Alternative Functional Forms Research Articles

DC24: A new density coherence functional for multiconfiguration density-coherence functional theory.

In this study, we explored several alternative functional forms to construct more accurate and more physical density coherence (DC) functionals for multiconfiguration density-coherence functional theory. Each functional is parameterized against the same database as used in our previous work. The best DC functional, which is called DC24, has a more physical interpretation, and-as a side benefit-it also has a mean unsigned error of 1.73 kcal/mol, which is a 9% improvement as compared to the previous functional. The article also contains a new definition of the unpaired electron density, which may be useful in other contexts as well.

The Impact of Development on Antidepressant and Placebo Response in Anxiety Disorders: A Bayesian Hierarchical Meta-Analytic Examination of Randomized Controlled Trials in Children, Adolescents, and Adults.

Background: Understanding how development influences medication and placebo responses in anxiety disorders could inform treatment decisions, including age-specific first- versus second-line psychopharmacological interventions. Objective: To meta-analytically compare the trajectory of selective serotonin reuptake inhibitors (SSRIs), serotonin-norepinephrine reuptake inhibitors (SNRIs), and placebo response in youth and adults with anxiety disorders. Methods: Weekly symptom severity data were extracted from prospective, randomized, parallel-group, placebo-controlled trials of SSRIs and SNRIs in children, adolescents, and adults with anxiety disorders (generalized, separation, and social anxiety disorders as well as panic disorder). Treatment response was modeled for the standardized change in continuous measures of anxiety using a Bayesian hierarchical model. Change in symptom severity was evaluated as a function of time, and post hoc analyses were conducted to determine the sensitivity of these results across sample heterogeneity and alternative functional forms. Results: Data were included from 11 trials of youth (SSRI, κ = 7; SNRI, κ = 4) and 71 studies of adults (SSRI, κ = 46; SNRI, κ = 25). In total, 1067 youth participated in SSRI trials and 1024 in SNRI trials. In total, 10,826 adults participated in SSRI trials (placebo, n = 5367; SSRI n = 5,459) and 6232 in SNRI trials (placebo, n = 3,128; SNRI n = 3,094). A logarithmic model best described the response. Placebo response was similar in youth and adults (mean difference = -1.98 ± 6.21, 95% credible interval [CrI]: -10.2 to 14.2, p = 0.750), and statistically significant improvement from baseline emerged by week 2 in both adults (mean difference: -18.34 + 1.017, 95% CrI: -20.3 to 16.3, p < 0.001) and youth (mean difference: -23.74 + 3.736, 95% CrI: -31.1 to -16.4, p < 0.001). SSRIs produced similar improvements for youth and adults (p = 0.129), but SNRIs produced slower improvement in youth than adults (p = 0.018). Conclusions: Antidepressant-related improvement occurs early in youth and adults with anxiety disorders. SSRI response is similar in adults and youth; however, SNRIs produce greater responses in adults than youth, potentially representing a developmental effect.

Volatility-dependent probability weighting and the dynamics of the pricing kernel puzzle

In order to estimate volatility-dependent probability weighting functions, we obtain risk neutral and physical densities from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) stochastic volatility and jumps model. Across volatility levels, we find pronounced inverse S-shapes, i.e. small probabilities are overweighted, and probability weighting almost monotonically increases in volatility, indicating higher skewness preferences and crash aversion in volatile market environments. Moreover, by estimating probabilistic risk attitudes, equivalent to the share of risk aversion related to probability weighting, we shed further light on the pricing kernel puzzle. While pricing kernels estimated from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) model display the typical U-shape as documented in the literature, pricing kernels—net of probability weighting—are strictly monotonically decreasing and thus in line with economic theory. Equivalently, we find risk aversion to be positive across wealth levels. Our results are robust to alternative maturities, wealth percentiles, alternative functional forms, a nonparametric empirical setting and variations of the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) coefficient estimates.

Evaluating a Targeted Minimum Loss-Based Estimator for Capture-Recapture Analysis: An Application to HIV Surveillance in San Francisco, California.

The capture-recapture method is a common tool used in epidemiology to estimate the size of "hidden" populations and correct the underascertainment of cases, based on incomplete and overlapping lists of the target population. Log-linear models are often used to estimate the population size yet may produce implausible and unreliable estimates due to model misspecification and small cell sizes. A novel targeted minimum loss-based estimation (TMLE) model developed for capture-recapture makes several notable improvements to conventional modeling: "targeting" the parameter of interest, flexibly fitting the data to alternative functional forms, and limiting bias from small cell sizes. Using simulations and empirical data from the San Francisco, California, Department of Public Health's human immunodeficiency virus (HIV) surveillance registry, we evaluated the performance of the TMLE model and compared results with those of other common models. Based on 2,584 people observed on 3 lists reportable to the surveillance registry, the TMLE model estimated the number of San Francisco residents living with HIV as of December 31, 2019, to be 13,523 (95% confidence interval: 12,222, 14,824). This estimate, compared with a "ground truth" of 12,507, was the most accurate and precise of all models examined. The TMLE model is a significant advancement in capture-recapture studies, leveraging modern statistical methods to improve estimation of the sizes of hidden populations.

Using joint models to study the association between CD4 count and the risk of death in TB/HIV data

BackgroundThe association structure linking the longitudinal and survival sub-models is of fundamental importance in the joint modeling framework and the choice of this structure should be made based on the clinical background of the study. However, this information may not always be accessible and rationale for selecting this association structure has received relatively little attention in the literature. To this end, we aim to explore four alternative functional forms of the association structure between the CD4 count and the risk of death and provide rationale for selecting the optimal association structure for our data. We also aim to compare the results obtained from the joint model to those obtained from the time-varying Cox model.MethodsWe used data from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) AIDS Treatment programme, the Starting Antiretroviral Therapy at Three Points in Tuberculosis (SAPiT) study, an open-label, three armed randomised, controlled trial between June 2005 and July 2010 (N=642). In our analysis, we combined the early and late integrated arms and compared results to the sequential arm. We utilized the Deviance Information Criterion (DIC) to select the final model with the best structure, with smaller values indicating better model adjustments to the data.ResultsPatient characteristics were similar across the study arms. Combined integrated therapy arms had a reduction of 55% in mortality (HR:0.45, 95% CI:0.28-0.72) compared to the sequential therapy arm. The joint model with a cumulative effects functional form was chosen as the best association structure. In particular, our joint model found that the area under the longitudinal profile of CD4 count was strongly associated with a 21% reduction in mortality (HR:0.79, 95% CI:0.72-0.86). Where as results from the time-varying Cox model showed a 19% reduction in mortality (HR:0.81, 95% CI:0.77-0.84).ConclusionsIn this paper we have shown that the “current value” association structure is not always the best structure that expresses the correct relationship between the outcomes in all settings, which is why it is crucial to explore alternative clinically meaningful association structures that links the longitudinal and survival processes.

The impact of lifestyle guidance intervention on health outcomes among Japanese middle-aged population with metabolic syndrome: A regression discontinuity study

Metabolic syndrome (MetS) prevalence has increased globally with considerable morbidity and economic burden at both individual and national levels. Japan is the first and only country that has introduced a nationwide lifestyle guidance intervention program to manage and control MetS. We conducted a quasi-experiment approach—regression discontinuity design—to evaluate the impact of this intervention on health outcomes at the population level. We retrospectively collected data of adults aged ≥35 years who participated in health checkups in 2015. Age in 2015 was used as the assignment variable, and an age of 40 years old was the threshold because those with MetS aged ≥40 were required to receive lifestyle guidance intervention. Among 26,772 MetS adults, those who received the intervention had significant reductions in obesity measurements (bodyweight, waist circumference, and body mass index [BMI]) after 1 year of this intervention. Blood pressure was also significantly reduced in men after 1 year of undertaking the intervention. The results were similar when including demographic, socioeconomic, and behavioral covariates and using alternative functional forms to estimate the impact, or when bandwidths around intervention thresholds were changed. Our results showed that lifestyle guidance intervention for MetS has an important impact on weight loss and blood pressure reduction at the population level. This intervention could address the high burden of obesity and cardiovascular diseases in Japan and other countries with an unmet need for MetS prevention and management.

The local and global mental health effects of the Covid-19 pandemic

This paper investigates the mental health effects of the local and global level Covid-19 pandemic among the UK population. To identify the effect, we use a high-quality dataset and an original strategy where we match the previous day’s confirmed pandemic cases to a four-month panel of individual mental health information observed during the interview next day. The approach suggested in this paper aims to identify the average mental health effect on the overall population for the first and second waves of the pandemic. Using a linear fixed-effects model specification, we report robust findings that the average mental health in the UK is substantially reduced by the local and global pandemic. The total reduction in the average mental health of the UK population during our sampling period (April - June, 2020) is about 1.5% for the local and 2.4% for the global cases, which sum up to a 3.9% reduction. Extrapolating the total reduction in average mental health during the first wave of the pandemic (February - September, 2020) sums up to 2.8% while the effect is as large as 9.6% for the first and second waves together, which covers roughly a year since the start. An extensive robustness check suggests that the findings are stable with respect to alternative pandemic datasets, measures, estimators, functional forms, and time functions. The characteristics of the most vulnerable individuals (e.g., elderly, chronic illness, and job security concerns) and their household conditions (e.g., living alone and no private space) are explored. The paper discusses on the implications of the results.

Smoking habits in Mexico: Upward and downward comparisons of economic status

AbstractWhile experimental and behavioral economics have extensively studied the role of both upward and downward comparisons of economic status, the latter have been largely neglected in secondary data studies. The scarce existing evidence shows mixed results and is essentially limited to analyses of subjective well‐being in high‐income countries. Using nationally representative data from Mexico with almost 45,000 personal records, we disentangle the role of absolute wealth, relative deprivation, and relative affluence as explanatory variables for smoking behavior. We find robust evidence of greater smoking at higher levels of absolute achievement and relative deprivation and lower smoking at higher levels of relative affluence. Results hold for a variety of indicators of smoking habits, reflecting both smoking prevalence and intensity. Compared to men, we find that women tend to have stronger associations between the three facets of economic status and smoking prevalence. Results are robust to the use of alternative functional forms and reference groups for the measurement of relative deprivation and relative affluence.

Police Performance Rankings Depend on the Functional Form of the Index: A Comment on Bearfield, Maranto, and Wolf

Bearfield, Maranto, and Wolf advise policy-makers to measure policing outcomes using a metric that includes rates of homicide, police-related civilian deaths (PRCD), and poverty. They present such an index, which they call the Police Performance Index (PPI). But alternative functional forms that are equally plausible can lead to different rankings of police departments, and therefore different policy conclusions.

Ekonometrijsko ispitivanje uticaja prihoda na rashode domaćinstva

The subject of this paper is the econometric examination of the impact of income on expenditures, i.e. on the demand for package holidays of households in Serbia. The aim of this paper is to quantify the impact of income on household expenditures for package holidays in the country and abroad on the basis of alternative functional forms of Engel curves and elasticities derived from them. The starting research hypothesis is that with the increase in household income, the share of expenditures for tourist arrangements in total household expenditures in Serbia remains approximately unchanged. As sources of data, Household Budget Surveys in Serbia were used, which were conducted every year, starting from 2006 (until 2019). Based on the different functional forms of Engel curves, the parameters of the impact of income on expenditures for package arrangements were estimated, and then income elasticities were estimated. In addition to the impact of income, the impact of qualitative characteristics of households and especially household heads on expenditures for tourist arrangements was examined. With the help of appropriate statistical tests, the basic research hypothesis was proven and the influence of socio-economic and demographic characteristics of households on the demand for package holidays was quantified.

Police Performance Rankings Depend on the Functional Form of the Index: A Comment on Bearfield, Maranto and Wolf

Bearfield, Maranto and Wolf (2020) advise policy-makers to measure policing outcomes using a metric that includes rates of homicide, police-related civilian deaths (PRCD) , and poverty. They present such an index, which they call the Police Performance Index (PPI). But alternative functional forms that are equally plausible can lead to different rankings of police departments, and therefore different policy conclusions.

Impact of community based screening for hypertension on blood pressure after two years: regression discontinuity analysis in a national cohort of older adults in China

ObjectiveTo estimate the causal impact of community based blood pressure screening on subsequent blood pressure levels among older adults in China.DesignRegression discontinuity analysis using data from a national cohort study.Setting2011-12...

Methodological Considerations in the Statistical Modeling of Catastrophe Bond Prices

AbstractThe problem of specifying and fitting a statistical model of the pricing of property catastrophe risk is addressed from a methodological perspective. Notable 21st century published efforts to do this are reviewed. The problem is framed in a business context and various strategic and tactical issues are investigated. A naïve application of ordinary least squares regression is seen to have undesirable consequences. Alternative approaches are offered, including weighted least squares with weights inversely proportional to capital requirements, and alternative functional forms. Recommendations are offered.

Tropical tree height and crown allometries for the Barro Colorado Nature Monument, Panama: a comparison of alternative hierarchical models incorporating interspecific variation in relation to life history traits

Abstract. Tree allometric relationships are widely employed for estimating forest biomass and production and are basic building blocks of dynamic vegetation models. In tropical forests, allometric relationships are often modeled by fitting scale-invariant power functions to pooled data from multiple species, an approach that fails to capture changes in scaling during ontogeny and physical limits to maximum tree size and that ignores interspecific differences in allometry. Here, we analyzed allometric relationships of tree height (9884 individuals) and crown area (2425) with trunk diameter for 162 species from the Barro Colorado Nature Monument, Panama. We fit nonlinear, hierarchical models informed by species traits – wood density, mean sapling growth, or sapling mortality – and assessed the performance of three alternative functional forms: the scale-invariant power function and the saturating Weibull and generalized Michaelis–Menten (gMM) functions. The relationship of tree height with trunk diameter was best fit by a saturating gMM model in which variation in allometric parameters was related to interspecific differences in sapling growth rates, a measure of regeneration light demand. Light-demanding species attained taller heights at comparatively smaller diameters as juveniles and had shorter asymptotic heights at larger diameters as adults. The relationship of crown area with trunk diameter was best fit by a power function model incorporating a weak positive relationship between crown area and species-specific wood density. The use of saturating functional forms and the incorporation of functional traits in tree allometric models is a promising approach for improving estimates of forest biomass and productivity. Our results provide an improved basis for parameterizing tropical plant functional types in vegetation models.

Interspecific variation in tropical tree height and crown allometries in relation to life history traits

&lt;p&gt;&lt;strong&gt;Abstract.&lt;/strong&gt; Tree allometric relationships are widely employed to estimate forest biomass and production, and are basic building blocks of dynamic vegetation models. In tropical forests, allometric relationships are often modeled by fitting scale-invariant power functions to pooled data from multiple species, an approach that fails to reflect finite size effects at the smallest and largest sizes, and that ignores interspecific differences in allometry. Here, we analyzed allometric relationships of tree height (9884 individuals) and crown area (2425) with trunk diameter using species-specific morphological and life history data of 162 species from Barro Colorado Island, Panamá. We fit nonlinear, hierarchical models informed by species traits and assessed the performance of three alternative functional forms: the scale-invariant power function, and the saturating Weibull and generalized Michaelis-Menten (gMM) functions. The relationship of tree height with trunk diameter was best fit by a saturating gMM model in which variation in allometric parameters was related to interspecific differences in sapling growth rates, a measure of regeneration light demand. Light-demanding species attained taller heights at comparatively smaller diameters as juveniles and had shorter asymptotic heights at larger diameters as adults. The relationship of crown area with trunk diameter was best fit by a power function model incorporating a weak positive relationship between crown area and species-specific wood density. The use of saturating functional forms and the incorporation of functional traits in tree allometric models is a promising approach to improve estimates of forest biomass and productivity. Our results provide an improved basis for parameterizing tropical tree functional types in vegetation models.&lt;/p&gt;

Terrorism and international air travel: A gravity approach

AbstractWe present a theoretical model (adapted from the structural gravity model by Anderson and van Wincoop, American Economic Review, 93, 2003, 170) to capture the effects of terrorism on air passenger traffic between nations affected by terrorism. We then use equations derived from this model, in conjunction with alternative functional forms for trade costs, to estimate the effects of terrorism on bilateral air passenger service flows from 58 source countries to 26 destination countries during 2000–14. An additional small‐scale terrorist incident in the origin country and destination country together results in a reduction in bilateral air passenger travel by, at least, 1.3% and 0.81%, respectively, for pairs of countries located 1,000 and 2,000 km or less apart. The adverse impact of transnational terrorism is approximately five times larger. Terrorism adversely impacts bilateral air passenger travel both by reducing national output and especially by increasing psychological distress. Last but not the least, international air passenger travel is found to be extremely sensitive to fatal terrorist attacks and terrorist attacks on targets such as airports, travel or tourists.

Maturity in competing tourism destinations: the case of Tenerife

PurposeThe main purpose of this paper is to contribute to the ongoing literature on the pertinence of TALC (tourism area life cycle) to model and analyse mature destinations, using quantitative data and alternative functional forms. With this purpose, this work analyses the recent data on tourist demand in Tenerife (Canary Islands), which is supposed to be playing the role of “refuge” with respect to other competing resorts, when the latter ones present political instability after the so-called Arab Springs, particularly the Middle East and North Africa.Design/methodology/approachTo analyse the data, and to explore potential epiphenomenon, nonlinear competing regression analysis were performed (logistic, Gaussian and logarithmic), taking into account some insights from tourism life cycle theories.FindingsSome suggestions are presented for political management of these destinations that are still working under a moratorium on tourist infrastructure.Research limitations/implicationsOnce the TALC is accepted – even under discussion – in the scholarly fore, certain incentives arise to identify, interpret and communicate signals of maturity. Public funds and specific policies (moratoria) can then be solicited to political instances. Further empirical research, complementary quantitative approaches, along with new data that confronts the evolution of demand in Tenerife with paulatine reactivation of competing destinations, will be strongly required to overcome the limitations of this first attempt and to properly determine the effectiveness of rejuvenation policies. Besides, additional quantitative data should be considered to explore the potential explanatory factors beyond the time series analysis into models that are more theoretical.Originality/valueThe results suggest that the diagnosis of maturity was at least premature in the first place, poorly based on data analysis and fast in promoting specific policies whose effectiveness is under discussion even after decades.

Development of Safety Performance Functions: Incorporating Unobserved Heterogeneity and Functional Form Analysis

To improve transportation safety, this study applies Highway Safety Manual (HSM) procedures to roadways while accounting for unobserved heterogeneity and exploring alternative functional forms for Safety Performance Functions (SPFs). Specifically, several functional forms are considered in Poisson and Poisson-gamma modeling frameworks. Using 5 years (2011–2015) of crash, traffic, and road inventory data for two-way, two-lane roads in Tennessee, fixed- and random-parameter count data models are calibrated. The models account for important methodological concerns of unobserved heterogeneity and omitted variable bias. With a validation dataset, the calibrated and uncalibrated HSM SPFs and eight new Tennessee-specific SPFs are compared for prediction accuracy. The results show that the statewide calibration factor is 2.48, suggesting rural two-lane, two-way road segment crashes are at least 1.48 times greater than what HSM SPF predicts. Significant variation in four different regions in Tennessee is observed with calibration factors ranging between 2.02 and 2.77. Among all the SPFs considered, fully specified Tennessee-specific random parameter Poisson SPF outperformed all competing SPFs in predicting out-of-sample crashes on these road segments. The best-fit random parameter SPF specification for crash frequency includes the following variables: annual average daily traffic, segment length, shoulder width, lane width, speed limit, and the presence of passing lanes. Significant heterogeneity is observed in the effects of traffic exposure-related variables on crash frequency. The study shows how heterogeneity-based models can be specified and used by practitioners for obtaining accurate crash predictions.

Experimental investigation of alternative transmission functions: Quantitative evidence for the importance of nonlinear transmission dynamics in host-parasite systems.

Understanding pathogen transmission is crucial for predicting and managing disease. Nonetheless, experimental comparisons of alternative functional forms of transmission remain rare, and those experiments that are conducted are often not designed to test the full range of possible forms.To differentiate among 10 candidate transmission functions, we used a novel experimental design in which we independently varied four factors—duration of exposure, numbers of parasites, numbers of hosts and parasite density—in laboratory infection experiments.We used interactions between amphibian hosts and trematode parasites as a model system and all candidate models incorporated parasite depletion. An additional manipulation involving anaesthesia addressed the effects of host behaviour on transmission form.Across all experiments, nonlinear transmission forms involving either a power law or a negative binomial function were the best‐fitting models and consistently outperformed the linear density‐dependent and density‐independent functions. By testing previously published data for two other host–macroparasite systems, we also found support for the same nonlinear transmission forms.Although manipulations of parasite density are common in transmission studies, the comprehensive set of variables tested in our experiments revealed that variation in density alone was least likely to differentiate among competing transmission functions. Across host–pathogen systems, nonlinear functions may often more accurately represent transmission dynamics and thus provide more realistic predictions for infection.

On Modeling Insurance Risk Pricing

The problem of specifying and fitting a statistical model of the pricing of property catastrophe risk is addressed from a methodological perspective. Notable 21st century published efforts to do this are reviewed. The problem is framed in a business context and various strategic and tactical issues are investigated. A naive application of ordinary least squares regression is seen to have undesirable consequences. Alternative approaches are offered, including weighted least squares with weights inversely proportional to capital requirements, and alternative functional forms. Recommendations are offered.