Three-mode Principal Component Analysis Research Articles

Distinguishing dimensions of emotion dynamics across 12 emotions in adolescents' daily lives.

Research on emotion dynamics as indices of emotion functioning has become muddled by conceptual confusion, methodological heterogeneity, and seemingly conflicting results. One way to address this chaos is the study of profiles of emotion dynamics across 12 emotions and how they differ between 246 adolescents. The interpretation of these dynamic profiles was guided by auxiliary variables including age, personality, depressive symptoms, and social experiences. During 6 days, 246 adolescents (Mage = 14.20; 65% female) rated nine times daily the intensity of 12 emotions (cheerful, happy, energetic, joyful, content, relaxed, anxious, worried, irritable, insecure, down, and guilty) and their social experiences with family, friends, and classmates. Additional baseline measures included neuroticism, extraversion (Revised Junior Eysenck Personality Questionnaire Short Form), and depressive symptoms (Center for Epidemiological Studies Depression Scale). A three-mode principal component analysis (3MPCA Tucker3-based) model was estimated on the person-specific dynamic parameters of emotional intensity (mean), variability (standard deviation), instability (mean squared successive difference), and inertia (autocorrelation). The 3MPCA identified three emotion-mode components (positive affect, negative affect, and irritability) and three dynamic-mode components (emotional intensity, lability, and inertia). Five individual-mode components captured interactions between these modes, of which positive affect explained most variation in the data. These emotion dynamic profiles correlated differently with social experiences. Additional 3MPCA model structures based on imputed data (correcting missing autocorrelations) and affect scale composites (low- and high-arousal positive and negative affect) showed strong resemblance. The identified emotion dynamic profiles capture meaningful interpersonal differences in adolescents' emotional experiences and change. Future work should focus on irritability and positive affect as these were uniquely informative in adolescents' emotional experiences. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

How are various natural disasters cognitively represented?: a psychometric study of natural disaster risk perception applying three-mode principal component analysis

How are various natural disasters cognitively represented?: a psychometric study of natural disaster risk perception applying three-mode principal component analysis

A New Three-mode Principal Component Analysis to Estimate Tendencies of Individual Which Exist Independently on Stimuli

A New Three-mode Principal Component Analysis to Estimate Tendencies of Individual Which Exist Independently on Stimuli

Predicting long-term depression outcome using a three-mode principal component model for depression heterogeneity

BackgroundDepression heterogeneity has hampered development of adequate prognostic models. Therefore, more homogeneous clinical entities (e.g. dimensions, subtypes) have been developed, but their differentiating potential is limited because neither captures all relevant variation across persons, symptoms and time. To address this, three-mode Principal Component Analysis (3MPCA) was previously applied to capture person-, symptom- and time-level variation in a single model (Monden et al., 2015). This study evaluated the added prognostic value of such an integrated model for longer-term depression outcomes. MethodsThe Beck Depression Inventory (BDI) was administered quarterly for two years to major depressive disorder outpatients participating in a randomized controlled trial. A previously developed 3MPCA model decomposed the data into 2 symptom-components (‘somatic-affective’, ‘cognitive’), 2 time-components (‘recovering’, ‘persisting’) and 3 person-components (‘severe non-persisting depression’, ‘somatic depression’ and ‘cognitive depression’). The predictive value of the 3MPCA model for BDI scores at 3-year (n=136) and 11-year follow-up (n=145) was compared with traditional latent variable models and traditional prognostic factors (e.g. baseline BDI component scores, personality). Results3MPCA components predicted 41% and 36% of the BDI variance at 3- and 11-year follow-up, respectively. A latent class model, growth mixture model and other known prognostic variables predicted 4–32% and 3–24% of the BDI variance at 3- and 11-year follow-up, respectively. LimitationsOnly primary care patients were included. There was no independent validation sample. ConclusionAccounting for depression heterogeneity at the person-, symptom- and time-level improves longer-term predictions of depression severity, underlining the potential of this approach for developing better prognostic models.

Simultaneous Decomposition of Depression Heterogeneity on the Person-, Symptom- and Time-Level: The Use of Three-Mode Principal Component Analysis.

Although heterogeneity of depression hinders research and clinical practice, attempts to reduce it with latent variable models have yielded inconsistent results, probably because these techniques cannot account for all interacting sources of heterogeneity at the same time. Therefore, to simultaneously decompose depression heterogeneity on the person-, symptom and time-level, three-mode Principal Component Analysis (3MPCA) was applied to data of 219 Major Depression patients, who provided Beck Depression Inventory assessments every three months for two years. The resulting person-level components were correlated with external baseline clinical and demographic variables. The 3MPCA extracted two symptom-level components (‘cognitive’, ‘somatic-affective’), two time-level components (‘improving’, ‘persisting’) and three person-level components, characterized by different interaction-patterns between the symptom- and time-components (‘severe non-persisting’, ‘somatic depression’ and ‘cognitive depression’). This model explained 28% of the total variance and 65% when also incorporating the general trend in the data). Correlations with external variables illustrated the content differentiation between the person-components. Severe non-persisting depression was positively correlated with psychopathology (r=0.60) and negatively with quality of life (r=-0.50). Somatic depression was negatively correlated with physical functioning (r=-0.45). Cognitive depression was positively correlated with neuroticism (r=0.38) and negatively with self-esteem (r=-0.47). In conclusion, 3MPCA decomposes depression into homogeneous entities, while accounting for the interactions between different sources of heterogeneity, which shows the utility of the technique to investigate the underlying structure of complex psychopathology data and could help future development of better empirical depression subtypes.

Cultural Beliefs About Societal Change

People’s beliefs about where society has come from and where it is going have personal and political consequences. Here, we conduct a detailed investigation of these beliefs through re-analyzing Kashima, Shi, et al.’s (Study 2, n = 320) data from China, Australia, and Japan. Kashima, Shi, et al. identified a “folk theory of social change” (FTSC) belief that people in society become more competent over time, but less warm and moral. Using three-mode principal component analysis, an under-utilized analytical method in psychology, we identified two additional narratives: Utopianism/Dystopianism (people becoming generally better or worse over time) and Expansion/Contraction (an increase/decrease in both positive and negative aspects of character over time). Countries differed in endorsement of these three narratives of societal change. Chinese endorsed the FTSC and Utopian narratives more than other countries, Japanese held Dystopian and Contraction narratives more than other countries, and Australians’ narratives of societal change fell between Chinese and Japanese. Those who believed in greater economic/technological development held stronger FTSC and Expansion/Contraction narratives, but not Utopianism/Dystopianism. By identifying multiple cultural narratives about societal change, this research provides insights into how people across cultures perceive their social world and their visions of the future.

質的データに対する非計量三相主成分分析法

TUCKER3 (Tucker, 1966) is one of the methods of principal component analysis (PCA) for “quantitative” three-mode data. In this paper,we extend TUCKER3 to “nonmetric” three-mode PCA by deriving quantification scores. We also present an alternating least squares algorithm for finding optimal solution of nonmetric three-mode PCA by updating parameters such as quantification scores, loading matrices and core matrix successively. Calculating quantification scores of qualitative variables allows us to exclude arbitrariness which is included in questionnaire, such as the coding of nominal variables and the equality of intervals of ordinal variables. Two real data examples are given to illustrate the effectiveness of the proposed procedure.

Interação genótipo x local x regime alimentar em bovinos nelore por meio de componentes principais de três modos

O principal objetivo deste estudo foi aplicar componentes principais com múltiplas matrizes de dados para verificar a interação tripla genótipo x local x regime alimentar no valor genético do efeito direto do peso, aos 205 dias de idade. Foram utilizados touros com filhos em três regiões de produção do Nordeste Brasileiro (Maranhão, Mata e Agreste, e Recôncavo Baiano) e criados nos regimes alimentares a pasto ou com suplementação. Não se evidenciou interação genótipo x local para a característica estudada, entretanto, constatou-se interação do genótipo x regime alimentar. A utilização dos touros deve ser direcionada de acordo com o regime alimentar de seus filhos.

Three-Mode Principal Components Analysis of Daily Affect at Work

Affect was largely ignored in the organizational sciences until very recently. However, the impact of affect on dynamic process influencing workplace behavior is increasingly critical. This study employs the multi-way analytic techniques PARAFAC and the Tucker model in an attempt to clarify the three sources of variance in daily mood ratings. The 2 x 2 x 2 structure found here is largely consistent with work by Zevon and Tellegen (1982) and Tellegen, Watson, and Clark (1999), and bears on research into the nature of affective processes in workplace behavior.

Characterization of maize populations in different environmental conditions by means of Three-Mode Principal Components Analysis

M. Marticorena, S. Bramardi, and R. Defacio. 2010. Characterization of maize populations in different environmental conditions by means of Three-Mode Principal Components Analysis. Cien. Inv. Agr. 37(3): 91-103. Characterization of 31 native populations of maize conserved at the germplasm bank of the INTA Pergamino Experimental Station, Argentina, was achieved by evaluating 10 quantitative attributes in two different environmental situations. The experimental design generated three-way or three-mode data, repeated observations of a set of attributes for a set of individuals in different conditions. The information was displayed in a three-dimensional array, and the structure of the data was explored using Three-Mode Principal Component Analysis, the Tucker-2 Model. A group of populations was identified that displayed homogeneous behavior in the two environments with respect to the following traits: ear length, prolificacy, grains per meter, yield and 1000 kernel weight. However, another group of populations displayed opposite behavior for the traits of plant height and ear insertion height in the different environment conditions and is indicative of the existence of genotype-environment interaction. In conclusion, Three-Mode Principal Component Analysis is an important tool for characterizing plant genetic resources when their phenotypic values are likely to be affected by environmental conditions.

Richard A. Harshman (1943–2008), a man of ideas

Richard A. Harshman (1943–2008), a man of ideas

Selecting Among Multi-Mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria

Multi-mode partitioning models for N-way N-mode data reduce each of the N modes in the data to a small number of clusters that are mutually exclusive. Given a specific N-mode data set, one may wonder which multi-mode partitioning model (i.e., with which numbers of clusters for each mode) yields the most useful description of this data set and should therefore be selected. In this paper, we address this issue by investigating four possible model selection heuristics: multi-mode extensions of Calinski and Harabasz's (1974) and Kaufman and Rousseeuw's (1990) indices for one-mode k-means clustering and multi-mode partitioning versions of Timmerman and Kiers's (2000) DIFFIT and Ceulemans and Kiers's (2006) numerical convex hull based model selection heuristic for three-mode principal component analysis. The performance of these four heuristics is systematically compared in a simulation study, which shows that the DIFFIT and numerical convex hull heuristics perform satisfactory in the two-mode partitioning case and very good in the threemode partitioning case.

Multi-attribute responses of maize inbred lines across managed environments

In maize (Zea mays L.) breeding programs, selection among and within segregating progenies is based mainly on indirect selection criteria. A better understanding of the environment influence on physiological attributes of maize inbred lines is important to the identification and selection of superior inbred lines as well as to successful hybrid seed production. In this study, the size and form of genotype (G) and genotype × environment (G × E) interaction effects for plant grain yield (PGY) and several physiological attributes were examined for 12 maize inbred lines grown in four managed environments, represented by two seasons (Y) and two nitrogen levels. Mixed model analysis revealed that the G effect was relatively high for attributes related to light capture, phenology, early biomass production, and numerical components of PGY. The G × E interaction effect explained most of the variability for PGY, harvest index (HI), and biomass production at maturity. Three-mode principal component analysis allowed us to: (1) describe the associations among multiple attributes across environments, (2) reveal the form of the main patterns of G × E interaction, (3) establish the importance of the genotype × year (G × Y) interaction for kernel number, HI, and biomass at maturity in determining PGY, (4) identify promising genotypes of high-PGY across environments, and (5) detect genotypes of similar response patterns for PGY but with a contrasting relative behavior for other attributes, which may permit the simultaneous selection for grain yield and desired secondary traits. Such selection results would contribute greatly in the identification of superior inbreds than selecting for grain yield alone.

Visualization of competitive market structure by means of choice data

This paper presents a method for visualizing competitive market structures based on scanner panel data where asymmetries are taken into account. For this, I combined consumer choice models based on mixed logit models with three-mode principal component analysis. This approach can be used to unfold a competitive market structure map. The methodology presented is able to quantify the clout and receptivity of various brands. The results can then be visualized over time. Using this approach, guidelines for promotional activities of new brands can be provided, and possible threats from the competition detected.

Climate variability and planktonic communities: The effect of an extreme event (severe drought) in a southern European estuary

As a consequence of climate change, flood and drought events are increasing in frequency throughout the world. Nevertheless, knowledge of the effects on zooplankton estuarine communities is still scarce. The present study aimed to examine zooplankton ecology over two contrasting environmental conditions: regular years and extreme dry years, in a shallow temperate southern European estuary, the Mondego Estuary (Portugal). Monthly samples were carried out during three consecutive years: 2003 characterized as a regular temperate year concerning precipitation and river flow, and an extremely dry period during 2004–2005. The spatial and temporal structure of the biological data was evaluated by a three-mode principal component analysis (PCA), which allowed us to distinguish three distinct ecological areas based on their biological composition and their relationship with hydrologic parameters. The severe drought in 2004–2005 was responsible for spatial shifts in the estuary regarding zooplankton community and interannual variability, with an increase in abundance and diversity during the period of low freshwater flow. This freshwater flow regime influenced the composition of the zooplankton community at the most upstream section of Mondego estuary (zone 3), with a replacement of the freshwater community by one predominantly dominated by estuarine organisms. The occurrence of such estuarine community contributed to the increase in zooplankton abundance which is ascribed to the estuarine species Acartia tonsa. The comparison with previous data obtained for this estuarine ecosystem, demonstrated the occurrence of a different scenario at times of high freshwater flow, being defined the existence of two sub-estuarine systems, the north and south arm, presenting the south one the highest values of abundance.

Investigating the physiological bases of predictable and unpredictable genotype by environment interactions using three-mode pattern analysis

Understanding of the underlying physiology of the genotype-specific responses to predictable and unpredictable environmental variation would improve the efficiency of selection within a complex target population of environments. Three-mode principal component analysis (PCA) can be used for interpreting the complex three-way (genotypes, environments, attributes) trial datasets from which this understanding should emerge. The efficiency of this method largely depends on the right combination between the biological and statistical models used, especially on the attributes selected to describe the genotypic responses and the centring of the three-way input data. In this study, we assessed the scope of yield determination models and double-centring of input data for generating some physiological understanding of the genotype×environment (G×E) interactions observed in a sunflower genotype–environment system and for developing ideotype-based breeding strategies. Double-centring of the three-way arrays permitted the separation of predictable and unpredictable G×E interactions. This, in combination with the use of models that explain the physiological bases of yield variation among genotypes, has served to identify three relevant sources of genotypic variation for use in a breeding program, namely: (i) attributes that can be selected to achieve specific adaptation to the target environment by emphasising predictable interactions (e.g. duration of grain filling, a trait associated with canopy stay green); (ii) attributes that allow the unpredictable G×E interactions to be accommodated, improving the linkage between managed-environments and target production environments (e.g. grain set); and (iii) genotypes of similar response pattern for yield but contrasting relative behaviour for the primary and secondary yield determinants. Breeding projects involving crosses between these genotypes could generate better opportunities for yield improvements for individual mega-environments.

Genotype by environment interaction and indirect selection for yield in sunflower: II. Three-mode principal component analysis of oil and biomass yield across environments in Argentina

The genotype by environment (G×E) interactions observed for sunflower oil yield in different regions of Argentina can be analyzed in terms of differences among genotypes in individual environments for its components grain number, grain weight, and oil content (yield analysis). Similarly, G×E interactions observed for oil-corrected grain yield can be analyzed in terms of its determinants total biomass and harvest index (physiological analysis). Three-mode (genotypes×environments×attributes) principal component analysis was applied to 10×21×4 and 10×11×3 matrices, for each of the first and the second analyses, respectively, to collectively interpret the changes in these attributes in a sunflower genotype–environment system, and to assess the relative importance of each trait as underlying determinant of the observed G×E interaction for oil yield. The 3×2×3 and 4×4×2 (genotypes×environments×attributes) principal component models explained about 65% of the variation computed for first and second approaches, respectively. For the yield analysis, the first environment component (54% of the variation) explained the common pattern of oil yield over environments and showed that oil content was highly positively correlated to oil yield, while grain number and grain weight showed lack of association with oil yield and were negatively correlated. The second environment component (11% of the variation) contrasted northern and central environments and showed that grain number is the main underlying determinant of the observed G×E interactions between these two mega-environments for oil yield. In the physiological analysis, the first environment component (29% of the variation) explained the common pattern of oil-corrected grain yield over environments and showed that harvest index was more strongly positively correlated to oil-corrected grain yield, but not to total oil-corrected biomass. The second environmental component (19% of the variation) contrasted northern and central environments and showed that oil-corrected biomass is the physiological attribute that is largely responsible for the G×E interactions for oil-corrected grain yield.

Three-mode principal components analysis: choosing the numbers of components and sensitivity to local optima.

A method that indicates the numbers of components to use in fitting the three-mode principal components analysis (3MPCA) model is proposed. This method, called DIFFIT, aims to find an optimal balance between the fit of solutions for the 3MPCA model and the numbers of components. The achievement of DIFFIT is compared with that of two other methods, both based on two-way PCAs, by means of a simulation study. It was found that DIFFIT performed considerably better than the other methods in indicating the numbers of components. The 3MPCA model can be estimated by the TUCKALS3 algorithm, which is an alternating least squares algorithm. In a study of how sensitive TUCKALS3 is at hitting local optima, it was found that, if the numbers of components are specified correctly, TUCKALS3 never hits a local optimum. The occurrence of local optima increased as the difference between the numbers of underlying components and the numbers of components as estimated by TUCKALS3 increased. Rationally initiated TUCKALS3 runs hit local optima less often than randomly initiated runs.

Three-mode principal component analysis of monitoring data from Venice lagoon

A data set obtained by 44 monthly determinations of 11 variables from 13 sampling sites in the Venice lagoon has been treated by three-mode principal component analysis. The results show that the sampling sites are grouped according to their geographical location, following an inner-outer lagoon direction. In terms of sampling periods, a very strong seasonal effect has been detected, together with an almost linear decrease in nutrients (P and NO - 3 ) and increase in eutrophication.

A case of extreme simplicity of the core matrix in three-mode principal components analysis

In three-mode Principal Components Analysis, theP ×Q ×R core matrixG can be transformed to simple structure before it is interpreted. It is well-known that, whenP=QR,G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, whenP=QR − 1,G can be transformed to have nearly all elements equal to values spectified a priori. A cllsed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation ofG are discussed.