Parsimonious Modeling Research Articles

Enhancing water management in Northern European lowland chalk streams: A parsimonious, high-resolution hydrological model using groundwater level as a proxy for baseflow

Study regionThe River Frome, a chalk stream in West Dorset, UK. Study focusHigh-resolution hydrological models are required to integrate with the current wave of high-frequency data and advance our understanding of pollutant sources, pathways, and sinks. This presents several challenges in chalk streams, as their high-permeability and unique hydrogeological characteristics often leads to complex models that are overparameterized and computationally burdensome. In this article, we develop a novel and parsimonious modelling approach to describe the surface hydrology for a chalk stream in high resolution (15-minute frequency, ≤ 100 m cross-section spacing), using groundwater levels as a proxy for spring discharges. New hydrological insights for the regionOur results show that chalk stream dry-weather flows can be simulated accurately and parsimoniously at high-resolution (Nash-Sutcliffe efficiency = 0.97, mean relative error = 2.86 %, for a five-year period). We also show that spring discharges are the dominant form of flow accretion in all seasons and are critical to dilute sewage treatment inputs during the ecological growing season, whilst runoff and quick-flow pathways in the river valley corridor contribute a small proportion to annual flow accretion (< 5.2 %). Due to its simplicity and few parameters to calibrate, this modelling approach has broad applicability in lowland permeable catchments. Management implications include expeditious investigations of high-resolution freshwater quality responses to pollution and informing abstraction limits to sustain robust ecological conditions.

Bayesian inference of frequency-specific functional connectivity in MEG imaging using a spectral graph model

Abstract Understanding the relationship between structural connectivity (SC) and functional connectivity (FC) of the human brain is an important goal of neuroscience. Highly detailed mathematical models of neural masses exist that can simulate the interactions between functional activity and structural wiring. These models are often complex and require intensive computation. Most importantly, they do not provide a direct or intuitive interpretation of this structure–function relationship. In this study, we employ the emerging concepts of spectral graph theory to obtain this mapping in terms of graph harmonics, which are eigenvectors of the structural graph’s Laplacian matrix. In order to imbue these harmonics with biophysical underpinnings, we leverage recent advances in parsimonious spectral graph modeling (SGM) of brain activity. Here, we show that such a model can indeed be cast in terms of graph harmonics, and can provide a closed-form prediction of FC in an arbitrary frequency band. The model requires only three global, spatially invariant parameters, yet is capable of generating rich FC patterns in different frequency bands. Only a few harmonics are sufficient to reproduce realistic FC patterns. We applied the method to predict FC obtained from pairwise magnitude coherence of source-reconstructed resting-state magnetoencephalography (MEG) recordings of 36 healthy subjects. To enable efficient model inference, we adopted a deep neural network-based Bayesian procedure called simulation-based inference. Using this tool, we were able to speedily infer not only the single most likely model parameters, but also their full posterior distributions. We also implemented several other benchmark methods relating SC to FC, including graph diffusion and coupled neural mass models. The present method was shown to give the best performance overall. Notably, we discovered that a single biophysical parameterization is capable of fitting FCs from all relevant frequency bands simultaneously, an aspect that did not receive adequate attention in prior computational studies.

Evidence of Groundwater Seepage and Mixing at the Vicinity of a Knickpoint in a Mountain Stream

AbstractStreamflow generation and biochemical hotspots are significantly influenced by groundwater contributions distributed along the drainage network. However, identifying the geomorphic landscape features that drive groundwater‐surface water interactions remains challenging. In this study, we investigate the role of knickpoints in controlling these interactions in a mountainous stream in Switzerland. We employ a combination of synoptic sampling of environmental tracers, endmember mixing calculations, and groundwater flow simulations. Our findings reveal substantial groundwater seepage concentrated near the knickpoint of the main river stem. Using parsimonious groundwater flow modeling, we validate the hypothesis that the topographical shape of the knickpoint enhances local groundwater discharge rates. We quantify that approximately 20% of the total catchment streamflow originates from around the knickpoint. These results indicate that knickpoints are significant hotspots for groundwater seepage and physicochemical mixing, providing a clear method for identifying major localized sources of streamflow generation.

Prediction of Early Adverse Events After THA: A Comparison of Different Machine-Learning Strategies Based on 262,356 Observations From the Nordic Arthroplasty Register Association (NARA) Dataset.

Preoperative risk prediction models can support shared decision-making before total hip arthroplasties (THAs). Here, we compare different machine-learning (ML) approaches to predict the six-month risk of adverse events following primary THA to obtain accurate yet simple-to-use risk prediction models. We extracted data on primary THAs (N = 262,356) between 2010 and 2018 from the Nordic Arthroplasty Register Association dataset. We benchmarked a variety of ML algorithms in terms of the area under the receiver operating characteristic curve (AUROC) for predicting the risk of revision caused by periprosthetic joint infection (PJI), dislocation or periprosthetic fracture (PPF), and death. All models were internally validated against a randomly selected test cohort (one-third of the data) that was not used for training the models. The incidences of revisions because of PJI, dislocation, and PPF were 0.8%, 0.4%, and 0.3%, respectively, and the incidence of death was 1.2%. Overall, Lasso regression with stable iterative variable selection (SIVS) produced models using only four to five input variables but with AUROC comparable to more complex models using all 32 variables available. The SIVS-based Lasso models based on age, sex, preoperative diagnosis, bearing couple, fixation, and surgical approach predicted the risk of revisions caused by PJI, dislocations, and PPF, as well as death, with AUROCs of 0.61, 0.67, 0.76, and 0.86, respectively. Our study demonstrates that satisfactory predictive potential for adverse events following THA can be reached with parsimonious modeling strategies. The SIVS-based Lasso models may serve as simple-to-use tools for clinical risk assessment in the future.

Towards parsimonious generative modeling of RNA families.

Generative probabilistic models emerge as a new paradigm in data-driven, evolution-informed design of biomolecular sequences. This paper introduces a novel approach, called Edge Activation Direct Coupling Analysis (eaDCA), tailored to the characteristics of RNA sequences, with a strong emphasis on simplicity, efficiency, and interpretability. eaDCA explicitly constructs sparse coevolutionary models for RNA families, achieving performance levels comparable to more complex methods while utilizing a significantly lower number of parameters. Our approach demonstrates efficiency in generating artificial RNA sequences that closely resemble their natural counterparts in both statistical analyses and SHAPE-MaP experiments, and in predicting the effect of mutations. Notably, eaDCA provides a unique feature: estimating the number of potential functional sequences within a given RNA family. For example, in the case of cyclic di-AMP riboswitches (RF00379), our analysis suggests the existence of approximately 1039 functional nucleotide sequences. While huge compared to the known <4000 natural sequences, this number represents only a tiny fraction of the vast pool of nearly 1082 possible nucleotide sequences of the same length (136 nucleotides). These results underscore the promise of sparse and interpretable generative models, such as eaDCA, in enhancing our understanding of the expansive RNA sequence space.

Assessment of land use/ land cover change derived catchment hydrologic response: An integrated parsimonious hydrological modeling and alteration analysis based approach

Land use/land cover (LULC) change, often a consequence of natural or anthropogenic drivers, plays a decisive role in governing global catchment dynamics, and subsequent impact on regional hydrology. Insight into the complex relationship between the drivers of LULC change and catchment hydrology is of utmost importance to decision makers. Contemplating the dynamic rainfall-runoff response of the Indian catchments, this study proposes an integrated modeling-based approach to identify the drivers and relative contribution to catchment hydrology. The proposed approach was evaluated in the tropical climate Nagavali River Basin (NRB) (9512 km2) of India. The Soil and Water Assessment Tool (SWAT) hydrological model, which uses daily-scale rainfall, temperature, wind speed, relative humidity, solar radiation, and streamflow information was integrated with the Indicators of Hydrologic Alteration (IHA) technique to characterize the plausible changes in the flow regime of the NRB. Subsequently, the Partial Least Squares Regression (PLSR) based modeling analysis was performed to quantify the relative contribution of individual LULC components on the catchment water balance. The outcomes of the study revealed that forest land has been significantly converted to agricultural land (45–59%) across the NRB resulting in mean annual streamflow increase of 3.57 m3/s during the monsoon season. The affinity between land use class and streamflow revealed that barren land (CN = 83–87) exhibits the maximum positive response to streamflow followed by the built-up land (CN = 89–91) and fallow land (CN = 88–93). The period 1985–1995 experienced an increased ET scenario (911–1050 mm), while the recent period (2005–2020) experienced reduced ET scenario owing to conversion of forest to agricultural land. Certainly, the study endorses adopting the developed methodology for understanding the complex land use and catchment-scale hydrologic interactions across global-scales for early watershed management planning.

Validation of the Root Analysis Score for C5 Viability in Patients With Pan–Brachial Plexus Injury

Pan-brachial plexus injury patients present a reconstructive challenge. The root analysis score, developed from parsimonious multivariable modeling of 311 pan-brachial plexus injury patients, determines the probability of having a viable C5 nerve based on four categories: positive C5 Tinel test, intact C5 nerve on computed tomography myelogram, lack of hemidiaphragmatic elevation, and absence of midcervical paraspinal fibrillations. Root analysis scores were calculated for a separate cohort of patients with pan-brachial plexus injuries. Scores were validated by the presence or absence of a graftable C5 root, based on supraclavicular exploration and intraoperative electrophysiologic testing. Receiver operating characteristic curve, accuracy, and concordance statistic of the scores were calculated. Patients were divided into three root analysis score cohorts: less than 50 (low), 50-75 (average), and 75-100 points (high) based on dividing the score into quartiles and combining the lowest two. The probability, sensitivity, and specificity of each cohort having an available C5 nerve were based on the intraoperative assessment. Eighty patients (mean age, 33.1 years; 15 women and 65 men) were included. Thirty-one patients (39%) had a viable C5 nerve. The root analysis calculator had an overall accuracy of 82.5%, a receiver operating characteristic of 0.87, and a concordance statistic of 0.87, demonstrating high overall predictive value; 6.5% of patients with a score of less than 50 (94% sensitivity and 43% specificity), 16.1% of patients with a score of 50-75 (94% sensitivity and 67% specificity), and 77.4% of patients with a score of 75-100 (77% sensitivity and 90% specificity) had a graftable C5 nerve. The root analysis score demonstrated high accuracy and predictive power for a viable C5 nerve. In patients with a score of less than 50, the necessity of supraclavicular root exploration should balance patient factors, presentation timing, and concomitant injuries. Diagnosis II.

Impact of calibrating a low-cost capacitance-based soil moisture sensor on AquaCrop model performance

Sensor data and agro-hydrological modeling have been combined to improve irrigation management. Crop water models simulating crop growth and production in response to the soil-water environment need to be parsimonious in terms of structure, inputs and parameters to be applied in data scarce regions. Irrigation management using soil moisture sensors requires them to be site-calibrated, low-cost, and maintainable. Therefore, there is a need for parsimonious crop modeling combined with low-cost soil moisture sensing without losing predictive capability.This study calibrated the low-cost capacitance-based Spectrum Inc. SM100 soil moisture sensor using multiple least squares and machine learning models, with both laboratory and field data. The best calibration technique, field-based piece-wise linear regression (calibration r2 = 0.76, RMSE = 3.13 %, validation r2 = 0.67, RMSE = 4.57 %), was used to study the effect of sensor calibration on the performance of the FAO AquaCrop Open Source (AquaCrop-OS) model by calibrating its soil hydraulic parameters.This approach was tested during the wheat cropping season in 2018, in Kanpur (India), in the Indo-Gangetic plains, resulting in some best practices regarding sensor calibration being recommended. The soil moisture sensor was calibrated best in field conditions against a secondary standard sensor (UGT GmbH. SMT100) taken as a reference (r2 = 0.67, RMSE = 4.57 %), followed by laboratory calibration against gravimetric soil moisture using the dry-down (r2 = 0.66, RMSE = 5.26 %) and wet-up curves respectively (r2 = 0.62, RMSE = 6.29 %). Moreover, model overfitting with machine learning algorithms led to poor field validation performance. The soil moisture simulation of AquaCrop-OS improved significantly by incorporating raw reference sensor and calibrated low-cost sensor data. There were non-significant impacts on biomass simulation, but water productivity improved significantly. Notably, using raw low-cost sensor data to calibrate AquaCrop led to poorer performances than using the literature. Hence using literature values could save sensor costs without compromising model performance if sensor calibration was not possible. The results suggest the essentiality of calibrating low-cost soil moisture sensors for crop modeling calibration to improve crop water productivity.

On understanding mountainous carbonate basins of the Mediterranean using parsimonious modeling solutions

Abstract. The study aims to demonstrate that an effective solution can be implemented for modeling complex carbonate basins, in the situation of limited data availability. Considering the alternative modeling approaches under circumstances of data shortage is more significant knowing the vulnerability and effectiveness of these kinds of basins to drought and climate change conditions. In this regard, a hybrid approach that combines time series analysis and reservoir modeling is proposed to describe behavior in carbonate basins. Time series analysis estimates the contributing area and response time of the fractured carbonate system beyond the catchment's hydrographic boundaries. The results obtained align with previous literature-based field surveys. This information is then used to develop a conceptual reservoir system using the GEOframe modeling system. The model is validated using in situ discharge observations and Earth observations (EO) data on evapotranspiration and snow. Model reliability is assessed using traditional goodness of fit indicators, hydrological signatures, and a novel statistical method based on empirical conditional probability. This approach enables detailed analysis and investigation of water budget components in Mediterranean carbonate catchments, highlighting their response to significant precipitation deficits. Overall, our results demonstrate that flows from carbonate rock areas outside the hydrographic boundaries significantly impact the water budget of the upper Nera River. The storage capacity of the carbonate basin plays a crucial role in sustaining river discharge during drought years. In a single dry year, meteorological drought is considerably attenuated, while in subsequent dry years, it is slightly intensified. Multi-year droughts result in slower recovery due to the time required for precipitation to replenish the depleted storage that supported river discharge in previous dry years. This unique behavior makes these basins particularly vulnerable to the more severe and frequent drought episodes expected under future climate change.

Integrated Hydrogeological Modelling for Sustainable Management of the Brindisi Plain Aquifer (Southern Italy)

Nowadays, changes in precipitation patterns together with the increasing water demand impose a sustainable management where the budget between water availability and demand is positively closed. A parsimonious hydrogeological modelling approach coupled with a soil water balance is developed and applied in order to quantify the hydrological and hydrogeological dynamics in a semi-arid region of the Mediterranean basin. In particular, the present work focuses on the hydrogeological dynamics of the catchment areas of Siedi, Foggia di Rau, Pigonati, and the Palmarini channels located in the Brindisi Plain, Southern Italy. In the last decades, in the Brindisi Plain the anthropization processes as well as the industrial and agricultural development have generated an intensive exploitation of both shallow and deep groundwater resources as well as their qualitative deterioration. A dry hydrologic year (2019–2020) caused a recharge deficit, resulting in a lowering of the groundwater level of the shallow aquifer compared to the expected seasonal value. The results evidence a sensitive natural system, where the variability of the rainfall regime combined with water withdrawal leads to a system that is very vulnerable to climate change impacts, such as the presence of erratic rainfall patterns affecting aquifer recharge. This study represents the first approach to couple a soil moisture balance model and groundwater flow model to assess the impact of changes in rainfall patterns on groundwater recharge for the Brindisi Plain aquifer. The developed integrated hydrogeological model can be applied to other sites with similar hydrogeological features and represents an important tool in order to evaluate the effectiveness of cost-effective sustainable actions for the management of the groundwater resources with respect to land-use practices and socio-economic aspects.

Combining a parsimonious mathematical model with infection data from tailor-made experiments to understand environmental transmission

Although most infections are transmitted through the environment, the processes underlying the environmental stage of transmission are still poorly understood for most systems. Improved understanding of the environmental transmission dynamics is important for effective non-pharmaceutical intervention strategies. To study the mechanisms underlying environmental transmission we formulated a parsimonious modelling framework including hypothesised mechanisms of pathogen dispersion and decay. To calibrate and validate the model, we conducted a series of experiments studying distance-dependent transmission of Campylobacter jejuni in broilers. We obtained informative simultaneous estimates for all three model parameters: the parameter of C. jejuni inactivation, the diffusion coefficient describing pathogen dispersion, and the transmission rate parameter. The time and distance dependence of transmission in the fitted model is quantitatively consistent with marked spatiotemporal patterns in the experimental observations. These results, for C. jejuni in broilers, show that the application of our modelling framework to suitable transmission data can provide mechanistic insight in environmental pathogen transmission.

Parsimonious item response theory modeling with the negative log-log link: The role of inflection point shift.

In item response theory (IRT) modeling, the magnitude of the lower and upper asymptote parameters determines the degree to which the inflection point shifts above or below P = 0.50. The current study examines the one-parameter negative log-log model (NLLM), which is characterized by a downward shift in the inflection point, among other distinctive psychometric properties. After detailing the statistical foundations of the NLLM, we present a series of simulation studies to establish item and person parameter estimation accuracy and to demonstrate that this parsimonious model addresses the "slipping" effect (i.e., unexpectedly incorrect answers) via an inflection point < 0.50 rather than through computationally difficult estimation of the upper asymptote. We then provide further support for these simulation results through empirical data analysis. Finally, we discuss how the NLLM contributes to recent methodological literature on the utility of asymmetric IRT models.

Distribution-Free Location-Scale Regression

We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modeling for arbitrary outcomes. We replace the strict parametric distribution formulating such a model by a transformation function, which in turn is estimated from data. Doing so not only makes the model distribution-free but also allows to limit the number of linear or smooth model terms to a pair of location-scale predictor functions. We derive the likelihood for continuous, discrete, and randomly censored observations, along with corresponding score functions. A plethora of existing algorithms is leveraged for model estimation, including constrained maximum-likelihood, the original GAMLSS algorithm, and transformation trees. Parameter interpretability in the resulting models is closely connected to model selection. We propose the application of a novel best subset selection procedure to achieve especially simple ways of interpretation. All techniques are motivated and illustrated by a collection of applications from different domains, including crossing and partial proportional hazards, complex count regression, nonlinear ordinal regression, and growth curves. All analyses are reproducible with the help of the tram add-on package to the R system for statistical computing and graphics.

Model-Based Tensor Low-Rank Clustering

ABSTRACT Tensors have become prevalent in business applications and scientific studies. It is of great interest to analyze and understand the heterogeneity in tensor-variate observations. We propose a novel tensor low-rank mixture model (TLMM) to conduct efficient estimation and clustering on tensors. The model combines the Tucker low-rank structure in mean contrasts and the separable covariance structure to achieve parsimonious and interpretable modeling. To implement efficient computation under this model, we develop a low-rank enhanced expectation-maximization (LEEM) algorithm. The pseudo E-step and the pseudo M-step are carefully designed to incorporate variable selection and efficient parameter estimation. Numerical results in extensive experiments demonstrate the encouraging performance of the proposed method compared to popular vector and tensor methods. Supplementary materials for this article are available online.

Reduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps

Objective. A data-driven technique for parsimonious modeling and analysis of dynamic cerebral autoregulation (DCA) is developed based on the concept of diffusion maps. Specifically, first, a state-space description of DCA dynamics is considered based on arterial blood pressure, cerebral blood flow velocity, and their time derivatives. Next, an eigenvalue analysis of the Markov matrix of a random walk on a graph over the dataset domain yields a low-dimensional representation of the intrinsic dynamics. Further dimension reduction is made possible by accounting only for the two most significant eigenvalues. The value of their ratio indicates whether the underlying system is governed by active or hypoactive dynamics, indicating healthy or impaired DCA function, respectively. We assessed the reliability of the technique by considering healthy individuals and patients with unilateral internal carotid artery (ICA) stenosis or occlusion. We computed the sensitivity of the technique to detect the presumed side-to-side difference in the DCA function of the second group (assuming hypoactive dynamics on the occluded or stenotic side), using McNemar’s chi square test. The results were compared with transfer function analysis (TFA). The performance of the two methods was also compared under the assumption of missing data. Main results. Both diffusion maps and TFA suggested a physiological side-to-side difference in the DCA of ICA stenosis or occlusion patients with a sensitivity of 81% and 71%, respectively. Further, both two methods suggested the difference between the occluded or stenotic side and any two sides of the healthy group. However, the diffusion maps captured additional difference between the unoccluded side and the healthy group, that TFA did not. Furthermore, compared to TFA, diffusion maps exhibited superior performance when subject to missing data. Significance. The eigenvalues ratio derived using the diffusion maps technique can be potentially used as a reliable and robust biomarker for assessing how active the intrinsic dynamics of the autoregulation is and for indicating healthy versus impaired DCA function.

PALM: Patient-centered treatment ranking via large-scale multivariate network meta-analysis

The growing number of available treatment options has led to urgent needs for reliable answers when choosing the best course of treatment for a patient. As it is often infeasible to compare a large number of treatments in a single randomized controlled trial, multivariate network meta-analyses (NMAs) are used to synthesize evidence from trials of a subset of the treatments, where both efficacy and safety related outcomes are considered simultaneously. However, these large-scale multiple-outcome NMAs have created challenges to existing methods due to the increasing complexity of the unknown correlations between outcomes and treatment comparisons. In this paper, we proposed a new framework for PAtient-centered treatment ranking via Large-scale Multivariate network meta-analysis, termed as PALM, which includes a parsimonious modeling approach, a fast algorithm for parameter estimation and inference, a novel visualization tool for presenting multivariate outcomes, termed as the origami plot, as well as personalized treatment ranking procedures taking into account the individual’s considerations on multiple outcomes. In application to an NMA that compares 14 treatment options for labor induction, we provided a comprehensive illustration of the proposed framework and demonstrated its computational efficiency and practicality, and we obtained new insights and evidence to support patient-centered clinical decision making.

Conditional mixture modelling for heavy‐tailed and skewed data

Overparameterization is a serious concern for multivariate mixture models as it can lead to model overfitting and, as a result, mixture order underestimation. Parsimonious modelling is one of the most effective remedies in this context. In Gaussian mixture models, the majority of parameters is associated with covariance matrices and parsimonious models based on factor analysers and spectral decomposition of dispersion parameters are the most popular in literature. Some drawbacks of these models include the lack of flexibility in imposing different covariance structures for individual components and limitations in modelling compact clusters. Recently introduced conditional mixture models provide substantial flexibility in addressing these concerns. The components of such mixtures are formulated as a product of conditional distributions with univariate Gaussian densities being the primary choice. However, the presence of heavy tails or skewness in any dimension can lead to fitting problems. We propose a flexible model that is free of the above‐mentioned limitations and name it a contaminated transformation conditional mixture model and demonstrate on a series of simulation studies that it can effectively account for skewness and heavy tails. Applications to real‐life data sets show good results and highlight the promise of the proposed model.

Parsimonious Gaussian copula modelling through constrained Cholesky decomposition for data with temporal dependence

Using the Gaussian copula modelling device from a perspective of latent variables, we consider the parsimonious modelling of generic types of data with the temporal dependence including those sequential observations being binary, categorical, and more. Different from the existing approaches, we directly investigate the covariance modelling in which a new kind of constraint is naturally developed to enable the identifiability of the latent Gaussian copula model. Then we develop a new latent variable framework concerning parsimoniously modelling the marginal means, variances, and covariances of the latent Gaussian variables with appealing practical interpretations. Our new framework broadly extends the joint mean-covariance modelling approaches based on the modified Cholesky decompositions to the regression analysis with broad types of response variables. Theoretical properties are then established for the resulting estimators of the parsimonious model. We demonstrate the performance of the proposed approaches with simulations and the real data analysis.

Robust variable selection via nonconcave penalties with an upgraded parsimonious dynamic covariance modeling

We present a new parsimonious method for joint mean-covariance modeling based on M-estimation and nonconcave penalty. In this paper, the robustness of the proposed model was aimed at addressing the issue when the working matrix is misspecified and a spot of outliers exist in the dataset. The proposed approach outperforms the traditional method in robustness and variable selections for longitudinal data analysis, particularly when the dataset contains a spot of outliers. The simulation results back up the theoretical findings, and the methodology is further illustrated via an analysis of a real progesterone data example.

Interaction Effects in Health State Valuation Studies: An Optimal Scaling Approach

ObjectivesThis study aimed to introduce a parsimonious modeling approach that enables the estimation of interaction effects in health state valuation studies. MethodsInstead of supplementing a main-effects model with interactions between each and every level, a more parsimonious optimal scaling approach is proposed. This approach is based on the mapping of health state levels onto domain-specific continuous scales. The attractiveness of health states is then determined by the importance-weighted optimal scales (ie, main effects) and the interactions between these domain-specific scales (ie, interaction effects). The number of interaction terms only depends on the number of health domains. Therefore, interactions between dimensions can be included with only a few additional parameters. The proposed models with and without interactions are fitted on 3 valuation data sets from 2 different countries, that is, a Dutch latent-scale discrete choice experiment (DCE) data set with 3699 respondents, an Australian time trade-off data set with 400 respondents, and a Dutch DCE with duration data set with 788 respondents. ResultsImportant interactions between health domains were found in all 3 applications. The results confirm that the accumulation of health problems within health states has a decreasing marginal effect on health state values. A similar effect is obtained when so-called N3 or N5 terms are included in the model specification, but the inclusion of 2-way interactions provides superior model fits. ConclusionsThe proposed interaction model is parsimonious, produces estimates that are straightforward to interpret, and accommodates the estimation of interaction effects in health state valuation studies with realistic sample size requirements. Not accounting for interactions is shown to result in biased value sets, particularly in stand-alone DCE with duration studies.