Include Interaction Terms Research Articles

Assessing the effect of concerns about contraceptive-induced fertility impairment on hormonal contraceptive use by parity and residence: evidence from PMA Ethiopia 2020 cross-sectional survey

ObjectivesThis study aims to describe patterns of beliefs about contraceptive-induced infertility and assess their relationship with current contraceptive use, including whether these relationships vary by parity and residence.DesignWe use data...

Student characteristics and effort during test-taking

BackgroundAchievement tests are designed as measurement tools for student knowledge and learning, but also reflect student effort during the test. Understanding better what determines differences in (different dimensions of) effort can help in understanding what measured achievement differences reflect. AimWe analyze how test-taking effort relates to students’ demographic characteristics, past attainment and personality traits. Data13,791 9th grade students in the Netherlands, administered in 2012, 2014 and 2016, answering a total of 449,956 observations. MethodsWe distinguish between two measures of effort: solution behavior and response time given solution behavior. We estimate multi-level cross-classified models that include individual and test characteristics as predictors. We further include interaction terms between question position and individual characteristics, to identify how effort decline across the test differs by student type. ResultsGirls, high achievers, more agreeable, more conscientious and less extravert students exert more effort. Differences by past achievement are especially large and further increase along the test, while differences in other characteristics tend to be more stable. Effort differences by socioeconomic status are relatively small. ConclusionsSystematic differences between different types of students can partly reflect differences in test effort across these groups. Thus, test effort should be considered when analyzing achievement gaps and differences across learning outcomes. Tests with different test lengths imply different measures of educational inequality through differential effort declines.

The consequences of neglected confounding and interactions in mixed-effects meta-regression: An illustrative example.

Analysts seldom include interaction terms in their meta-regression model, which can introduce bias if an interaction is present. We illustrate this by reanalysing a meta-regression study in acute heart failure. Based on a total of 285 studies, the 1-year mortality rate related to acute heart failure is considered and the connection to the study-level covariates year of recruitment and average age of study participants are of interest. We show that neglecting a possibly confounding variable and an interaction term might lead to erroneous inference and conclusions. Based on our results and accompanying simulations, we recommend to include possible confounders and interaction terms, whenever they are plausible, in mixed-effects meta-regression models.

The Heterogeneous Effects of Urban Form on CO2 Emissions: An Empirical Analysis of 255 Cities in China

Urban form is closely related to CO2 emissions and the accurate estimation of the impact of urban form on CO2 emissions plays an important role in tackling climate change caused by the emission of greenhouse gases. In this paper, we quantitatively investigate the effects of urban form on CO2 emission and its efficiency from three perspectives: urban expansion, compactness, and complexity. By using panel quantile regression with fixed effects, we show that: (1) The estimation results about the relationship between urban form and CO2 emission and its efficiency are consistent with the literature. (2) The partial effects of urban form without controlling for socioeconomic factors are heterogeneous throughout the conditional distribution of CO2 emission and its efficiency. (3) Taking into consideration that the partial effects of urban form on CO2 emission and its efficiency might depend on the magnitude of socioeconomic factors, we include interaction terms into our model and find that the interaction effects between socioeconomic factors and urban form are heterogeneous across cities with different levels of CO2 emission and its efficiency. Our empirical findings shed light on the optimization of urban form in improving the CO2 emission efficiency, providing policy makers with effective ways of reducing CO2 emissions across cities with different levels of CO2 emissions.

Should models of monetary policy asymmetry include interaction terms?

This paper investigates whether the response of U.S. output to a monetary policy shock is symmetric to the direction of the shock, the size of the shock, and the phase of the business cycle. Many papers in this literature use models that contain only one type of asymmetry; however, looking at individual types of asymmetry may not be enough, and interactions between the asymmetries may be important. My results show that business cycle and directional asymmetry are important and that stimulative monetary policy shocks taken during recessions have little effect on output. This result is missed in models that do not consider multiple types of asymmetry and their interactions.

Predation risk can modify the foraging behaviour of frugivorous carnivores: Implications of rewilding apex predators for plant-animal mutualisms.

Apex predators play key roles in food webs and their recovery can trigger trophic cascades in some ecosystems. Intra‐guild competition can reduce the abundances of smaller predators and perceived predation risk can alter their foraging behaviour thereby limiting seed dispersal by frugivorous carnivores. However, little is known about how plant–frugivore mutualisms could be disturbed in the presence of larger predators.We evaluated the top‐down effect of the regional superpredator, the Iberian lynx Lynx pardinus, on the number of visits and fruits consumed by medium‐sized frugivorous carnivores, as well as the foraging behaviour of identified individuals, by examining the consumption likelihood and the foraging time.We carried out a field experiment in which we placed Iberian pear Pyrus bourgaeana fruits beneath fruiting trees and monitored pear removal by frugivorous carnivores, both inside and outside lynx ranges. Using camera traps, we recorded the presence of the red fox Vulpes vulpes, the Eurasian badger Meles meles and the stone marten Martes foina, as well as the number of fruits they consumed and their time spent foraging.Red fox was the most frequent fruit consumer carnivore. We found there were fewer visits and less fruit consumed by foxes inside lynx ranges, but lynx presence did not seem to affect badgers. We did not observe any stone marten visits inside lynx territories. The foraging behaviour of red foxes was also altered inside lynx ranges whereby foxes were less efficient, consuming less fruit per unit of time and having shorter visits. Local availability of fruit resources, forest coverage and individual personality also were important variables to understand visitation and foraging in a landscape of fear.Our results show a potential trophic cascade from apex predators to primary producers. The presence of lynx can reduce frugivorous carnivore numbers and induce shifts in their feeding behaviour that may modify the seed dispersal patterns with likely consequences for the demography of many fleshy‐fruited plant species. We conclude that knowledge of the ecological interactions making up trophic webs is an asset to design effective conservation strategies, particularly in rewilding programs.

Should Models of Monetary Policy Asymmetry Include Interaction Terms?

Should Models of Monetary Policy Asymmetry Include Interaction Terms?

Associations between arsenic, cadmium, and selenium exposure and oxidative stress in rural residents of northern Laos

BACKGROUND AND AIM: Oxidative stress is an important consequence of exposure to arsenic and cadmium, but it is unclear to what extent low-level exposures contribute to oxidative stress. Additionally, previous studies suggested that selenium suppresses the toxicity of arsenic and cadmium. This study aimed to examine associations between arsenic and cadmium exposure and oxidative damage to DNA and lipid in rural residents of northern Laos, considering selenium interactions with the two toxic elements. METHODS: We collected data on general characteristics (village, sex, age, smoking, drinking, height, and weight) and a single spot urine sample from the participants (n = 341). Urinary concentrations of arsenic, cadmium, and selenium were measured by inductively coupled plasma mass spectrometry to estimate their exposure/intake levels. Urinary 8-hydroxy-2'-deoxyguanosine (8-OHdG) and 8-isoprostane concentrations were measured by liquid chromatography-tandem mass spectrometry (oxidative stress biomarkers of DNA and lipid, respectively). Multiple linear regression analyses examined associations of urinary concentrations of arsenic and cadmium with those of oxidative stress markers, adjusted for covariates. We performed additional analyses to include interaction terms between urinary concentrations of arsenic/cadmium and selenium. RESULTS:Geometric means of specific gravity-adjusted urinary concentrations of arsenic, cadmium, selenium, 8-OHdG, and 8-isoprostane were 40.0, 1.38, 11.7, 3.89, and 0.934 µg/L, respectively. Urinary concentration of arsenic and cadmium showed positive associations with that of 8-isoprostane. We also observed that there were significant interactions between arsenic and selenium in the association with 8-OHdG (Coefficient (95% CI) = -0.21 (-0.37, -0.05)) and between cadmium and selenium in the association with 8-isoprostane (Coefficient (95% CI) = -0.14 (-0.25, -0.03)). CONCLUSIONS:Our findings suggested that arsenic and cadmium exposure were positively associated with oxidative stress in rural residents of northern Laos. Additionally, selenium might have protective effects on arsenic-/cadmium-induced oxidative stress. KEYWORDS: Heavy metals, Chemical exposures, Environmental epidemiology

Out-of-Sample Prediction in Multidimensional P-Spline Models

The prediction of out-of-sample values is an interesting problem in any regression model. In the context of penalized smoothing using a mixed-model reparameterization, a general framework has been proposed for predicting in additive models but without interaction terms. The aim of this paper is to generalize this work, extending the methodology proposed in the multidimensional case, to models that include interaction terms, i.e., when prediction is carried out in a multidimensional setting. Our method fits the data, predicts new observations at the same time, and uses constraints to ensure a consistent fit or impose further restrictions on predictions. We have also developed this method for the so-called smooth-ANOVA model, which allows us to include interaction terms that can be decomposed into the sum of several smooth functions. We also develop this methodology for the so-called smooth-ANOVA models, which allow us to include interaction terms that can be decomposed as a sum of several smooth functions. To illustrate the method, two real data sets were used, one for predicting the mortality of the U.S. population in a logarithmic scale, and the other for predicting the aboveground biomass of Populus trees as a smooth function of height and diameter. We examine the performance of interaction and the smooth-ANOVA model through simulation studies.

A general cell–fluid Navier–Stokes model with inclusion of chemotaxis

The main purpose of this work is to explore a general cell–fluid model which is based on a mixture theory formulation that accounts for the interplay between oxytactically (chemotaxis toward gradient in oxygen) moving bacteria cells in water and the buoyance forces caused by the difference in density between cells and fluid. The model involves two mass balance and two general momentum balance equations, respectively, for the cell and fluid phase, combined with a convection–diffusion–reaction equation for oxygen. In particular, the momentum balance equations include interaction terms which describe the cell–fluid drag force effect. Hence, the model is an extension of the classical Navier–Stokes equation in two different ways: (i) inclusion of two phases (cell and fluid) instead of one; (ii) inclusion of a chemotactic transport mechanism. The model can be understood as a natural generalization of the much studied chemotaxis-Stokes model explored by [I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J. O. Kessler and R. E. Goldstein, Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. USA 102 (2005) 2277–2282]. First, we explore the model for parameters in a range which ensures that it lies close to the previously studied chemotaxis-Stokes model (essentially very low cell volume fraction). Main observations are (i) formation of sinking finger-shaped plumes and (ii) convergence to plumes that possibly can be stationary (i.e. persist over time). The general cell–fluid model provides new insight into the role played by the cell–fluid interaction term which controls the competition between gravity segregation and chemotaxis effect on the formation of cell plumes. Second, we explore cases with large cell volume fraction (far beyond the regime captured by the chemotaxis-Stokes model), which gives rise to rich pattern-formation behavior. The general cell–fluid model opens for exploring a hierarchy of different “submodels”. Hence, it seems to be an interesting model for further investigations of various, general cell–fluid spatio-temporal evolution dynamics, both from an experimental and mathematical point of view.

A simulation-based tree method for building linear models with interactions

Linear models are the most common predictive models for a continuous, discrete or categorical response and often include interaction terms, but for more than a few predictors interactions tend to be neglected because they add too many terms to the model. In this paper, we propose a simulation-based tree method to detect the interactions, which contributes to the predictions. In the method, we first bootstrap the observations and randomly choose a number of variables to build trees. The interactions between the roots and the corresponding leaves are collected. The times of each interaction that appear are counted. To obtain the benchmark of the number of each interaction that appears in the trees, the response values are substituted by randomly generated values and then we repeat the procedure. The interactions with occurrence frequency more than the benchmark are put into the regression models. Finally, we select variables by running LASSO for the model with main effects and the interactions obtained. In the experiments, our method shows good performances, especially for the data set with many interactions.

Canonical system of equations for 1D water waves

AbstractOne of the essential tasks of the theory of water waves is a construction of simplified mathematical models, which are applied to the description of complex events, such as wave breaking, appearing of freak waves in the assumption of weak nonlinearity. The Zakharov equation and its simplification, such as nonlinear Schrodinger equations and Dysthe equations, are among them. Recently, for unidirectional waves, the so‐called super compact equation was derived in Ref. 1. In the present article, the waves moving in both directions are considered. Namely, the waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four‐wave interactions of water waves allows describing the evolution of these two groups as a system of two equations. One of the significant consequences of this decomposition is the conservation of the number of waves in each particular group. To derive this system of equations, a particular canonical transformation is used. This transformation is possible due to the miraculous cancellation of the four‐wave interaction for some groups of waves in the one‐dimensional wave field. The obtained equations are remarkably simple. They can be called a canonical system of equations. They include a nonlinear wave term together with an advection term that can describe the initial stage of wave‐breaking. They also include interaction terms (between counter‐streaming waves). It is also suitable for analytical study as well as for numerical simulation.

VANISH regularization for generalized linear models

Marketers increasingly face modeling situations where the number of independent variables is large and possibly approaching or exceeding the number of observations. In this setting, covariate selection and model estimation present significant challenges to usual methods of inference. These challenges are exacerbated when covariate interactions are of interest. Most extant regularization methods make no distinction between main and interaction terms in estimation. The linear VANISH model is an exception to these methods. The linear VANISH model is a regularization method for models with interaction terms that ensures proper model hierarchy by enforcing the heredity principle. We derive the generalized VANISH model for nonlinear responses, including duration, discrete choice, and count models widely used in marketing applications. In addition, we propose a VANISH model that allows to account for unobserved consumer heterogeneity via a mixture approach. In three empirical applications we demonstrate that our proposed model outperforms main effects models as well as other methods that include interaction terms.

Job-Related Determinants of Unhealthy Lifestyles.

We investigate whether job-related characteristics are related to unhealthy lifestyles. We consider two components of unhealthy lifestyles, namely smoking behavior and overweight. For our study, we use data from the German Socio-Economic Panel (SOEP). Depending on our dependent variables, we apply tobit and ordered probit estimations. We further run fixed-effects estimations since the panel structure of the SOEP allows us to follow individuals over time. Furthermore, we include interaction terms into our analysis and examine whether there are age differences concerning the relation between job-related characteristics and unhealthy lifestyles. We find evidence that time pressure and overtime, in particular, are associated to unhealthy lifestyles. Furthermore, we find that the relationship between overtime, fixed-term contracts, commuting, and unhealthy lifestyles is particularly pronounced for the elderly. Employees who experience high time pressure or who work more hours than defined in their employment contract are more at risk of practicing unhealthy lifestyles. The relations between overtime, fixed-term contracts, commuting, and unhealthy lifestyles are getting stronger with age.

Modeling and Interpreting Interactions in Accounting Research

This study examines the use of linear regressions that include interaction terms, finding frequent interpretation errors in published accounting research. We provide insights on how to estimate, interpret, and present interactive regression models, and explain seldom-used but easily-implemented methods to report conditional marginal effects. We also examine the use of interaction terms in tax and financial reporting trade-off studies, evaluating the conceptual fit between a regression model with interactions and alternative definitions of trade-off. Although we advocate the use of interactive models, noise levels common in accounting research greatly reduce the ability to detect interaction effects.

Modeling and interpreting regressions with interactions

This study examines the use of linear regressions that include interaction terms, finding frequent interpretation errors in published accounting research. We provide insights on how to estimate, interpret, and present interactive regression models, and explain seldom-used but easily-implemented methods to report conditional marginal effects. We also examine the use of interaction terms in tax and financial reporting trade-off studies, evaluating the conceptual fit between a regression model with interactions and alternative definitions of trade-off. Although we advocate the use of interactive models, noise levels common in accounting research greatly reduce the ability to detect interaction effects.

Mortality After Osteoporotic Fractures: What Proportion Is Caused by Fracture and Is Preventable?

Mortality After Osteoporotic Fractures: What Proportion Is Caused by Fracture and Is Preventable?

Macroeconomic fluctuations and sexually transmitted infections in Mexico by level of state development

Sexually transmitted infections (STIs) are a major public health burden globally and especially in developing countries. The relationship between macroeconomic fluctuations and STIs rates has received scant attention in the literature. In this paper we examine the relationship between economic fluctuations and the incidence rates of STIs in Mexico. Mexico offers an exceptional setting because there is a wide range of development across states and the availability of good quality data that covers a lengthy period. We assemble a unique panel of state-level annual data for the 1993-2012 period, for each of the 32 Mexican states. The data include incidence rates by STI type and age group. Economic activity is measured using GDP per capita and explanatory variables are employed to control for the supply of health care and relevant demographic characteristics. We use the human development index for each state to generate three indicator variables that reflect the level of development: top ten, middle twelve, and bottom ten. Our empirical estimation employs the data at the state-year level and includes time and state fixed effects as well as state time trends. The dependent variables in our econometric specifications are the all-ages and age-specific incidence rates of each STI. The real GDP per capital is our control variables of interest. We include interaction terms to reflect the potential for differing effects depending on whether the state in question is in the top, middle, or bottom level of development. Our estimates indicate that there are important differences along a number of dimensions in how economic fluctuations affect STI incidence rates. In terms of economic development, there is generally no relationship in the top states, a procyclical relationship in the middle states, and a mixed relationship in the bottom states. The associations also vary by type of STI, where the trichomoniasis incidence rate is largely countercylical (especially in the bottom states) and the other types (gonorrhea, herpes and syphilis) are generally procyclical. Finally, the largest relationships are mostly found in the 45-64 age group, whereas there is less of a relationship for the oldest age group. Our findings suggest that during economic expansions, public health officials may want to devote additional resources to efforts to reduce risky sexual behaviors in the middle and bottom states. These efforts could include public awareness advertising, greater efforts at STI testing, and attempts at reducing prostitution.

Regression calibration with instrumental variables for longitudinal models with interaction terms, and application to air pollution studies.

In this paper, we derive forms of estimators and associated variances for regression calibration with instrumental variables in longitudinal models that include interaction terms between two unobservable predictors and interactions between these predictors and covariates not measured with error; the inclusion of the latter interactions generalize results we previously reported. The methods are applied to air pollution and health data collected on children with asthma. The new methods allow for the examination of how the relationship between health outcome leukotriene E4 (LTE4, a biomarker of inflammation) and two unobservable pollutant exposures and their interaction are modified by the presence or absence of upper respiratory infections. The pollutant variables include secondhand smoke and ambient (outdoor) fine particulate matter. Simulations verify the accuracy of the proposed methods under various conditions.

Statistical interactions and Bayes estimation of log odds in case-control studies.

This paper is concerned with the estimation of the logarithm of disease odds (log odds) when evaluating two risk factors, whether or not interactions are present. Statisticians define interaction as a departure from an additive model on a certain scale of measurement of the outcome. Certain interactions, known as removable interactions, may be eliminated by fitting an additive model under an invertible transformation of the outcome. This can potentially provide more precise estimates of log odds than fitting a model with interaction terms. In practice, we may also encounter nonremovable interactions. The model must then include interaction terms, regardless of the choice of the scale of the outcome. However, in practical settings, we do not know at the outset whether an interaction exists, and if so whether it is removable or nonremovable. Rather than trying to decide on significance levels to test for the existence of removable and nonremovable interactions, we develop a Bayes estimator based on a squared error loss function. We demonstrate the favorable bias-variance trade-offs of our approach using simulations, and provide empirical illustrations using data from three published endometrial cancer case-control studies. The methods are implemented in an R program, and available freely at http://www.mskcc.org/biostatistics/~satagopj .