Functional Form Models Research Articles

Physics-constrained Gaussian process for life prediction under in-phase multiaxial cyclic loading with superposed static components

Under multiaxial fatigue loading, the superposed static components are additional factors for life prediction models to be considered. The increased dimension in fatigue data imposes difficulties in pattern recognition using existing functional form models. A framework to build a Gaussian process (GP) model for lifetime prediction under multiaxial loading was developed to solve this problem. Physically consistent constraints were imposed by applying a novel technique on the GP model to control its behavior and to decrease an overfitting risk. The model consistency with the rotationally invariant principle of damage was provided by the application of the critical plane concept. The framework was demonstrated to have excellent prediction capability on S355 steel and 7075-T651 aluminum alloy. Five well-known fatigue models of functional forms were also implemented for comparison. Detailed parametric studies were presented for the training sample effect, GP kernel effect, and model predictability.

The influence of aggregation level and category construction on estimation quality for freight trip generation models

This paper analyzes the impacts of aggregation level and category construction on the relevance and quality of freight trip generation (FTG) models. More precisely, constant generations and functional form models are compared, as well as activity and activity-workforce categories. The paper proposes a method to compare constant generation and functional form models on different category classifications based on MAPE estimations. Functional forms are assessed via linear regression and compared using Pearson coefficient. Results show that the aggregation level has not always a positive impact on the model’s accuracy and the choice of suitable functional form leads to more accurate models.

Neural network approach toB→Xuℓν

We use artificial neural networks to parameterize the shape functions in inclusive semileptonic $B$ decays without charm. Our approach avoids the adoption of functional form models and allows for a straightforward implementation of all experimental and theoretical constraints on the shape functions. The results are used to extract $|V_{ub}|$ in the GGOU framework and compared with the original GGOU paper and the latest HFAG results, finding good agreement in both cases. The possible impact of future Belle-II data on the $M_X$ distribution is also discussed.

Non-additive response of larval ringed salamanders to intraspecific density

Conditions experienced in early developmental stages can have long-term consequences for individual fitness. High intraspecific density during the natal period can affect juvenile and eventually adult growth rates, metabolism, immune function, survival, and fecundity. Despite the important ecological and evolutionary effects of early developmental density, the form of the relationship between natal density and resulting juvenile phenotype is poorly understood. To test competing hypotheses explaining responses to intraspecific density, we experimentally manipulated the initial larval density of ringed salamanders (Ambystoma annulatum), a pond-breeding amphibian, over 11 densities. We modeled the functional form of the relationship between natal density and juvenile traits, and compared the relative support for the various hypotheses based on their goodness of fit. These functional form models were then used to parameterize a simple simulation model of population growth. Our data support non-additive density dependence and presents an alternate hypothesis to additive density dependence, self-thinning and Allee effects in larval amphibians. We posit that ringed salamander larvae may be under selective pressure for tolerance to high density and increased efficiency in resource utilization. Additionally, we demonstrate that models of population dynamics are sensitive to assumptions of the functional form of density dependence.

Cautionary Note on Computing Site-Specific Recreational Demand Elasticities and Welfare Estimates

This cautionary note achieves three important integrative goals. First is justifying the need for applied agricultural and resource economists to increasingly use flexible modeling techniques, such as the Box-Cox power family of transformations model, for reducing specification bias in recreational demand estimation. Second is demonstrating that findings from fitting inflexible functional form models tend to generate incorrect public policies on consumer welfare estimates. Third is establishing the importance of evaluating the demand elasticity estimates not only at the mean data values but also at the different data points, including at extreme data values, in the observed data space.

Variation in elemental stoichiometry and RNA:DNA in four phyla of benthic organisms from coral reefs

Summary The elemental composition of organisms has been linked to traits such as growth rates, through investment of phosphorus (P) in RNA (called the Growth Rate Hypothesis) and through ecological processes such as susceptibility to predation and herbivory. To test the predictions of the Growth Rate Hypothesis, we assessed the elemental composition and RNA of four phyla of common, co‐occurring benthic coral reef organisms, corals, and green, brown and red macroalgae, whose patterns of dominance are predicted to be strongly influenced by differences in growth and herbivory and thus elemental stoichiometry. We assessed the importance of phylogeny and functional form, two important attributes for predicting the composition of macroalgal communities, on the variation in elemental composition. Over these widely divergent taxonomic groups of organisms, we found support for links between elemental composition and RNA in tissues. The RNA:DNA in corals was positively correlated with % nitrogen (N) and negatively correlated with carbon (C):N ratios of tissues while RNA:DNA and RNA concentrations in macroalgae were positively correlated with %N, N:P ratios and negatively correlated with C:N ratios. Corals had higher concentrations of P and lower C:P ratios than macroalgae. Among the macroalgal lineages, C:P was higher in the brown algae than in red and green algae. Overall, the variation in elemental composition of macroalgae was relatively low compared with the variation reported for terrestrial plants and similar to that in corals. Analysis of phylogenetic sources of variation (family and genus) in elemental composition and RNA found that genus accounted for a significant proportion of variation in both corals and macroalgae (15–47%), but the largest source of variation (50–97%) was unexplained by our statistical model and thus likely attributable to species and environmental factors. Although elemental composition of macroalgae did not vary in a way that was consistent with functional form models, genera with larger thalli had higher tissue N than smaller forms and more lineages with greater complexity of form had lower C:P ratios than less complex brown algal lineages. Our data indicate that the despite relatively low levels of variation in elemental composition compared with terrestrial organisms, elemental stoichiometry varied significantly among coral reef taxa and with the structure of organisms and thus may have potential for predicting variation in growth rates and patterns of consumption on coral reefs.

Coordinating a Supply Chain with Price and Advertisement Dependent Stochastic Demand

This paper investigates pricing and ordering as well as advertising coordination issues in a single-manufacturer single-retailer supply chain, where the manufacturer sells a newsvendor-type product through the retailer who faces a stochastic demand depending on both retail price and advertising expenditure. Under the assumption that the market demand has a multiplicative functional form, the Stackelberg and cooperative game models are developed, and the closed form solution to each model is provided as well. Comparisons and insights are presented. We show that a properly designed revenue-cost-sharing contract can achieve supply chain coordination and lead to a Pareto improving win-win situation for channel members. We also discuss the allocation of the extra joint profit according to individual supply chain members' risk preferences and negotiating powers.

On the Discrepancy of Recent European Ground-Motion Observations and Predictions from Empirical Models: Analysis of KiK-net Accelerometric Data and Point-Sources Stochastic Simulations

Ground-motion amplitudes from recent European earthquakes of moderate magnitudes have been observed to be systematically smaller than the values expected from a number of popular empirical ground-motion prediction equations used for seismic hazard analysis. It has been suggested that these discrepancies are caused by regional variations in seismotectonic character and as a consequence that seismic hazard estimates using these ground-motion models would be too high. In the present article, we explore the hypothesis that the discrepancy can simply be explained by the fact that these models adopt magnitude-independent functional forms (letting Y designate the response spectral acceleration M designate the magnitude, then d log Y / dM is assumed independent of both magnitude and distance). The data collected by the KiK-net array (see the [Data and Resources][1] section) provides a unique opportunity to test this hypothesis and to analyze some of the pitfalls of deriving magnitude-independent functional form models and applying them for predictions of ground motion from smaller events (and vice versa). Borehole rock KiK-net ground-motion data (337 events, 3894 records) have been used to derive empirical ground-motion models with magnitude-independent functional forms for various magnitude ranges. By using these new ground-motion models and stochastic simulations, we discuss the ground-motion distance decays and magnitude effects for ground-motion models obtained with different magnitude range datasets. This analysis clearly indicates that response spectral amplitudes of ground motions from large earthquakes decay slower with distance than those from small earthquakes and confirms that the magnitude scaling of ground motion decreases as earthquake magnitude increases. Using stochastic simulations, we demonstrate that the observed decay in scaling could be a mixture of geometrical decay from extended sources and the fact that response spectral values instead of Fourier spectral values are considered. New ground-motion models (with functional forms including coefficients to model the observed magnitude-dependent scaling and decay rate) have finally been calculated for both surface and borehole site conditions of the analyzed dataset. These models show similar decays for intermediate period or moderate magnitude earthquakes. Our site classifications remove most of the statistical trend of the site effect and suggest that source and path effects could dominate the aleatory variability. [1]: #sec-16

Seaweed–herbivore interactions at a small scale: direct tests of feeding deterrence by filamentous algae

High growth rates and temporal or spatial opportunism are considered central to the success of filamentous algae, in particular for escaping or minimising the effects of herbivory. However, the role of chemical defences in filamentous algae has received far less attention. We investigated possible chemical feeding deterrence by filamentous red algae that have conspicuous cellular inclusions (Asparagopsis armata, Anotrichium tenue and Balliella amphiglanda) and 2 others without inclusions (Callithamnion korfense and Ulva sp.). The 3 algae with cellular inclusions were consumed at lower rates by a generalist amphipod, Hyale nigra, than the other 2 algae. To determine the potential role of chemical defences for A. armata, we conducted tests against herbivores using algae in which the production of halogenated metabolites was manipulated. This manipulation had no effect on carbon and nitrogen values of the algae, and allowed us to directly test the role of algal secondary metabolites in defence against herbivores without using artificial diets. Bromide (+) algae (with halogenated metabolites) deterred grazing by 2 mesograzers (Hyale nigra and juvenile abalone Haliotis rubra), which consumed up to 4 times more bromide (–) (metabolite-free) algae than bromide (+) algae. Juveniles of the sea hare Aplysia parvula were not deterred by the chemical defences in bromide (+) A. armata. In field assays, artificial diets containing a crude extract of A. armata were also active against herbivores. Although functional form models typically predict that tolerance—not resistance—should be the key defensive strategy for marine algae with simple architecture, this study demonstrates that resistance traits may also be important and more broadly utilised in filamentous species.

The pervasiveness of pharmaceutical expenditure inertia in the OECD countries

This paper constructs and estimates an economic model for testing statistically the strength of possible ‘expenditure inertia’ as a plausible reason for rising drug expenditures of the Organization for Economic Cooperation and Development (OECD) countries. The ethical drugs sector in the OECD health care systems is increasingly targeted as the major culprit in the rising cost. Using multiple regression analysis, and the maximum likelihood estimation method, the data of each country (taken from OECD Health Data, 1997) were first tested for functional form optimality with the Box-Cox power family transformations model. Drug expenditure elasticities, at data means, were computed using each country's optimal regression model estimates. The results indicate that the traditionally fitted a priori limited functional form models (e.g., linear, log–log) are not globally consistent with data across countries. The effect of a one-period lagged real per-capita drug expenditure (capturing inertia or habit persistence) on current period real per-capita prescription expenditure is statistically significant in most countries. Pharmaceutical demands are inelastic, and tend to behave like a necessity, as expected. Since the significant effects of economic, demographic, and other drivers of high drug spending differ across countries, country-specific implications and policy suggestions for cost controls ought to differ.

Determinants of Health Expenditure Growth of the OECD Countries: Jackknife Resampling Plan Estimates

Due to the lack of internal consistency across unit root and cointegration test methods for short time-series data, past research findings conflict on whether the OECD health expenditure data are stationary. Stationarity reasonably guarantees that the estimated OLS relationship is nonspurious. This paper departs from past investigations that applied asymptotic statistical tests of unit root to insufficient time-series lengths. Instead, data were calibrated in annual growth rates, in 5-year (1968-72, ..., 1993-97) partitions, for maximum likelihood estimation using flexible Box-Cox transformations model and bias-reducing jackknife resampling plan for data expansion. The drivers of OECD health care spending growth are economic and institutional. Findings from the growth convergence theory affirm that health care expenditure growth accords with conditional beta convergence. Statistical significance and optimal functional form models are not unique across the growth period models. Our findings exemplify the benefits of jackknife resampling plan for short data series, and caution researchers against imposing faulty functional forms and applying asymptotic statistical methods to short time-series regressions. Policy implications are discussed.

A comparative study on growth limits of Listeria monocytogenes as affected by temperature, pH and aw when grown in suspension or on a solid surface

The growth/no growth response of a mixture of five strains of Listeria monocytogenes in tryptic soy broth and on tryptic soy agar was monitored in combination treatments of temperature (4–30°C), pH (4.24–6.58) and a w (0.900–0.993) for 30 days. A significant difference between the growth limits of the pathogen in broth and agar was observed. At 25°C the minimum pH values that permitted growth in broth and agar were 4.45 and 5.10, respectively, while the respective a w limits were 0.900 and 0.945. Although the growth limits increased as the temperature decreased in both systems, a relatively constant difference between broth and agar was observed at all temperatures tested. The growth/no growth data of the pathogen in broth and agar were modelled using logistic polynomial regression. The concordance indexes were 99.8% for the broth model and 99.9% for the agar model, indicating a good fit to the observed data in both cases. The present study points out the importance of substrate structure and type of microbial growth on the effect of food preservation parameters, and provides quantitative data in a functional form (models) that may be valuable in efforts to improve safety of liquid as well as solid foods by means of more accurate predictive models.

A robust estimation of hedonic price models: least absolute deviations estimation

Conventional parametric estimation of the hedonic price models is not robust to heteroscedastic and/or non-normal error structure. This paper applies least absolute deviations (LAD) estimation as a robust approach to estimating the hedonic price models, using the Korea housing markets data. The paper finds that LAD estimation produces more reasonable results and that it proves robust in a situation where other estimation results based on various functional form models produce inaccurate or misleading results.

Paradigm lost: reconsidering functional form and group hypotheses in marine ecology.

Although functional form and functional group models for marine algae have been used extensively, there is little general literature support for these models, and many studies have shown that associated hypotheses are often incorrect. In functional form/group models, a wide range of ecological and physiological functions are assumed to be correlated with general algal form or morphology. In contrast, functional group approaches have been used most successfully in terrestrial and aquatic systems when groupings are based on a particular function rather than overall plant morphology, and when addressing ecosystem-level questions. In this type of functional group approach, a given set of species would likely be grouped differently depending on the function under consideration. Functional groupings are appropriate for many situations and questions, but not all. Certainly, grouping taxa by a particular function can be very useful and often necessary for many ecosystem-level questions and modeling, especially where qualitative results are more important than quantitative predictions, and when there are too many species in a system to consider them all individually. However, when one considers species-species interactions or questions about population biology, the specific responses of individual species must be considered. To make functional group models more useful, we recommend that groupings be based on specific functions (e.g. nutrient uptake rates, photosynthesis rates, herbivore resistance, disturbance resistance, etc.) rather than gross morphology. Explicit testing of performance of a particular function should be made before generalizations can be assumed, and groupings should be used for questions/approaches where they are most appropriate. If models fail when tested, they should be modified using the additional information to generate new hypotheses and models, and then retested.

Feeding ecology of the Antarctic herbivorous gastropod Laevilacunaria antarctica Martens

The grazing activity of the Antarctic prosobranch gastropod Laevilacunaria antarctica on macroalgae was investigated in order to evaluate its position in the shallow water food web of Potter Cove, King George Island, Antarctica. From 12 abundant macroalgal species tested in feeding experiments, L. antarctica avoided only three species, the brown algae Ascoseira mirabilis, Phaeurus antarcticus, and Himantothallus grandifolius, significantly. The gastropod can be classified as a general feeder on macroalgae in the rocky intertidal and shallow waters of Potter Cove. Comparative grazing experiments showed that epiphytic diatoms contribute about 2/3 to the total diet of L. antarctica. Mean abundance and biomass of the snails in this area were 292.0±135.3 (S.D.) ind m −2 and 1.549±1.021 (S.D.) g AFDW m −2, respectively. The total consumption of macroalgae by the population of L. antarctica in Potter Cove is estimated to be 118 kJ m −2 year −1. This alone, however, is not sufficient to sustain the standing stock of gastropods in the investigation area. Grazing experiments showed that feeding on macroalgae which carry epiphytic diatoms is about three times higher than on macroalgae without epiphytes. It is therefore concluded that the population of L. antarctica in Potter Cove is maintained by consumption of both epiphytic diatoms and macroalgae. Feeding experiments showed that chemical compounds of macroalgae are not active in a chemical defense against grazing of L. antarctica. It is therefore discussed that structural characteristics of the algae can explain the low grazing rate of L. antarctica on some macroalgal species. Various models explaining macroalgal–herbivore relationships based on functional groups of algae are considered. The predictions on the feeding of L. antarctica derived from these functional form models in many cases correspond with the results derived from feeding experiments in this study. They are, however, inconsistent regarding grazing on or avoidance of some algal species and thereby obscure important information on special adaptations of organisms, e.g. L. antarctica, in macroalgal–herbivore interactions.

Functional Form and Spatial Interaction Models

This paper is an examination of functional form and functional misspecification in regression-based spatial interaction models. Box–Cox transformations are used to model US state-to-state labor migration. Attention is given to the production-constrained gravity model, the competing and intervening destinations (CID) model, and an extension of the CID model which uses dummy variables and an iterative transformation procedure. Statistical evidence supports the argument that the use of highly restrictive log-linear specifications may be inappropriate and problematic. Implications for spatial interaction modeling using general nonrestrictive functional forms are discussed.

Testing the unbiasedness hypothesis of foreign exchange rates and the analysis of transformations

Recent researchers have utilized various functional forms for testing the hypothesis that the forward rate is an unbiased predictor of future spot rates in foreign exchange markets. We compare a large number of these functional forms for a similar time period and test their consistency with the data for five major currencies. Our results imply that certain functional form models may be inappropriate for some currencies. Researchers must, therefore, be cautious of misspecification due to erroneous functional forms when testing the unbiased forward rate hypothesis.

Floristics, phenology, and ecology of the sublittoral marine algae in an unstable cobble habitat (Plum Cove, Cape Ann, Massachusetts, USA)

Abstract The floristics, phenology, and ecology of the sublittoral benthic marine algae in an unstable cobble habitat (Plum Cove, Cape Ann, Massachusetts, USA) were studied. Monthly collections (November 1981–October 1982) were made using SCUBA at 4–5 m MLW. Seventy-two species (three Cyanophyta, 12 Chlorophyta, 20 Phaeophyta, and 37 Rhodophyta) were identified. Crustose and turf algae dominate the cobbles. Crustose algae are reproductive throughout the year and upright species are invariably immature and nonreproductive. The ecology of crustose algae in this habitat does not conform to functional-form models as currently presented. The instability of the cobbles appears to determine the composition and life-form of the dominant algal species. These results emphasize the role of physical disturbance in structuring algal communities on unstable substrata.

Structural resistance of algae to herbivores

Experiments were conducted to determine the forces required for two limpet species to remove tissue from three different types of algae. This was done by using the radulae of the limpets, mimicking the way they use this feeding apparatus. For both Acmaea mitra Rathke (a specialist herbivore) and Notoacmea scutum (Rathke) (a generalist herbivore), Iridaea cordata (Turn.) Bory (a thin, bladed red alga) required the most force; Hedophyllum sessile (C.Ag.) Setch. (a thick, bladed brown alga) the next; and Pseudolithophyllum whidbeyensi (a crustose, calcified alga) required the least amount of force for tissue removal. These results are the inverse of the predictions made by current functional form and functional group models which use the thallus form as a predictor of herbivore resistance. Thallus form alone is a poor predictor of structural resistance to molluscan feeding; the material properties of the alga, the feeding apparatus of the herbivore, and the mode of feeding all must be considered.

Functional Forms and the Capital Asset Pricing Model

the functional form model in the context of the returns for 85 mutual funds. Their findings document the presence of significant transformation parameters; how? ever, the impact on estimates of systematic risk does not appear to be substantial. The purposes of this paper are twofold. The first purpose is to derive and test a more generalized form of the CAPM?more general with respect to functional form and also within the context of investment horizons. The second purpose is to investigate nonlinearities, as in [4], and to extend the analysis to a large sam? ple of individual securities. The functional form models to be empirically tested are derived in Section II. Section III discusses the estimation techniques applied to the proposed models and describes the data used in the study. The results are presented in Section IV, along with a discussion of their implications for the horizon problem and the estimation of systematic risk. A summary of the pertinent findings of the study appears in Section V.