the study uses mean crop yield deviation over the study periods. Based on the random effect logit regression result, the study found that there is a concave relationship between weather variation and decision of temporary labour migration. This argument supports the theory of New Economics of Labour Migration (NELM), which highlights the decision of labour migration not only maximise the households’ utility but it helps to minimise the risks.

Keywords: temporary migration, socioeconomic factors, weather variation, crop yield, logit estimation

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Authors: Rizki Nor Amelia, Farida A. Setiawati

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This study aimed to: (1) describe the characteristics of teacher-made test instrument used to measure the ability of students’chemistry, and (2) identify the presence of the compability difficulty level set by teachers to difficulty level by empirical results. Based on these objectives, this study was a descriptive research. The analysis in this study used the Rasch model and Chi-square statistics. Analysis using Rasch Model was based on the response patterns of high school students to the teacher-made test instrument on chemistry subject Academic Year 2015/2016 in the Yogyakarta. The sample of this research were 358 students taken by cluster random sampling technique. The analysis showed that: (1) a teacher-made tests instrument has a medium on the mean difficulty level. This instrument is capable to measure the ability on the interval of -0,259 ≤ θ ≤ 0,659 logit. Maximum Test Information Function obtained at 18.187 on the ability +0,2 logit; (2) 100% items categorized either as easy or difficult by rasch model is match with the teachers’ judgment; while 37 items are categorized according to rasch model which 8.10% and 10.81% categorized as easy and difficult items respectively according to the teachers, the others are medium categorized. Overall, the distribution of the level of difficulty formulated by the teachers has the distinction (not match) to the level of difficulty based on the empirical results.

Keywords: chemistry, items parameter fitness, Rasch model, teacher-made test

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Authors: Alma Sobrevilla

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Using panel data from Mexico, this paper studies the determinants of women’s intrahousehold decision-making power using a generalised ordered logit model. Fixed effects estimations are also carried out to solve potential endogeneity coming from unobservable time-invariant factors. Finally, the paper analyses quadratic and community divergence effects of education on power. Results show heterogeneity in the effect of each of the determinants across different levels of decision-making power and suggest the presence of a significant quadratic effect of education. Having more education than the community average has a negative effect on power, supporting the notion that women tend to compensate their success outside the household with submissive attitudes at home.

Keywords: women, decision-making power, intrahousehold, Mexico

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: Tayebeh Saghapour, Sara Moridpour, Russell George Thompson

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One of the common aims of transport policy makers is to switch people’s travel to active transport. For this purpose, a variety of transport goals and investments should be programmed to increase the propensity towards active transport mode choice. This paper aims to investigate whether built environment features in neighbourhoods could enhance the odds of active transportation. The present study introduces an index measuring public transport accessibility (PTAI), and a walkability index along with socioeconomic variables to investigate mode choice behaviour. Using travel behaviour data, an ordered logit regression model is applied to examine the impacts of explanatory variables on walking trips. The findings indicated that high rates of active travel are consistently associated with higher levels of walking and public transport accessibility.

Keywords: active transport, public transport accessibility, walkability, ordered logit model

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Authors: Saheed Olakunle Sanusi, Israel Ajibade Adedeji

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The study analysed the effect of microfinance on the profit level of small and medium scale enterprises in Lagos. The data for the study were obtained by simple random sampling, and total of one hundred and fifty (150) small and medium scale enterprises (SMEs) were sampled for the study. Seventy-five (75) each are microfinance users and non-users. Data were analysed using descriptive statistics, logit model, t-test and ordinary least square (OLS) regression. The mean profit of the enterprises using microfinance is ₦16.8m, while for the non-users of microfinance is ₦5.9m. The mean profit of microfinance users is statistically different from the non-users. The result of the logit model specified for the determinant of access to microfinance showed that three of specified variables- educational status of the enterprise head, credit utilisation and volume of business investment are significant at P < 0.01. Enterprises with many years of experience, highly educated enterprise heads and high volume of business investment have more potential access to microfinance. The OLS regression model indicated that three parameters namely number of school years, the volume of business investment and (dummy) participation in microfinance were found to be significant at P < 0.05. These variables are therefore significant determinants of impacts of microfinance on profit level in the study area. The study, therefore, concludes and recommends that to improve the status of small and medium scale enterprises for an increase in profit, the full benefit of access to microfinance can be enhanced through investment in social infrastructure and human capital development. Also, concerted efforts should be made to encouraged non-users of microfinance among SMEs to use it in order to boost their profit.

Keywords: credit utilisation, logit model, microfinance, small and medium enterprises

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Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb

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The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.

Keywords: DCF, PCF, throughput, NS2

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Authors: Huynh Viet Khai, Mitsuyasu Yabe

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The study investigated the economic value of biodiversity attributes that could provide policy-makers reliable information to estimate welfare losses due to biodiversity reductions and analyse the trade-off between biodiversity and economics. In order to obtain the non-market benefits of biodiversity conservation, an indirect utility function and willingness to pay for biodiversity attributes were applied using the approach of choice modelling with the analysis of conditional logit model. The study found that Mekong Delta residents accepted their willingness to pay for VND 913 monthly for a one percent increase in healthy vegetation, VND 360 for an additional mammal species and VND 2,440 to avoid the welfare losses of 100 local farmers.

Keywords: choice modelling, genetic resources, wetland conservation, marginal willingness to pay

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Authors: Ritika Jain, Rajnish Kumar

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The Department of Public Enterprises had made submissions of Self Evaluation Reports, for the purpose of corporate governance, mandatory for all central government owned enterprises. Despite this, an alarming 40% of the enterprises did not do so. This study examines the impact of external policy tools and internal firm-specific factors on corporate governance of central public sector enterprises (CPSEs). We use a dataset of all manufacturing and non-financial services owned by the central government of India for the year 2010-11. Using probit, ordered logit and Heckman’s sample selection models, the study finds that the probability and quality of corporate governance is positively influenced by the CPSE getting into a Memorandum of Understanding (MoU) with the central government of India, and hence, enjoying more autonomy in terms of day to day operations. Besides these, internal factors, including bigger size and lower debt size contribute significantly to better corporate governance.

Keywords: corporate governance, central public sector enterprises (CPSEs), sample selection, Memorandum of Understanding (MoU), ordered logit, disinvestment

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Authors: Shabnam Najafi, Metin Turkay

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Network design problem (NDP) is used to determine the set of optimal values for certain pre-specified decision variables such as capacity expansion of nodes and links by optimizing various system performance measures including safety, congestion, and accessibility. The designed transportation network should improve objective functions defined for the system by considering the route choice behaviors of network users at the same time. The NDP studies mostly investigated the random demand and route selection constraints separately due to computational challenges. In this work, we consider both random demand and route selection constraints simultaneously. This work presents a nonlinear stochastic model for land use and road network design problem to address the development of different functional zones in urban areas by considering both cost function and air pollution. This model minimizes cost function and air pollution simultaneously with random demand and stochastic route selection constraint that aims to optimize network performance via road capacity expansion. The Bureau of Public Roads (BPR) link impedance function is used to determine the travel time function in each link. We consider a city with origin and destination nodes which can be residential or employment or both. There are set of existing paths between origin-destination (O-D) pairs. Case of increasing employed population is analyzed to determine amount of roads and origin zones simultaneously. Minimizing travel and expansion cost of routes and origin zones in one side and minimizing CO emission in the other side is considered in this analysis at the same time. In this work demand between O-D pairs is random and also the network flow pattern is subject to stochastic user equilibrium, specifically logit route choice model. Considering both demand and route choice, random is more applicable to design urban network programs. Epsilon-constraint is one of the methods to solve both linear and nonlinear multi-objective problems. In this work epsilon-constraint method is used to solve the problem. The problem was solved by keeping first objective (cost function) as the objective function of the problem and second objective as a constraint that should be less than an epsilon, where epsilon is an upper bound of the emission function. The value of epsilon should change from the worst to the best value of the emission function to generate the family of solutions representing Pareto set. A numerical example with 2 origin zones and 2 destination zones and 7 links is solved by GAMS and the set of Pareto points is obtained. There are 15 efficient solutions. According to these solutions as cost function value increases, emission function value decreases and vice versa.

Keywords: epsilon-constraint, multi-objective, network design, stochastic

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Authors: Khalil Ahmad Kakar

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In developing countries increasing the automobile and low capacity public transport (para-transit) which are creating congestion, pollution, noise, and traffic accident are the most critical quandary. These issues are under the analysis of assessors to break down the puzzle and propose sustainable urban public transport system. Kabul city is one of those urban areas that the inhabitants are suffering from lack of tolerable and friendly public transport system. The city is the most-populous and overcrowded with around 4.5 million population. The para-transit is the only dominant public transit system with a very poor level of services and low capacity vehicles (6-20 passengers). Therefore, this study after detailed investigations suggests bus rapid transit (BRT) system in Kabul City. It is aimed to mitigate the role of informal transport and decreases congestion. The research covers three parts. In the first part, aggregated travel demand modelling (four-step) is applied to determine the number of users for para-transit and assesses BRT network based on higher passenger demand for public transport mode. In the second part, state preference (SP) survey and binary logit model are exerted to figure out the utility of existing para-transit mode and planned BRT system. Finally, the impact of predicted BRT system on para-transit is evaluated. The extracted outcome based on high travel demand suggests 10 km network for the proposed BRT system, which is originated from the district tenth and it is ended at Kabul International Airport. As well as, the result from the disaggregate travel mode-choice model, based on SP and logit model indicates that the predicted mass rapid transit system has higher utility with the significant impact regarding the reduction of para-transit.

Keywords: BRT, para-transit, travel demand modelling, Kabul City, logit model

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Authors: Xizhen Zhou, Yanjie Ji

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The charging behavior of drivers provides a reference for the planning and management of charging facilities. Based on the real trajectory data of electric vehicles, this study explored the influence of the surrounding environments of the parking spot on charging decisions. The built environment, the condition of vehicles, and the nearest charging station were all considered. And the mixed binary logit model was used to capture the impact of unobserved heterogeneity. The results show that the number of fast chargers in the charging station, parking price, dwell time, and shopping services all significantly impact the charging decision, while the leisure services, scenic spots, and mileage since the last charging are opposite. Besides, factors related to unobserved heterogeneity include the number of fast chargers, parking and charging prices, residential areas, etc. The interaction effects of random parameters further illustrate the complexity of charging choice behavior. The results provide insights for planning and managing charging facilities.

Keywords: charging decision, trajectory, electric vehicle, infrastructure, mixed logit

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Authors: K. B. Ramappa, A. V. Manjunatha

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Consumerism in India is witnessing unprecedented growth driven by favourable demographics, rising young and working population, rising income levels, urbanization and growing brand orientation. In addition, the increasing level of awareness on health, hygiene and quality has made the consumers to think on the fairly traded goods and brands. This has made retailing extremely important to everyone because without retailers’ consumers would not have access to day-to-day products. The increased competition among different retailers has contributed significantly towards rising consumer awareness on quality products and brand loyalty. Many existing empirical studies have mainly focused on net saving of consumers at organised retail via-a-vis unorganised retail shops. In this article, authors have analysed the Bangalore consumers' attitudes towards buying of fruits and vegetables and their choice of retail outlets. The primary data was collected from 100 consumers belonging to the Bangalore City during October 2014. Sample consumers buying at supermarkets, convenience stores and hypermarkets were purposively selected. The collected data was analyzed using descriptive statistics and multinomial logit model. It was found that among all variables, quality and prices were major accountable factors for buying fruits and vegetables at organized retail shops. The empirical result of multinomial logit model reveals that annual net income was positively associated with the Big Bazar and Food World consumers and negatively associated with the Reliance Fresh, More and Niligiris consumers, as compared with the HOPCOMS consumers. Per month expenditure on fruits and vegetables was positively and age of the consumer was negatively related to the consumers’ choice of buying at modern retail markets. Consumers were willing to buy at modern retail outlets irrespective of the distance.

Keywords: organized retailers, consumers' attitude, consumers' preference, fruits, vegetables, multinomial logit, Bangalore

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Authors: Sivanandan Balakrishnan, Sara Moridpour, Richard Tay

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Heavy vehicles make a significant contribution to many developed economies, including Australia, because they are a major means of transporting goods within these countries. With the increase in road freight, there will be an increase in the heavy vehicle traffic proportion, and consequently, an increase in the possibility of collisions involving heavy vehicles. Crashes involving heavy vehicles are a major road safety concern because of the higher likelihood of fatal and serious injury, especially to any small vehicle occupant involved. The primary objective of this research is to identify the factors influencing injury severity to occupants in vehicle collisions involving heavy vehicle at T- intersection using a binary logit model in Victoria, Australia. Our results show that the factors influencing injury severity include occupants' gender, age and restraint use. Also, vehicles' type, movement, point-of-impact and damage, time-of-day, day-of-week and season, higher percentage of trucks in traffic volume, hit pedestrians, number of occupants involved and type of collisions are associated with severe injury.

Keywords: binary logit model, heavy vehicle, injury severity, T-intersections

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Authors: Shatha S. Alhily

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The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.

Keywords: derivative, integral means, self conformal maps, univalent function

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Authors: Hamidou Diallo, Marianne Guille

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This paper identifies leading triggers of deficient episodes in terms of GDP growth based on a sample of countries at different stages of development over 1994-2017. Using logit models, we build early warning systems (EWS), and our results show important differences between developing countries (DCs) and advanced economies (AEs). For AEs, the main predictors of the probability of entering in a GDP growth deficient episode are the deterioration of external imbalances and the vulnerability of fiscal position while DCs face different challenges that need to be considered. The key indicators for them are first, the low ability to pay their debts, and second, their belonging or not to a common currency area. We also build homogeneous pools of countries inside AEs and DCs. The evolution of the proportion of AE countries in the riskiest pool is marked first, by three distinct peaks just after the high-tech bubble burst, the global financial crisis, and the European sovereign debt crisis, and second by a very low minimum level in 2006 and 2007. In contrast, the situation of DCs is characterized first by the relative stability of this proportion and then by an upward trend from 2006, that can be explained by a more unfavorable socio-political environment leading to shortcomings in the fiscal consolidation.

Keywords: currency area, early warning system, external imbalances, fiscal vulnerability, GDP growth, public debt

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Authors: Farida, M. Shehu, Shehu U. R. Aliyu

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Access to finance has been recognized in the literature as one of the major impediments confronting small scale businesses (SSBs). This largely arises due to high lending rate, religious inclinations, collateral, etc. Islamic mode finance operates under Profit and Loss Sharing (PLS) arrangement between a borrower (business owner) and a lender (Islamic bank). This paper empirically assesses the determinants of predisposition of small scale business operators in Fagge local government area, Kano State, Nigeria, towards the PLS. Cross-sectional data from a sample of 291 small scale business operators was analyzed using logit and probit regression models. Empirical results reveal that while awareness and religion inclination positively drive interest towards the PLS, lending rate and collateral work against it. The paper, therefore, strongly recommends more advocacy campaigns and setting up of more Islamic banks in the country to cater for the financing and religious needs of SSBs in the study area.

Keywords: Islamic finance, logit and probit models, profit and loss sharing small scale businesses, finance, commerce

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang

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A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.

Keywords: beta function, compressor map, interpolation error, map optimization tool

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Authors: Michalis Linardakis, Vasilis Grammatikopoulos, Athanasios Gregoriadis, Kalliopi Trouli

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Discrete choice models belong to the family of Conjoint analysis that are applied on the preferences of the respondents towards a set of scenarios that describe alternative choices. The scenarios have been pre-designed to cover all the attributes of the alternatives that may affect the choices. In this study, we examine how preschool educators integrate physical activities into their everyday teaching practices through the use of discrete choice models. One of the advantages of discrete choice models compared to other more traditional data collection methods (e.g. questionnaires and interviews that use ratings) is that the respondent is called to select among competitive and realistic alternatives, rather than objectively rate each attribute that the alternatives may have. We present the effort to construct and choose representative attributes that would cover all possible choices of the respondents, and the scenarios that have arisen. For the purposes of the study, we used a sample of 50 preschool educators in Greece that responded to 4 scenarios (from the total of 16 scenarios that the orthogonal design resulted), with each scenario having three alternative teaching practices. Seven attributes of the alternatives were used in the scenarios. For the analysis of the data, we used multinomial logit model with random effects, multinomial probit model and generalized mixed logit model. The conclusions drawn from the estimated parameters of the models are discussed.

Keywords: conjoint analysis, discrete choice models, educational data, multivariate statistical analysis

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Authors: Bi-Huei Tsai

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Previous studies on financial distress prediction choose the conventional failing and non-failing dichotomy; however, the distressed extent differs substantially among different financial distress events. To solve the problem, “non-distressed”, “slightly-distressed” and “reorganization and bankruptcy” are used in our article to approximate the continuum of corporate financial health. This paper explains different financial distress events using the two-stage method. First, this investigation adopts firm-specific financial ratios, corporate governance and market factors to measure the probability of various financial distress events based on multinomial logit models. Specifically, the bootstrapping simulation is performed to examine the difference of estimated misclassifying cost (EMC). Second, this work further applies macroeconomic factors to establish the credit cycle index and determines the distressed cut-off indicator of the two-stage models using such index. Two different models, one-stage and two-stage prediction models, are developed to forecast financial distress, and the results acquired from different models are compared with each other, and with the collected data. The findings show that the two-stage model incorporating financial ratios, corporate governance and market factors has the lowest misclassification error rate. The two-stage model is more accurate than the one-stage model as its distressed cut-off indicators are adjusted according to the macroeconomic-based credit cycle index.

Keywords: Multinomial logit model, corporate governance, company failure, reorganization, bankruptcy

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Authors: Slobodan B. Tričković

Abstract:

We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

Abstract:

The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.

Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function

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