Optimal Scaling Approach Research Articles

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.

Multivariate analysis of Just-About-Right data with optimal scaling approach

In consumer research, Just-About-Right (JAR) scales are commonly used to identify sensory attributes perceived to be at their optimal level or, on the contrary, at too high or too low level. For most of the published works, JAR data are combined with overall liking scores to identify a top list of sensory attributes that might be considered for product reformulation, optimization or characterization. The penalty analysis is a popular and relevant way to get these information but each attribute is considered independently. However, considering all the attributes may provide a complementary point of view and component-based multivariate analyses (e.g Principal Component Analysis or Multiple Correspondence Analysis) could be applied to investigate the relationships between attributes. The analysis of JAR scales with multivariate methods has not been addressed much in the sensory community. JAR scales being bipolar, they will be considered as nominal and Principal Component Analysis with Optimal Scaling (PCAOS) is investigated. This method performs a component-based multivariate analysis with an optimal quantification of JAR data. This method is applied to a JAR sensory experiment on French cheeses.

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

Nonlinear Generalized Structured Component Analysis

Generalized Structured Component Analysis (GSCA) represents component-based structural equation modeling. Currently, GSCA is geared only for the analysis of quantitative data. In this paper, GSCA is extended to deal with qualitative data through data transformation. In particular, the optimal scaling approach is adopted for data transformation as it can be readily coupled with the GSCA estimation procedure. An alternating least-squares algorithm is developed that involves two phases for estimation of model and data parameters. Two empirical applications are presented to demonstrate the usefulness of the proposed method.

SVM-Maj: a majorization approach to linear support vector machines with different hinge errors

Support vector machines (SVM) are becoming increasingly popular for the prediction of a binary dependent variable. SVMs perform very well with respect to competing techniques. Often, the solution of an SVM is obtained by switching to the dual. In this paper, we stick to the primal support vector machine problem, study its effective aspects, and propose varieties of convex loss functions such as the standard for SVM with the absolute hinge error as well as the quadratic hinge and the Huber hinge errors. We present an iterative majorization algorithm that minimizes each of the adaptations. In addition, we show that many of the features of an SVM are also obtained by an optimal scaling approach to regression. We illustrate this with an example from the literature and do a comparison of different methods on several empirical data sets.

Die Konstruktion eines empirisch bestimmten Sozialschichtindexes mittels optimaler Skalierung am Beispiel von Deutschland

Numerous epidemiological studies have shown an association between social status and disease. In alcohol research, socio-economic status (SES) has been associated with drinking patterns, misuse and alcohol problems. SES is a construct which is usually built by using the indicators education, occupation or income separately or combined as a summary score. However, either approach involves theoretical assumptions about the explanatory value of a chosen indicator before the data have been analysed. In this study we have created a gender-specific metric social status indicator for Germany by using all three single SES-indicators (education, occupation, income). We used national representative data from a postal survey from 2000. The age range was restricted to 25 - 59 years. To construct the indicator we used optimal scaling (categorical principal components analysis). Therefore no theoretical assumptions were necessary about the hierarchical order of educational or occupational categories. The optimal-scaling approach allows variables to be scaled on different levels. We used education and occupation as the original categorical data and income (equivalent income) as continuous data. The result of the scaling is a two-dimensional solution. The first dimension explains that variance which could be described by status consistencies (corresponding levels for education, occupation and income). The second dimension of the indicator results from the low correlation between education and income for some individuals (status inconsistencies). The two-dimensional indicator yields differentiated results which would not be visible using a one-dimensional SES-indicator such as education or a summary score. With regard to drinking patterns there are clear differences between middle or low-educated women or men with higher incomes and other social groups. Middle or low-educated men or women with a high income are more likely to be heavy episodic drinkers than people in other social status groups.

Maximum likelihood principal component analysis of time-of-flight secondary ion mass spectrometry spectral images

Many modern surface analytical instruments are able to acquire huge amounts of data in the form of spectral images. Time-of-flight secondary ion mass spectrometry (TOF-SIMS), for instance, can easily generate a complete mass spectrum at each point in a two-dimensional or three-dimensional spatial array. The challenge for the data analyst, then, is to garner the analytically useful information from the overwhelming quantity of raw spectral data. Factor analysis techniques such as principal component analysis (PCA) have proven quite useful in this endeavor. Standard PCA, however, assumes that noise in the data is uniform, that is, that it does not depend on the magnitude of signal. This is clearly not correct for methods that rely on particle counting where the noise is governed by Poisson statistics. In this case, properly accounting for heteroscedasticity is essential to extracting the chemical information into a minimum number of factors while optimally excluding noise. Maximum likelihood PCA (MLPCA) is one approach to addressing this issue. MLPCA can, in principle, incorporate a separate uncertainty estimate for each individual observation in a data set. This article will present a MLPCA analysis of a simple and intuitive TOF-SIMS spectral image. The results show that there is a trade-off between the number of uncertainty parameters included in the model and the quality of each and, in fact, using poor estimates may be worse than ignoring the noise characteristics altogether. The best results were obtained by using a low-rank approximation to the noise rather than individual estimates. MLPCA will also be compared with an optimal scaling approach. For the particular example given, the added benefits of MLPCA do not outweigh the greatly increased computational demands of the technique.

Optimal scaling of TOF-SIMS spectrum-images prior to multivariate statistical analysis

Time-of-flight secondary ion mass spectrometry (TOF-SIMS) is capable of generating huge volumes of data. TOF-SIMS spectrum-images, comprising complete mass spectra at each point in a spatial array, are easily acquired with modern instrumentation. With the addition of depth profiling, spectra can be collected from up to three spatial dimensions leading to data sets that are seemingly unlimited in size. Multivariate statistical techniques such as principal component analysis, multivariate curve resolution and other factor analysis methods are being used to meet the challenge of turning that mountain of data into analytically useful knowledge. These methods work by extracting the essential chemical information embedded in the high dimensional data into a limited number of factors that describe the spectrally active pure components present in the sample. A review of the recent literature shows that the mass spectral data are often scaled prior to multivariate analysis. Common preprocessing steps include normalization of the pixel intensities, and auto- or variance-scaling of the mass spectra. In this paper, we will demonstrate that these pretreatments can lead to less than satisfactory results and, in fact, can be counterproductive. By taking the Poisson nature of the data into consideration, however, a scaling method can be devised that is optimal in a maximum likelihood sense. Using a simple and intuitive example, we will demonstrate the superiority of the optimal scaling approach for estimating the number of pure components, for segregating the chemical information into as few components as possible, and for discriminating small features from noise.

Searching for policy priorities in the formulation of a freight transport strategy: a canonical correlation analysis of freight industry attitudes

Abstract An efficient and effective freight transport strategy can be aided by early professional contributions from key stakeholders. One broad group who have historically been given limited opportunity to influence the drafting of a freight strategy, are commercial road users and shippers who manufacture and distribute goods. Utilising a data set collected in Australia in 1996 from a sample of organisations involved directly and indirectly in road freight transportation, views were sought on road infrastructure changes, new road infrastructure, non-road infrastructure needs and transport policies. An optimal scaling approach using non-linear canonical correlation is implemented to search for structural relationships between the underlying policy and infrastructure dimensions and the various industry categories. This framework provides a powerful mechanism for identifying differences among stakeholders in terms of their support for or opposition to specific policies. Results reveal the considerable differences in attitudes associated with the component parts of the freight industry.

Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation

A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.

Comparing Multiattribute Attitude Models by Optimal Scaling

A method Is proposed for determining the best possible fit that can be obtained by rescaling the multiplicative components of multiattribute attitude models. This optimal scaling approach is illustrated on both cross-sectional and intra-individual data. It is concluded that valid comparisons between the performance of competing multiattribute attitude models must be made between optimally-scaled versions.