Factor Score Estimates Research Articles

On the Added Value of Multiple Factor Score Estimates in Essentially Unidimensional Models.

Measures initially designed to be single-trait often yield data that are compatible with both an essentially unidimensional factor-analysis (FA) solution and a correlated-factors solution. For these cases, this article proposes an approach aimed at providing information for deciding which of the two solutions is the most appropriate and useful. The procedures we propose are an FA extension of the "added-value" procedures initially proposed for subscale scores in educational testing. The basic principle is that the multiple FA solution is defensible when the factor score estimates of the primary factors are better measures of these factors than score estimates derived from a unidimensional or second-order solution. Methodologically, new results are obtained, and relations with factor indeterminacy measures and second-order FA are discussed. The procedures have been implemented in a noncommercial and widely known program for exploratory FA. The functioning of the proposal is assessed by means of a simulation study, and its usefulness is illustrated with a real-data example in the personality domain.

Assessing the quality and usefulness of factor-analytic applications to personality measures: A study with the statistical anxiety scale

Factor analysis (FA) is the most widely used modeling approach for developing and assessing psychometric personality measures. Furthermore, the appropriateness of an FA application of this type is generally judged on the sole basis of model-data fit, a criterion which is clearly insufficient. This article proposes a multi-faceted approach for assessing (a) the strength and replicability of the factorial solution, (b) the accuracy and effectiveness of the factor score estimates, and (c) the closeness to unidimensionality in measures that were initially designed to be single-trait. The proposal was applied to a measure of statistical anxiety, the SAS, and the main results were the following: (a) both the unidimensional and the oblique solutions were well defined and replicable, and they led to accurate factor score estimates; and (b) unidimensional-based scores were effective over the full practical range of trait values whereas the ranges of the more specific factors in the oblique solution were narrower. It is submitted that the use of the proposal and the accompanying criteria has important advantages and can help to raise standards in FA applications in personality.

Assessing the Quality and Appropriateness of Factor Solutions and Factor Score Estimates in Exploratory Item Factor Analysis.

This article proposes a comprehensive approach for assessing the quality and appropriateness of exploratory factor analysis solutions intended for item calibration and individual scoring. Three groups of properties are assessed: (a) strength and replicability of the factorial solution, (b) determinacy and accuracy of the individual score estimates, and (c) closeness to unidimensionality in the case of multidimensional solutions. Within each group, indices are considered for two types of factor-analytic models: the linear model for continuous responses and the categorical-variable-methodology model that treats the item scores as ordered-categorical. All the indices proposed have been implemented in a noncommercial and widely known program for exploratory factor analysis. The usefulness of the proposal is illustrated with a real data example in the personality domain.

Cognitive Ability in Late Life and Onset of Physical Frailty: The Lothian Birth Cohort 1936.

ObjectivesTo investigate whether poorer cognitive ability is a risk factor for development of physical frailty and whether this risk varies according to cognitive domain.DesignProspective longitudinal study with 6‐year follow‐up.SettingEdinburgh, Scotland.ParticipantsMembers of the Lothian Birth Cohort 1936 (N = 594).MeasurementsFrailty was assessed at ages 70 and 76 using the Fried criteria. Cognitive function was assessed at age 70, 73, and 76. Factor score estimates were derived for baseline level of and change in four cognitive domains: visuospatial ability, memory, processing speed, and crystallized cognitive ability.ResultsHigher baseline levels of processing speed, memory, visuospatial ability and crystallized ability at age 70, and less decline in speed, memory, and crystallized ability were associated with less risk of becoming physically frail by age 76. When all cognitive domains were modelled together, processing speed was the only domain associated with frailty risk, for a standard deviation (SD) increment in initial level of processing speed, the risk of frailty was 47% less (0.53 95% confidence interval (CI) = 0.33–0.85) after adjustment for age, sex, baseline frailty status, social class, depressive symptoms, number of chronic physical diseases, levels of inflammatory biomarkers, and other cognitive factor score estimates; for a SD increment in processing speed change (less decline) risk of frailty was 74% less (RRR = 0.26, 95% CI = 0.16–0.42). When additional analyses were conducted using a single test of processing speed that did not require fast motor responses (inspection time), results were similar.ConclusionsThe speed with which older adults process information and the rate at which this declines over time may be an important indicator of the risk of physical frailty.

Assessing the Equitable and Sustainable Well-Being of the Italian Provinces

In recent years there has been an increasing interest in the measurement of well-being of individuals and societies. Influenced by the “beyond GDP” initiative, in 2012 the Italian National Institute of Statistics (ISTAT) and the National Council for Economics and Labour launched the Equitable and Sustainable Well-being (BES, from the Italian acronym of “Benessere Equo e Sostenibile”) project, a set of 134 indicators aimed at capturing the Italian well-being. Lately, the debate on how to measure the well-being moved from the national level to the local one. Following this new trend, ISTAT introduced a set of 88 indicators for the local well-being (at NUTS3 level), the so called “Provinces’ BES”. Based on this project, aim of the paper is to provide an exploratory analysis for detecting groups of Italian provinces that share similar well-being profiles. In particular, we first apply a factor analysis with the aim to reduce the high number of indicators and, grounded on these results, we then create groups of the Italian provinces, applying the cluster analysis, in order to find similarity among them. Finally, based on the result of the factor analysis, for each domain and for each Italian province, we construct a composite indicator that is a linear combination of the estimated factor scores, with weights based on the Gini index of concentration.

Reliability Estimates for Three Factor Score Estimators

Estimates for the reliability of Thurstone’s regression factor score estimator, Bartlett’s factor score estimator, and McDonald’s factor score estimator were proposed. Moreover, conditions for equal reliability of the factor score estimators were presented and the reliability estimates were compared by means of simulation studies. Under conditions inducing unequal reliabilities, reliability estimates were largest for the regression score estimator and lowest for McDonald’s factor score estimator. We provide an R-script and an SPSS-script for the computation of the respective reliability estimates.

Lower Bounds to the Reliabilities of Factor Score Estimators.

Under the general common factor model, the reliabilities of factor score estimators might be of more interest than the reliability of the total score (the unweighted sum of item scores). In this paper, lower bounds to the reliabilities of Thurstone's factor score estimators, Bartlett's factor score estimators, and McDonald's factor score estimators are derived and conditions are given under which these lower bounds are equal. The relative performance of the derived lower bounds is studied using classic example data sets. The results show that estimates of the lower bounds to the reliabilities of Thurstone's factor score estimators are greater than or equal to the estimates of the lower bounds to the reliabilities of Bartlett's and McDonald's factor score estimators.

Improving Factor Score Estimation Through the Use of Observed Background Characteristics

A challenge facing nearly all studies in the psychological sciences is how to best combine multiple items into a valid and reliable score to be used in subsequent modeling. The most ubiquitous method is to compute a mean of items, but more contemporary approaches use various forms of latent score estimation. Regardless of approach, outside of large-scale testing applications, scoring models rarely include background characteristics to improve score quality. This article used a Monte Carlo simulation design to study score quality for different psychometric models that did and did not include covariates across levels of sample size, number of items, and degree of measurement invariance. The inclusion of covariates improved score quality for nearly all design factors, and in no case did the covariates degrade score quality relative to not considering the influences at all. Results suggest that the inclusion of observed covariates can improve factor score estimation.

Evaluating bifactor models: Calculating and interpreting statistical indices.

Bifactor measurement models are increasingly being applied to personality and psychopathology measures (Reise, 2012). In this work, authors generally have emphasized model fit, and their typical conclusion is that a bifactor model provides a superior fit relative to alternative subordinate models. Often unexplored, however, are important statistical indices that can substantially improve the psychometric analysis of a measure. We provide a review of the particularly valuable statistical indices one can derive from bifactor models. They include omega reliability coefficients, factor determinacy, construct reliability, explained common variance, and percentage of uncontaminated correlations. We describe how these indices can be calculated and used to inform: (a) the quality of unit-weighted total and subscale score composites, as well as factor score estimates, and (b) the specification and quality of a measurement model in structural equation modeling. (PsycINFO Database Record

Multiple Imputation of missing values in exploratory factor analysis of multidimensional scales: estimating latent trait scores

<p>Researchers frequently have to analyze scales in which some participants have failed to respond to some items. In this paper we focus on the exploratory factor analysis of multidimensional scales (i.e., scales that consist of a number of subscales) where each subscale is made up of a number of Likert-type items, and the aim of the analysis is to estimate participants’ scores on the corresponding latent traits. Our approach uses the following steps: (1) multiple imputation creates several copies of the data, in which the missing values are imputed; (2) each copy of the data is subject to independent factor analysis, and the same number of factors is extracted from all copies; (3) all factor solutions are simultaneously orthogonally (or obliquely) rotated so that they are both (a) factorially simple, and (b) as similar to one another as possible; (4) latent trait scores are estimated for ordinal data in each copy; and (5) participants’ scores on the latent traits are estimated as the average of the estimates of the latent traits obtained in the copies. We applied the approach in a real dataset where missing responses were artificially introduced following a real pattern of non-responses and a simulation study based on artificial datasets. The results show that our approach was able to compute factor score estimates even for participants that have missing data.</p>

A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts

In the common factor model the observed data is conceptually split into a common covariance producing part and an uncorrelated unique part. The common factor model is fitted to the data itself and a new method is introduced for the simultaneous estimation of loadings, unique variances, factor scores, and unique parts. The method is based on Minimum Rank Factor Analysis and allows for the percentage of explained common variance to be computed. Taking into account factor indeterminacy, an explicit description of the complete class of solutions for the factor scores and unique parts is given. The method is evaluated in a simulation study and fitted to a dataset in the literature.

Using estimated factor scores from a bifactor analysis to examine the unique effects of the latent variables measured by the WAIS-IV on academic achievement.

This study used estimated factor scores from a bifactor analysis of the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV) to examine the unique effects of its latent variables on academic achievement. In doing so, we addressed the potential limitation of multicollinearity in previous studies of the incremental validity of the WAIS-IV. First, factor scores representing psychometric g and 4 group factors representing the WAIS-IV index scales were computed from a bifactor model. Subtest and composite scores for the Wechsler Individual Achievement Test-Third Edition (WIAT-II) were then predicted from these estimated factor scores in simultaneous multiple regression. Results of this study only partially replicated the findings of previous research on the incremental validity of scores that can be derived from performance on the WAIS-IV. Although we found that psychometric g is the most important underlying construct measured by the WAIS-IV for the prediction of academic achievement in general, results indicated that the unique effect of Verbal Comprehension is also important for predicting achievement in reading, spelling, and oral communication skills. Based on these results, measures of both psychometric g and Verbal Comprehension could be cautiously interpreted when considering high school students' performance in these areas of achievement.

Qualidade Física de Solos em Uso Agrícola na Região Semiárida do Estado da Bahia

RESUMO A conversão de uma condição natural para uma de uso agrícola pode impor mudanças em atributos, propriedades e processos do solo e trazer consequências ambientais para a região de sua abrangência. O objetivo deste trabalho foi avaliar a qualidade física do solo em áreas agrícolas de municípios do entorno do lago de Sobradinho, região semiárida do Estado da Bahia, tendo como ferramenta técnicas estatísticas de análise multivariada. Inicialmente, aplicaram-se as análises estatísticas descritiva e de correlação e o teste de normalidade, que serviram como pressupostos para realizar análise fatorial e estimativa dos escores fatoriais. Com base nesses, determinou-se o índice de qualidade física de solo para as profundidades de 0,00-0,10; 0,10-0,20; e 0,20-0,40 m, respectivamente, cujo principal objetivo foi classificar os solos como bom, regular e ruim, de acordo com o desempenho dos seus atributos físicos. Em seguida, realizou-se a análise discriminante para validação dos índices construídos a partir dos resultados da análise fatorial, bem como conhecer os atributos físicos do solo que influenciam e estão associados à qualidade desse na área agrícola da região. A densidade do solo (Ds), macroporosidade (Ma) e microporosidade (Mi) foram os atributos que se destacaram como indicadores de qualidade, pois apresentaram maior peso relativo nos modelos de discriminação dos sítios amostrados: Ds, Ma e Mi, nas camadas de 0,00-0,10 e 0,10-0,20 m; e Mi e Ds, de 0,20-0,40 m, sugerindo que nas condições estudadas essas variáveis são as principais responsáveis pela qualidade física dos solos. No geral, a qualidade física do solo não foi considerada ideal, fato que pode ser atribuído às práticas de manejo adotadas e, sobretudo, aos baixos teores de matéria orgânica e à textura extremamente arenosa, conferindo fragilidade aos solos da região.

Searching for causal networks involving latent variables in complex traits: Application to growth, carcass, and meat quality traits in pigs.

Structural equation models (SEQM) can be used to model causal relationships between multiple variables in multivariate systems. Among the strengths of SEQM is its ability to consider causal links between latent variables. The use of latent variables allows modeling complex phenomena while reducing at the same time the dimensionality of the data. One relevant aspect in the quantitative genetics context is the possibility of correlated genetic effects influencing sets of variables under study. Under this scenario, if one aims at inferring causality among latent variables, genetic covariances act as confounders if ignored. Here we describe a methodology for assessing causal networks involving latent variables underlying complex phenotypic traits. The first step of the method consists of the construction of latent variables defined on the basis of prior knowledge and biological interest. These latent variables are jointly evaluated using confirmatory factor analysis. The estimated factor scores are then used as phenotypes for fitting a multivariate mixed model to obtain the covariance matrix of latent variables conditional on the genetic effects. Finally, causal relationships between the adjusted latent variables are evaluated using different SEQM with alternative causal specifications. We have applied this method to a data set with pigs for which several phenotypes were recorded over time. Five different latent variables were evaluated to explore causal links between growth, carcass, and meat quality traits. The measurement model, which included 5 latent variables capturing the information conveyed by 19 different phenotypic traits, showed an acceptable fit to data (e.g., χ/df = 1.3, root-mean-square error of approximation = 0.028, standardized root-mean-square residual = 0.041). Causal links between latent variables were explored after removing genetic confounders. Interestingly, we found that both growth (-0.160) and carcass traits (-0.500) have a significant negative causal effect on quality traits (-value ≤ 0.001). This result may have important implications for strategies for pig production improvement. More generally, the proposed method allows further learning regarding phenotypic causal structures underlying complex traits in farm species.

A common spatial factor analysis model for measured neighborhood-level characteristics: The Multi-Ethnic Study of Atherosclerosis

The purpose of this study was to reduce the dimensionality of a set of neighborhood-level variables collected on participants in the Multi-Ethnic Study of Atherosclerosis (MESA) while appropriately accounting for the spatial structure of the data. A common spatial factor analysis model in the Bayesian setting was utilized in order to properly characterize dependencies in the data. Results suggest that use of the spatial factor model can result in more precise estimation of factor scores, improved insight into the spatial patterns in the data, and the ability to more accurately assess associations between the neighborhood environment and health outcomes.

Common Etiological Sources of Anxiety, Depression, and Somatic Complaints in Adolescents: A Multiple Rater twin Study.

Somatic complaints in children and adolescents may be considered part of a broader spectrum of internalizing disorders that include anxiety and depression. Previous research on the topic has focused mainly on the relationship between anxiety and depression without investigating how common somatic symptoms relate to an underlying factor and its etiology. Based on the classical twin design with monozygotic and dizygotic twins reared together, our study aimed to explore the extent to which the covariation between three phenotypes in adolescent girls and boys can be represented by a latent internalizing factor, with a focus on both common and specific etiological sources. A population-based sample of twins aged 12-18 years and their mothers and fathers (N = 1394 families) responded to questionnaire items measuring the three phenotypes. Informants' ratings were collapsed using full information maximum likelihood estimated factor scores. Multivariate genetic analyses were conducted to examine the etiological structure of concurrent symptoms. The best fitting model was an ACE common pathway model without sex limitation and with one substantially heritable (44%) latent factor shared by the phenotypes. Concurrent symptoms also resulted from shared (25%) and non-shared (31%) environments. The factor loaded most on depression symptoms and least on somatic complaints. Trait-specific influences explained 44% of depression variance, 59% of anxiety variance, and 65% of somatic variance. Our results suggest the presence of a general internalizing factor along which somatic complaints and mental distress can be modeled. However, specific influences make the symptom types distinguishable.

Contamination assessments of surface water in coastal lagoon (Maluan Bay, China) incorporating biomarker responses and bioaccumulation in hepatopancreas of exposed shrimp (Litopenaeus vannamei)—an integrative approach

Maluan Bay, characterized by various degrees of anthropogenic contamination, is considered as one of the most industrialized and urbanized coastal lagoon in China, where large amounts of metal contaminants in surface water and biota were detected in previous studies. However, no clear discriminating power among sampling sites could be made only through comparisons between contaminant levels and Environmental Quality Standards and especially biological-based monitoring integrating biomarkers and bioaccumulation of exposure are scarce. For this purpose, antioxidants enzymes (superoxide dismutase, catalase, and glutathione peroxidase) and glutathione-S-transferase were assessed using the hepatopancreas of shrimp Litopenaeus vannamei after 7days laboratory exposure under controlled conditions to characterize the effects of polluted waters to shrimps. The metal concentrations of sampled water and bioaccumulation in hepatopancreatic tissues were also analyzed, and data were linked to biomarkers' responses by multivariate (principal component analysis-factor) analysis. A representation of estimated factor scores was performed to confirm the factor descriptions classifying the pollution status and characterizing the studied sites, which pointed out the impact of multiple sources of contaminants to the water quality and provided further evidences to the existence of clear pollution and toxicological gradients in critical areas. The results of the present investigation underlined that the integrated approach could be a powerful tool for the identification of causal toxic contaminants in complex mixtures and the assessment of human-induced environmental quality of the system in coastal zones.

Estimation of Factor Scores of Impressions of Question and Answer Statements

To eliminate mismatches between the intentions of questioners and respondents, we have conducted impression evaluation experiment and nine factors are obtained. Factor scores of the statements used in the experiments are obtained. Those of other statements, however, cannot be obtained. This paper proposes a method of estimating the factor scores of other statements through multiple regression analysis applied to those feature values of statements. Syntactic information of statements, word imageability, closing sentence expressions, word familiarity and notation validity are adopted as feature values of statements. It is shown that overall estimation accuracy is very good for all the factors. This research uses the data of “Yahoo! Chiebukuro” given to National Institute of Informatics by Yahoo Japan Corporation.

Using exploratory factor analysis of FFQ data to identify dietary patterns among Yup'ik people

An FFQ developed by the Center for Alaska Native Health Research for studies in Yup'ik people includes market foods and subsistence foods such as moose, seal, waterfowl and salmon that may be related to disease risk. Because the FFQ contains >100 food items, we sought to characterize dietary patterns more simply for use in ongoing pharmacogenomics studies. Exploratory factor analysis was used to derive a small number of 'factors' that explain a substantial amount of the variation in the Yup'ik diet. We estimated factor scores and measured associations with demographic characteristics and biomarkers. South-west Alaska, USA. Yup'ik people (n 358) aged ≥18 years. We identified three factors that each accounted for ≥10 % of the common variance: the first characterized by 'processed foods' (e.g. salty snacks, sweetened cereals); the second by 'fruits and vegetables' (e.g. fresh citrus, potato salad); and the third by 'subsistence foods' (seal or walrus soup, non-oily fish). Participants from coastal communities had higher values for the 'subsistence' factor, whereas participants from inland communities had higher values for the 'fruits and vegetables' factor. A biomarker of marine intake, δ 15N, was correlated with the 'subsistence' factor, whereas a biomarker of corn- and sugarcane-based market food intake, δ 13C, was correlated with 'processed foods'. The exploratory factor analysis identified three factors that appeared to reflect dietary patterns among Yup'ik based on associations with participant characteristics and biomarkers. These factors will be useful for chronic disease studies in this population.

A Comparison of Factor Score Estimation Methods in the Presence of Missing Data: Reliability and an Application to Nicotine Dependence

Factor score estimation is a controversial topic in psychometrics, and the estimation of factor scores from exploratory factor models has historically received a great deal of attention. However, both confirmatory factor models and the existence of missing data have generally been ignored in this debate. This article presents a simulation study that compares the reliability of sum scores, regression-based and expected posterior methods for factor score estimation for confirmatory factor models in the presence of missing data. Although all methods perform reasonably well with complete data, expected posterior-weighted (full) maximum likelihood methods are significantly more reliable than sum scores and regression estimators in the presence of missing data. Factor score reliability for complete data can be predicted by Guttman's 1955 formula for factor communality. Furthermore, factor score reliability for incomplete data can be reasonably approximated by communality raised to the power. An empirical demonstration shows that the full maximum likelihood method best preserves the relationship between nicotine dependence and a genetic predictor under missing data. Implications and recommendations for applied research are discussed.