Multi-response Approach Research Articles

Optimizing micro-EDM with carbon-coated electrodes: A multi-criteria approach

The pursuit of precision machining in engineering materials has ignited an imperative to advance electrical discharge machining (EDM) techniques. This study is a deep dive into the domain of micro-electrical discharge machining ([Formula: see text]EDM) with a specific focus on the utilization of carbon-coated tool electrodes. The primary objective is to elucidate the influence of carbon-coated electrodes on vital machining parameters, including machining depth (Z coordinate), tool wear rate (TWR) and overcut (OC) in [Formula: see text]EDM operations. Moreover, the investigation extends to scrutinizing surface characteristics generated by [Formula: see text]EDM with carbon-coated tool electrodes. To enhance performance, carbon-coated tungsten carbide tool electrodes are employed for machining titanium alloy (Ti–6Al–4V) workpieces. The optimization process seeks to identify the optimal combination of process parameters using a Taguchi-DEAR-based multi-response approach. Experimental findings reveal that integrating carbon-coated electrodes significantly improves the [Formula: see text]EDM process, leading to enhanced surface performance metrics. Notably, this study identifies specific parameter settings that effectively optimize machining quality indicators. By achieving a voltage of 160[Formula: see text]V, a capacitance of 10,000[Formula: see text]pF and a tool rotation of 600[Formula: see text]RPM, the research contributes valuable insights into the intricate realm of [Formula: see text]EDM, highlighting the potential for enhanced surface performance through strategic parameter manipulation.

Multi-Response Optimization Analysis of the Milling Process of Asphalt Layer Based on the Numerical Evaluation of Cutting Regime Parameters

The present study aimed to optimize the process parameters (milling depth and advanced speed) for an asphalt milling operation using a multi-response approach based on Taguchi design of experiments (DOE) and Grey Relational Analysis (GRA). Nine simulations tests were conducted using Discrete Element Method (DEM) in order to determine the forces acting on the cutting tooth support and tip. The considered performance characteristics were cutting forces (smaller is better category) and chip section area (larger is better category). A Grey Relational Grade (GRG) was determined from GRA, allowing to identify the optimal parameter levels for the asphalt milling process with multiple performance characteristics. It was found that that the optimal milling parameters for multi-response analysis are a milling depth of 200 mm and an advanced speed of 30 mm/min. Furthermore, analysis of variance (ANOVA) was used to determine the most significant factor influencing the performance characteristics. The analysis results revealed that the dominant factor affecting the resultant cutting force was milling depth, while the main factor affecting chip section area was the advanced speed. Optimizing milling efficiency is essential in machining operations. A key factor in this direction is comprehending the interplay between chip removal and cutting forces. This understanding is fundamental for achieving increased productivity, cost-effectiveness, and extended tool lifespan during the milling process.

Consumer perception of plant-based yoghurt: Sensory drivers of liking and emotional, holistic and conceptual associations

Plant-based (PB) yoghurts is a rapidly expanding food category with the potential to reduce many of the negative environmental impacts associated with the farming of dairy cattle and related greenhouse gas emissions. Within the context of growing consumer demand for PB products, this research aimed to identify the main drivers of consumer acceptance of PB yoghurts through data drawn from a consumer study of 113 adult New Zealand participants who tasted a representative range of commercially available vanilla-flavoured PB yoghurts, and provided sample evaluations using a multi-variable measurement approach comprised of liking ratings, emotional responses, sensory characterisations, and holistic / conceptual perceptions. The primary finding of this study was that the overall acceptability of currently available PB yoghurts is low, leading to poor attitudes and low willingness to consume PB yoghurts. The examined products were characterised by the presence of several sensory attributes that negatively impacted consumer liking, either because they were unexpected or because their intensity level was too high. Among the main sensory issues identified were perceived sourness (acidity), lumpy appearance and non-white colour. In contrast, vanilla flavour and a creamy/smooth texture were identified as the main drivers of liking. The multi-response approach used in this study enabled a comprehensive characterisation of the products. One of the key insights gained was that negative emotional activation, caused by the presence of unexpected sensory attributes in the samples, was the main driver of product rejection. This was likely due to the disparity between consumers’ sensory expectations, formed primarily based on their experience with dairy yoghurts, and the actual experience upon tasting the PB yoghurts. Overall, the findings indicate that the sensory properties of currently available PB yoghurts are a significant barrier to their adoption by most consumers and that addressing these sensory deficiencies is essential to achieving mainstream market acceptance of these products.

“Beyond liking” measures in food-related consumer research supplement hedonic responses and improve ability to predict consumption

Sensory and consumer science is concerned with measuring perceptual and affective responses to consumer products. Historically, hedonic responses (degree of liking or preference for a set of test products) have been the primary measure of product performance in food-related consumer research, but recent years have seen an increase in the uptake of perceptual measures that go “beyond liking”, with interest primarily focusing on product-elicited emotions, conceptualisations and situational appropriateness. Although the ultimate purpose of collecting such responses is that they are predictive of what consumers will like, choose and consume in their everyday life, such data are very rarely validated against actual consumer behaviour.Against this backdrop, the present research aimed to evaluate the ability of emotional, conceptual, and situational appropriateness responses to predict a behaviourally relevant measure of product performance – frequency of past consumption. Two (online) consumer studies were conducted with US adults, using salads (Study 1, n = 606) and non-alcoholic beverages (Study 2, n = 603) as product categories. In each study, the predictive ability of each set of measures was benchmarked against that of expected liking to identify the optimal (most predictive of consumption) combination of product-related measures.Both studies provided evidence that all included measures (liking, emotional, conceptual, and situational responses) were significantly correlated with frequency of past consumption, and importantly, that inclusion of “beyond liking” measures improved behavioural prediction over and above models based on hedonic responses only. These findings confirmed that liking in and of itself is insufficient as a predictor of consumption and supported calls for the purposeful combination of different response types using “global” or multi-response approaches. Differences between the two studies pertaining to the relative importance of liking and the best combination of predictors were uncovered, suggesting that the optimal combination of “beyond liking” measures in practical applications is likely to be study-specific.

Optimization of antioxidants recovery from wild thyme (Thymus serpyllum L.) by ultrasound-assisted extraction: Multi-response approach

The main goal of this study was to valorize Thymus serpyllum L., the by-product of filter-tea production, for extraction of polyphenols with high antioxidant capacity by ultrasound-assisted extraction (UAE). Herbal dust is formed during the preparation of raw material for tea packaging, it is separated as a fraction which is unusable in the tea industry and distinguished as an industrial waste. In order to optimize the process, three levels, three variables, face-centered central composite experimental design within the response surface methodology (RSM) was applied. Temperature (50, 65 and 80 °C), extraction time (40, 55 and 70 min) and ethanol concentration (45, 60 and 75 %) were used as independent variables. Selected responses were total extraction yield (Y) and total phenols yield (TP), as well as antioxidant activity parameters obtained by DPPH, ABTS and FRAP assays. Results were fitted to a second-order polynomial model and goodness of fit was determined by regression analysis and analysis of variance (ANOVA). Good accordance between experimental and predicted values was achieved, which suggested that obtained models could be used for multi-response optimization in order to maximize yields of target responses and improve antioxidant potential of T. serpyllum liquid extracts. Furthermore, UAE provided advantages comparing to conventional solid-liquid extraction in terms of antioxidant activity and total extraction and total phenols yield. Therefore, it could be concluded that T. serpyllum herbal dust could be used as raw material for production of antioxidant-rich extracts.

How useful are perception- and experienced-based measures in predicting actual food choice? Evidence from an in-store field experiment using a multi-response approach

Multi-response approaches have gained popularity in product-based research for obtaining deeper and more generalizable product insights related to product performance. Through a natural in-store field experiment, this study examined how perception-based and experience-based measures, within a multi-response approach, serve to predict actual product choice. We investigated consumers’ evaluation and acceptance of a novel biofortified orange-fleshed sweetpotato (OFSP) puree bread with a set of 141 (Treatment A: OFSP bread) and 204 (Treatment B: other bread) randomly selected bread buyers in Nairobi, Kenya. Non-parametric machine learning methods were used for partitioning and predictive purposes. They included unbiased conditional inference trees and theory-based model-based recursive partitioning. After identifying an individual specific reference product, we first examined how Just-About-Right scaling for sensory evaluation related to nutritional beliefs, liking, and economic valuation. The latter measure was based on an incentive-compatible and consequential Becker-DeGroot-Marshak approach. The results revealed structural differences in the way that the evaluation of sensory attributes are predictive of the perception-based measures. Liking evaluation was strongly predictive of actual choice, while the economic valuation was only weakly so. Notably, neither nutritional beliefs as a food quality characteristics nor any of the dimensions related to product conceptualizations by CATA counts, including that of emotions, were predicative of the actual choice. These results suggest a further need to develop and integrate measures related to circumstantially derived state of wanting to better predict actual product choice in a natural environment.

Performance assessment of hard coating on rock cutting bit and process parameter optimization through multi-response approach using DEAR-Taguchi technique

Performance assessment of hard coating on rock cutting bit and process parameter optimization through multi-response approach using DEAR-Taguchi technique

A novel approach for non-normal multi-response optimisation problems

Various creative multi-response optimisation approaches have been developed in the literature. Most of these researches are based on the normality assumption of the response distribution. However, this assumption does not necessarily hold in some real cases, such as non-normal multiple responses. Also, the reproducibility of optimisation results does not hold in some practical applications due to the variability of predicted responses associated with model uncertainty. In this paper, a novel approach is proposed to address the issues for non-normal multi-response optimisation. The proposed method not only identifies significant effects for each response by incorporating factorial effect principles into the framework of the Bayesian generalised linear models (GLMs) but also takes into account the model uncertainty and the variability of predicted responses by using the Bayesian sampling technique and Pareto optimal strategy. Furthermore, the optimal parameter settings are found by using grey incidence analysis (GIA). Besides, two examples are used to illustrate the effectiveness of the proposed method. The results show that the proposed method not only effectively identify significant factors but also find more satisfactory parameter settings when the reliability and reproducibility of optimisation results are considered simultaneously.

Effects of “craft” vs. “traditional” labels to beer consumers with different flavor preferences: A comprehensive multi-response approach

Common definitions of craft-style beers emphasize that they are brewed by small, local breweries and that they have complex, novel and, often, bold flavors. In recent research conducted with declared craft beer drinkers who tasted beers in a blind condition, Jaeger et al. (2020) [FQAP, 103884] identified the existence of two preference segments. One segment (Craft-style Likers) preferred the characteristic complex, novel and bold flavors of many craft-style beers, while the other segment (Traditional-style Likers) preferred the less complex and milder flavors associated with traditional-style beers. In the present research, a multivariate response approach that included the evaluation of liking, sensory, holistic/conceptual, and cognitive/emotional/situational responses, as well as beer-related attitudes and behaviors, was used to assess the same set of six beers in a similar sample of declared craft beer drinkers (n = 122) as used in our previous study. However, beers were now labeled to reflect the style of the beer (craft vs. traditional) and the size (small vs. large) and regional origin (local vs. international) of the brewer. Results confirmed the existence of the same two preference segments. Although the effects of labeling the beers in accordance with their craft- vs. traditional-style natures did not influence sensory, holistic/conceptual or cognitive responses, they did influence emotional and situational responses. For craft-style beer likers, the information increased their positive emotions and the situational uses for craft-style beers, while for the traditional-style beer likers the labeling had a corresponding positive effect on their judgments of the traditional style beers. The results confirm previous findings on beer and product labeling, which show that sensory properties are less susceptible to extrinsic information effects than are affective, emotional and other, non-sensory product judgments. Implications for craft and traditional brewers are discussed and suggestions for future research presented.

Multi-response approaches in product-focused investigations: Methodological variations across three case studies

Consumers’ product experiences are increasingly uncovered using approaches that extend beyond acceptability and sensory perception. The present research is situated in this context and adopts a multi-response approach to jointly obtain attitudinal, conceptual, emotional, situational and/or sensorial evaluations. With the aim of greater methodological understanding, three case studies were conducted with samples in three product categories (fruit- and vegetable-based beverages (n = 10), seafood (n = 6) and chocolate (n = 7)) using consumers from New Zealand (n = 196), India (living in New Zealand) (n = 138) and China (n = 167), conducted in central location (CLT) or home-use test (HUT) settings. Showcasing this multi-response approach and demonstrating its versatility in product research is the main contribution of the research. Across the three case studies different combinations of response types and scaling formats were successfully used (including CATA (check-all-that-apply) questions, yes/no questions and rating scales), and it was also found that tasted foods and written stimuli (food names) served equally well as stimuli. The degree of liking or disliking for individual samples was a useful benchmark against which to interpret the other types of responses, and situational appropriateness, obtained as item-by-use (IBU) responses always contributed unique insights. Facial emoji to obtain product-emotion associations yielded less valuable insights than a conceptualisation task. As expected, and in accordance with the rationale for adopting a multi-response approach, the combination of response types yielded greater stimuli insights than would otherwise have been gained. This held for each of the three case studies and supported future applications using a multi-response approach that extends beyond many related initiatives by including four response types in each case study.

Hybrid multi-response optimization of friction stir spot welds: failure load, effective bonded size and flash volume as responses

Friction stir spot welding (FSSW) is a multi-input multi-response process. Effective multi-response optimization of welds is desirable to create welds with a balance of quality responses. In order to eliminate the subjectivity (uncertainty and engineering judgment) with the existing multi-response Taguchi-based Grey relational analysis, principal component analysis (PCA) was integrated into it. The PCA helps in determining the effective optimal weighting values required for the estimation of Grey relational grade (GRG). As a result, tool rotational speed, plunge depth and dwell time were employed as input parameters while failure load (FL), expelled flash volume (EFV) and effective bonded size (EBS) of conical pin friction stir spot-welded joint of AA2219-O alloy were the chosen output responses. EFV was minimized while FL and EBS of the joints were maximized using this hybrid multi-response approach. From the analysis of variance of GRG and its response graphs, the significant parameters and their levels were obtained. Experimental results confirmed the effectiveness and robustness of this method. In addition, three critical zones were observed on the fracture surfaces of joints, namely, tool impelled unbonded zone, partially bonded zone and effective bonded/nugget zone. The weld nugget failed by circumferential nugget shear mode.

Microrespirometric model calibration applied to wastewater processes

Microrespirometry is a recently developed method that combines classical respirometry and microreactor systems, for the characterization of microbial cultures. This method, which allows multiple simultaneous replicates from a single low-volume biomass sample, can improve and simplify the model calibration exercise by providing more and better experimental data. To follow up on the interest in microrespirometry, two model wastewater treatment processes were set up and used for model calibration: an aerobic degradation of 4-chlorophenol by acclimated sludge, and a synthetic wastewater treatment by activated sludge, which were well described by a Haldane model and a modified ASM3 model, respectively. For each process, the model parameters were estimated by model fitting, minimizing the objective function for each replicate independently, and minimizing the objective function for all replicates simultaneously (multiresponse approach). Parameter confidence intervals were determined for all parameter estimates, and the impacts of measurement errors, number of replicates, and parameter correlation were assessed. It was observed that the multiresponse approach presents several advantages, including single-step parameter estimation, independent of the number of replicates, and determination of confidence intervals that include the main sources of uncertainty. It was concluded that microrespirometry is a high-throughput and convenient method for model calibration.

Optimizing the Production Parameters for Pellets Made from Pistachio Tree Pruning Using Multi-response Optimization

Biomass is considered as a renewable source of energy that can be used as a partial replacement for fossil fuels. Biomass pellets are produced by pressing the ground plant residues and they are directly burned to generate heat. Production variables can highly affect the final heat quality of the pellets. In this study, pellets were made from the pruning residues of pistachio trees and the effects of production variables including: moisture content in three levels of 8, 12 and 16%, wb; particle size in three levels of fine, medium and coarse; and temperature in three levels of 100, 75, 50 °C on the quality characteristic of the pellets were investigated. The quality characteristics included: strength factor, durability, density and friction of the pellets. The production variables were also simultaneously optimized using a multi-response approach by RSM and desirability function. The experimental results, based on full factorial experimental approach, indicated that the considered production factors had significant effect on all of the quality characteristics (α = 0.05). The quality characteristics were expressed as functions of production variables using a quadratic model for each characteristic. The models showed high degrees of fit for each case (R2 > 0.97). The resulted optimized values were: 100 °C for temperature, 11.7% for moisture content and 1.65 mm for particle size.

Water Resources Impact Assessment Under Climate Change Scenarios in Mediterranean Watersheds

Climate models project a reduction in annual precipitation and an increase in temperature, which may lead to runoff shortages and a consequent water availability reduction, in some Mediterranean regions, such as southern Portugal. The impacts on water availability under different climate change scenarios are assessed using SHETRAN, a physically-based and spatially-distributed hydrological model. SHETRAN is calibrated and validated against daily runoff measurements at outlet and internal sections and against phreatic surfaces using a multi-basin, multi-location and multi-response approach. Nash-Sutcliff efficiency, volume deviation and coefficient of determination ranged, respectively, from 0.58 to 0.76, 0.59 to 0.79 and −9 to 15 %, in the calibration period, and from 0.54 to 0.75, 0.54 to 0.77 and −14 to 12 %, in the validation period. Three GCM and two RCM are used for control (1961–1990) and scenario (2071–2100) periods, under the A2 SRES emission scenario. Observed bias in the climate models’ projected precipitation and temperature are corrected with three bias correction methods. For the scenario period the climate models project a change in precipitation from +1.5 to −65 % and an increase in temperature from +2.7 to +5.9 °C. This trend in climate change projection is reflected in the annual runoff that decreases drastically, between 13 and 90 %, in southern Portugal by the end of the century. The runoff reduction is greater in all watersheds in Autumn and Spring with higher agreement between models and bias correction methods. The runoff decrease seems greater in the Guadiana river basin which is already under significant water stress.

Multi-response calibration of a conceptual hydrological model in the semiarid catchment of Wadi al Arab, Jordan

A key factor for sustainable management of groundwater systems is the accurate estimation of groundwater recharge. Hydrological models are common tools for such estimations and widely used. As such models need to be calibrated against measured values, the absence of adequate data can be problematic. We present a nested multi-response calibration approach for a semi-distributed hydrological model in the semi-arid catchment of Wadi al Arab in Jordan, with sparsely available runoff data. The basic idea of the calibration approach is to use diverse observations in a nested strategy, in which sub-parts of the model are calibrated to various observation data types in a consecutive manner. First, the available different data sources have to be screened for information content of processes, e.g. if data sources contain information on mean values, spatial or temporal variability etc. for the entire catchment or only sub-catchments. In a second step, the information content has to be mapped to relevant model components, which represent these processes. Then the data source is used to calibrate the respective subset of model parameters, while the remaining model parameters remain unchanged. This mapping is repeated for other available data sources. In that study the gauged spring discharge (GSD) method, flash flood observations and data from the chloride mass balance (CMB) are used to derive plausible parameter ranges for the conceptual hydrological model J2000g. The water table fluctuation (WTF) method is used to validate the model. Results from modelling using a priori parameter values from literature as a benchmark are compared. The estimated recharge rates of the calibrated model deviate less than ±10% from the estimates derived from WTF method. Larger differences are visible in the years with high uncertainties in rainfall input data. The performance of the calibrated model during validation produces better results than applying the model with only a priori parameter values. The model with a priori parameter values from literature tends to overestimate recharge rates with up to 30%, particular in the wet winter of 1991/1992. An overestimation of groundwater recharge and hence available water resources clearly endangers reliable water resource managing in water scarce region. The proposed nested multi-response approach may help to better predict water resources despite data scarcity.

Multi-Response Optimization of Process Parameters for Low-Pressure Cold Spray Coating Process Using Taguchi and Utility Concept

Most of the existing multi-response optimization approaches focus on the subjective and practical know-how of the process. As a result, some confusion and uncertainty are introduced in the overall decision-making process. In this work, an approach based on a Utility theory and Taguchi quality loss function has been applied to the process parameters for low-pressure cold spray process deposition of copper coatings, for simultaneous optimization of more than one response characteristics. In the present paper, two potential response parameters, i.e., coating thickness and coating density, have been selected. Utility values based on these response parameters have been analyzed for optimization using the Taguchi approach. The selected input parameters of powder feeding arrangement, substrate material, air stagnation pressure, air stagnation temperature, and stand-off distance significantly improve the Utility function (raw data) comprising quality characteristics (coating thickness and coating density). The percentage contribution of the parameters to achieve a higher value of Utility function is substrate material (50.03%), stand-off distance (28.87%), air stagnation pressure (6.41%), powder feeding arrangement (4.68%), and air stagnation temperature (2.64%).

Multidimensional Assessment of Value Added by Teachers to Real-World Outcomes

Measuring teacher effectiveness is challenging since no direct estimate exists; teacher effectiveness can be measured only indirectly through student responses. Traditional value-added assessment (VAA) models generally attempt to estimate the value that an individual teacher adds to students' knowledge as measured by scores on successive administrations of a standardized test. Such responses, however, do not reflect the long-term contribution of a teacher to real-world student outcomes such as graduation, and cannot be used in most university settings where standardized tests are not given. In this paper, the authors develop a multiresponse approach to VAA models that allows responses to be either continuous or categorical. This approach leads to multidimensional estimates of value added by teachers and allows the correlations among those dimensions to be explored. The authors derive sufficient conditions for maximum likelihood estimators to be consistent and asymptotically normally distributed. The authors then demonstrate how to use SAS software to calculate estimates. The models are applied to university data from 2001 to 2008 on calculus instruction and graduation in a science or engineering field.

Method for Optimizing Coating Properties Based on an Evolutionary Algorithm Approach

In industry as well as many areas of scientific research, data collected often contain a number of responses of interest for a chosen set of exploratory variables. Optimization of such multivariable multiresponse systems is a challenge well suited to genetic algorithms as global optimization tools. One such example is the optimization of coating surfaces with the required absolute and relative sensitivity for detecting analytes using devices such as sensor arrays. High-throughput synthesis and screening methods can be used to accelerate materials discovery and optimization; however, an important practical consideration for successful optimization of materials for arrays and other applications is the ability to generate adequate information from a minimum number of experiments. Here we present a case study to evaluate the efficiency of a novel evolutionary model-based multiresponse approach (EMMA) that enables the optimization of a coating while minimizing the number of experiments. EMMA plans the experiments and simultaneously models the material properties. We illustrate this novel procedure for materials optimization by testing the algorithm on a sol-gel synthetic route for production and optimization of a well studied amino-methyl-silane coating. The response variables of the coating have been optimized based on application criteria for micro- and macro-array surfaces. Spotting performance has been monitored using a fluorescent dye molecule for demonstration purposes and measured using a laser scanner. Optimization is achieved by exploring less than 2% of the possible experiments, resulting in identification of the most influential compositional variables. Use of EMMA to optimize control factors of a product or process is illustrated, and the proposed approach is shown to be a promising tool for simultaneously optimizing and modeling multivariable multiresponse systems.

EFFECTS OF CA TREATMENT AND TEMPERATURE ON BROCCOLI COLOUR DEVELOPMENT

Broccoli combines high contents of vitamins, fibres and glucosinolates with a low calorie count and is sometimes referred to as the 'crown jewel of nutrition'. Colour is one of the most important quality attributes of broccoli, and yellowing due to senescence of broccoli florets is the main external quality problem in the broccoli supply chain. Controlled Atmosphere (CA) is a very effective method to maintain broccoli quality but the effects of CA on colour retention have not been studied extensively. The aim of this paper is to characterise the colour behaviour (measured by RGB colour image analysis) of broccoli as affected by CA and temperature. Data on colour behaviour and gas exchange were gathered for broccoli heads that were stored in containers at three temperatures and subjected to four levels of O 2 and three levels of CO 2 . Gas conditions and temperature have a clear effect on the colour change of broccoli especially at low O 2 in combination with high CO 2 . An integrated colour model is proposed that combines a colour model with a standard gas exchange model. The colour model is based on three differential equations describing the formation of (blue/green) chlorophyllide from the colourless precursor, the bidirectional conversion of chlorophyllide into (blue/green) chlorophyll, and the decay of chlorophyllide. During the first step of building the integrated model, gas exchange data were analysed simultaneously using multi response regression analysis. No fermentation was encountered for this batch of broccoli. During the second step it was found that only one of the reactions of the colour model, the decay of chlorophyllide, is affected by the gas conditions. In the final step, a multi-response approach was applied where gas exchange parameters were estimated using the gas exchange model, the colour parameters were estimated using the colour model with both models linked via the reaction rate constant affected by the gas conditions. Such a calibrated, integrated, model could be used as a tool for predicting colour change in the postharvest chain.

A Multiresponse method for fitting solid-phase activity coefficient models to ternary ion-exchange data

A popular method for fitting solid-phase activity coefficient models in the thermodynamics of ternary ion-exchange has been the Rational method. The standard statistical tests used to compare model functional forms are undefined in the Rational method because all of the dependent variables in the regression (Gibbs Energies) take the value of zero. The present study develops the mathematically equivalent but statistically improved approach of directly fitting Vanselow selectivity coefficients with multiresponse regression. In this multiresponse approach, the Gibbs Energy at equilibrium is set to zero, a selected model is substituted into the equilibrium expression in place of the solid-phase activity coefficients, and the activity coefficient model parameters are optimized numerically until the predicted Vanselow selectivity coefficients are as close as possible to the measured values. This Multiresponse method requires the use of restricted regression to ensure that the equilibrium constants obey the Triangle Rule. An advantage of the Multiresponse method is that it allows for calculation of the coefficient of determination ( R 2) and R 2 adj, which are statistics that can be used to compare solid-phase activity coefficient models. The example solid-phase activity coefficient models compared in this study are the Regular Solution model and a Cox mixture model. When applied to NH 4 +–Ca 2+–K + exchange on vermiculite, the R 2 adj statistics were found to be 0.944 for the Cox mixture model and 0.826 for the Regular Solution model. These results from the Multiresponse method indicate that the Cox mixture model is superior for this dataset.