British Journal of Mathematical and Statistical Psychology · 1971 · 81 citations · 0 references
Chosen DimensionalityMeasurement TheoryEngineeringMeasurementMechanical EngineeringEducationTrue DimensionalityMultiple ScaleTensile MechanicsDimensioning And TolerancingMultidimensional Scaling TechniqueStatistical AnalysisDimensional MetrologyMechanics ModelingData ScienceMultiscale AnalysisStressMechanicsNumerical SimulationQuantitative AnalysisApplied MeasurementStatisticsScaling AnalysisMultidimensional AnalysisEngineering AnalysisMechanics Of MaterialsQuantitative InterpretationMultiscale Modeling
The paper discusses quantitative interpretation of stress using random synthetic dissimilarity matrices. The study analyzes stress by generating synthetic dissimilarity matrices from random point configurations, adding fractional errors, and examining stress in various dimensions, including estimating the distribution of stress percentages. The results show how measurement error and dimensionality affect stress, enabling estimation of true dimensionality and measurement error, and helping assess the significance of multidimensional representations.
Some aspects of the quantitative interpretation of stress are discussed on the basis of random sets of synthetic dissimilarity matrices. In Section 1 the relation between measurement error and stress is studied. Synthetic dissimilarities are obtained starting from a random configuration of n points ( n = 8, 10, and 12) in t dimensions (1 ≤ t ≤ 3), and adding a fractional error to the interpoint distances. These dissimilarity sets are then analysed in m dimensions (1 ≤ m ≤ 5). The results give an idea of how the stress is influenced by measurement error and the chosen dimensionality of the analysis. In practice, the results can be used for estimating both the true dimensionality and the measurement error of a set of data. In Section 2 the probability distribution of the stress‐percentages in m dimensions (1 ≤ m ≤ 5) is estimated in cases of randomly chosen dissimilarities among n points (7 ≤ n ≤ 12). The results can be an aid in determining the significance of a multidimensional representation of experimental data.