Factor Score Estimates Research Articles

Exploring the Potential of Variational Autoencoders for Modeling Nonlinear Relationships in Psychological Data.

Latent variables analysis is an important part of psychometric research. In this context, factor analysis and other related techniques have been widely applied for the investigation of the internal structure of psychometric tests. However, these methods perform a linear dimensionality reduction under a series of assumptions that could not always be verified in psychological data. Predictive techniques, such as artificial neural networks, could complement and improve the exploration of latent space, overcoming the limits of traditional methods. In this study, we explore the latent space generated by a particular artificial neural network: the variational autoencoder. This autoencoder could perform a nonlinear dimensionality reduction and encourage the latent features to follow a predefined distribution (usually a normal distribution) by learning the most important relationships hidden in data. In this study, we investigate the capacity of autoencoders to model item-factor relationships in simulated data, which encompasses linear and nonlinear associations. We also extend our investigation to a real dataset. Results on simulated data show that the variational autoencoder performs similarly to factor analysis when the relationships among observed and latent variables are linear, and it is able to reproduce the factor scores. Moreover, results on nonlinear data show that, differently than factor analysis, it can also learn to reproduce nonlinear relationships among observed variables and factors. The factor score estimates are also more accurate with respect to factor analysis. The real case results confirm the potential of the autoencoder in reducing dimensionality with mild assumptions on input data and in recognizing the function that links observed and latent variables.

Development and validation of a questionnaire about reasons for academic cheating by nursing students: A cross-sectional study.

Cheating behavior is spreading among nursing students worldwide, necessitating the development of a validated questionnaire evaluating the reasons for such behavior. Nursing students (N = 482) from 2 universities in Saudi Arabia participated in this observational study. A survey containing items on socio-demographics and the 33-item Reasons for Cheating Scale (RCS) was completed by the respondents. The RCS had a 1-factor structure; the model fit indices were similar between the 1-, 2-, and 3-factor models, but the inter-factor correlations were too high for the 2- and 3-factor models. The measures of the quality of the factor score estimates were as follows: factor determinacy index, 0.987; expected a posteriori marginal reliability, 0.974; sensitivity ratio, 6.178; and expected percentage of true differences, 97.3%. The measures of the closeness to unidimensionality for the overall RCS were as follows: unidimensional congruence, 0.957; explained common variance, 0.875; and mean item residual absolute loading, 0.223. The intraclass correlation coefficient and McDonald's omega were 0.96 (CI: 0.93-0.98) and 0.962 (95% CI: 0.958-0.967), respectively. The severity score, infit, and outfit ranged from -0.847 to -2.015, 0.813 to 1.742, and 0.837 to 1.661, respectively. For all RCS items, the thresholds ranked τi1 < τi2 < τi3 < τi4 and showed invariance between the sexes. The RCS showed robust psychometric validity for both classical and item response theory parameters. It also had excellent test-retest reliability, internal consistency, item discrimination, factorial validity, measurement invariance, and ordered threshold level for the responses. Therefore, the RCS is a valid and reliable tool for assessing cheating behavior among nursing students.

Matrix Decomposition Approach for Structural Equation Modeling as an Alternative to Covariance Structure Analysis and Its Theoretical Properties

Matrix decomposition structural equation modeling (MDSEM) is introduced as a novel approach in structural equation modeling, contrasting with traditional structural equation modeling (SEM). MDSEM approximates the data matrix using a model generated by the hypothetical model and addresses limitations faced by conventional SEM procedures by emphasizing factor analysis with L 2 penalization. Key advantages of MDSEM include preventing improper solutions, the ability to compute observation-wise residuals without post-hoc factor score estimation and ease in identifying equivalent models. These benefits are attributed to its matrix decomposition techniques, allowing for direct model fitting to the data matrix, unlike the covariance structure fitting in CS-SEM. An iterative algorithm for parameter estimation is proposed, guaranteeing a monotonically decreasing function value. Theoretical properties of MDSEM are examined, revealing its shared characteristics with existing factor analysis and SEM. Numerical simulations and real data examples validate that MDSEM produces results comparable to existing methods when adequately calibrated.

Measuring the variability of personality traits with interval responses: Psychometric properties of the dual-range slider response format

Measuring the variability in persons’ behaviors and experiences using ecological momentary assessment is time-consuming and costly. We investigate whether interval responses provided through a dual-range slider (DRS) response format can be used as a simple and efficient alternative: Respondents indicate variability in their behavior in a retrospective rating by choosing a lower and an upper bound on a continuous, bounded scale. We investigate the psychometric properties of this response format as a prerequisite for further validation. First, we assess the test–retest reliability of factor-score estimates for the width of DRS intervals. Second, we test whether factor-score estimates of the visual analog scale (VAS) and the location of DRS intervals show convergent validity. Third, we investigate whether factor-score estimates for the DRS are uncorrelated between different personality scales. We present a longitudinal multitrait-multimethod study using two personality scales (Extraversion, Conscientiousness) and two response formats (VAS, DRS) at two measurement occasions (6–8 weeks apart) for which we estimate factor-score correlations in a joint item response theory model. The test–retest reliability of the width of DRS intervals was high (ρ^≥.73\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\\rho } \\ge .73$$\\end{document}). Also, convergent validity between location scores of VAS and DRS was high (ρ^≥.88\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\\rho } \\ge .88$$\\end{document}). Conversely, discriminant validity of the width of DRS intervals between Extraversion and Conscientiousness was poor (ρ^≥.94\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\\rho } \\ge .94$$\\end{document}). In conclusion, the DRS seems to be a reliable response format that could be used to measure the central tendency of a trait equivalently to the VAS. However, it might not be well suited for measuring intra-individual variability in personality traits.

A novel approach to model cumulative stress: Area under the s-factor curve

ObjectiveUsing a large longitudinal sample of adults from the Midlife in the United States (MIDUS) study, the present study extended a recently developed hierarchical model to determine how best to model the accumulation of stressors, and to determine whether the rate of change in stressors or traditional composite scores of stressors are stronger predictors of health outcomes. MethodWe used factor analysis to estimate a stress-factor score and then, to operationalize the accumulation of stressors we examined five approaches to aggregating information about repeated exposures to multiple stressors. The predictive validity of these approaches was then assessed in relation to different health outcomes. ResultsThe prediction of chronic conditions, body mass index, difficulty with activities of daily living, executive function, and episodic memory later in life was strongest when the accumulation of stressors was modeled using total area under the curve (AUC) of estimated factor scores, compared to composite scores that have traditionally been used in studies of cumulative stress, as well as linear rates of change. ConclusionsLike endogenous, biological markers of stress reactivity, AUC for individual trajectories of self-reported stressors shows promise as a data reduction technique to model the accumulation of stressors in longitudinal studies. Overall, our results indicate that considering different quantitative models is critical to understanding the sequelae and predictive power of psychosocial stressors from midlife to late adulthood.

Summed versus estimated factor scores: Considering uncertainties when using observed scores.

Summed versus estimated factor scores: Considering uncertainties when using observed scores.

USING INTERPERSONAL RELATIONSHIPS AND SOCIAL NETWORK TO UNDERSTAND ELDER MISTREATMENT RECURRENCE

Abstract The incidence of elder mistreatment are often recurrent rather than one-time. The recurrence of mistreatment contributes to severe physical and psychological problems for victims and negative social consequences. Poor interpersonal relationships and social isolation are the main factors of mistreatment occurrence in the literature. However, very few studies have considered how the quality of interpersonal relationships and the level of social networks affect the likelihood of mistreatment recurrence. We used the National Social Life, Health, and Aging Project waves 1 (2005–06) and 3 (2015–16) data for longitudinal analyses (N=1,592). The quality of interpersonal relationships (i.e., supportive relationship, strained relationship) and the level of social networks (i.e., social engagement, social isolation, and feeling safe in society) were conceptualized using factor analysis to estimate factor scores. Logistic regression models were built to predict the risk of recurrent mistreatment using interpersonal relationship quality and the level of the social networks. Controlling for demographic variables, victims in wave 1 with support from interpersonal relationships are more likely to experience reoccurring mistreatment (p&amp;lt; 0.05, OR=1.58). Model interaction effects indicated that older adults with strained interpersonal relationships and low social engagement are most at risk of experiencing mistreatment recurrence. The surprising finding that supportive interpersonal relationships are positively associated with mistreatment recurrence might indicate that those who support older adults are potential perpetrators. Identifying potential perpetrators and assessing the quality of interpersonal relationships and social networks are essential to preventing mistreatment recurrence.

Factor score estimation in multimethod measurement designs with planned missing data.

Multimethod measurement designs with planned missing data (MMM-PMD) aim at combining cheap proxy methods (e.g., self-reports) with an expensive gold standard method (e.g., biomarker) in order to improve the cost-efficiency of research designs. This article presents a comprehensive simulation study investigating whether accurate factor scores with trustworthy confidence or credible intervals for the gold standard method can be obtained in MMM-PMD designs. The results indicate that the Bartlett-FIML, regression-FIML, and fully Bayesian estimator perform equally well in terms of recovering the true rank-order and absolute level of the factor scores for subjects with complete data. However, for subjects with planned missing data the estimated factor scores are considerably biased and cannot be computed with the Bartlett-FIML estimator. The confidence or credible intervals for the estimated factor scores are trustworthy for complete cases. For subjects with planned missing data, the coverage rates vary considerably across conditions. Thus, the present study illustrates that individual scores from MMM-PMD designs should not be used for consequential individual decisions. Still, factor scores from MMM-PMD designs might be useful when used for secondary analyses that rely on group-level statistics like computing propensity scores for matching purposes or for factor score regression. The simulation results underline that multiple reliable proxy methods that are highly correlated with the gold standard method but are not highly correlated with each other should be administered to maximize the accuracy of the estimated factor scores as well as the trustworthiness of the corresponding confidence or credible intervals. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Thinking About Sum Scores Yet Again, Maybe the Last Time, We Don't Know, Oh No . . .: A Comment on.

The relative advantages and disadvantages of sum scores and estimated factor scores are issues of concern for substantive research in psychology. Recently, while championing estimated factor scores over sum scores, McNeish offered a trenchant rejoinder to an article by Widaman and Revelle, which had critiqued an earlier paper by McNeish and Wolf. In the recent contribution, McNeish misrepresented a number of claims by Widaman and Revelle, rendering moot his criticisms of Widaman and Revelle. Notably, McNeish chose to avoid confronting a key strength of sum scores stressed by Widaman and Revelle-the greater comparability of results across studies if sum scores are used. Instead, McNeish pivoted to present a host of simulation studies to identify relative strengths of estimated factor scores. Here, we review our prior claims and, in the process, deflect purported criticisms by McNeish. We discuss briefly issues related to simulated data and empirical data that provide evidence of strengths of each type of score. In doing so, we identified a second strength of sum scores: superior cross-validation of results across independent samples of empirical data, at least for samples of moderate size. We close with consideration of four general issues concerning sum scores and estimated factor scores that highlight the contrasts between positions offered by McNeish and by us, issues of importance when pursuing applied research in our field.

Comparing Methods for Factor Score Estimation in Structural Equation Modeling: The Role of Network Analysis

Precisely estimating factor scores is challenging, especially when models are mis-specified. Stemming from network analysis, centrality measures offer an alternative approach to estimating the scores. Using a two-fold simulation design with varying availability of a priori theoretical knowledge, this study implemented hybrid centrality to estimate factor scores and compared the performance with traditional methods, where both proper and improper specifications were considered. In supervised scenarios, network scores using hybrid centrality performed similarly to CFA scores for correctly specified models. The network scores were more accurate when sample sizes were small or test reliability was low, and also demonstrated higher robustness under misspecification. In the second fold, network scores performed better than EFA scores when structure knowledge was unavailable, as the LoGo algorithm of network analysis demonstrated the best performance in retaining the correct factor structure. The results suggest that network analysis can be a better choice for factor score estimation under various conditions.

Cognitive domain harmonization and cocalibration in studies of older adults.

Studies use different instruments to measure cognitirating cognitive tests permit direct comparisons of individuals across studies and pooling data for joint analyses. We began our legacy item bank with data from the Adult Changes in Thought study (n = 5,546), the Alzheimer's Disease Neuroimaging Initiative (n = 3,016), the Rush Memory and Aging Project (n = 2,163), and the Religious on such as the Mini-Mental State Examination, the Alzheimer's Disease Assessment Scale-Cognitive Subscale, the Wechsler Memory Scale, and the Boston Naming Test. CocalibOrders Study (n = 1,456). Our workflow begins with categorizing items administered in each study as indicators of memory, executive functioning, language, visuospatial functioning, or none of these domains. We use confirmatory factor analysis models with data from the most recent visit on the pooled sample across these four studies for cocalibration and derive item parameters for all items. Using these item parameters, we then estimate factor scores along with corresponding standard errors for each domain for each study. We added additional studies to our pipeline as available and focused on thorough consideration of candidate anchor items with identical content and administration methods across studies. Prestatistical harmonization steps such qualitative and quantitative assessment of granular cognitive items and evaluating factor structure are important steps when trying to cocalibrate cognitive scores across studies. We have cocalibrated cognitive data and derived scores for four domains for 76,723 individuals across 10 studies. We have implemented a large-scale effort to harmonize and cocalibrate cognitive domain scores across multiple studies of cognitive aging. Scores on the same metric facilitate meta-analyses of cognitive outcomes across studies or the joint analysis of individual data across studies. Our systematic approach allows for cocalibration of additional studies as they become available and our growing item bank enables robust investigation of cognition in the context of aging and dementia. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A Cautionary Note Regarding Multilevel Factor Score Estimates from Lavaan

To compute factor score estimates, lavaan version 0.6–12 offers the function lavPredict( ) that can not only be applied in single-level modeling but also in multilevel modeling, where characteristics of higher-level units such as working environments or team leaders are often assessed by ratings of employees. Surprisingly, the function provides results that deviate from the expected ones. Specifically, whereas the function yields correct EAP estimates of higher-level factors, the ML estimates are counterintuitive and possibly incorrect. Moreover, the function does not provide the expected standard errors. I illustrate these issues using an example from organizational research where team leaders are evaluated by their employees, and I discuss these issues from a measurement perspective.

Value-based decision-making network functional connectivity correlates with substance use and delay discounting behaviour among young adults

Substance use disorders are characterized by reduced control over the quantity and frequency of psychoactive substance use and impairments in social and occupational functioning. They are associated with poor treatment compliance and high rates of relapse. Identification of neural susceptibility biomarkers that index risk for developing a substance use disorder can facilitate earlier identification and treatment. Here, we aimed to identify the neurobiological correlates of substance use frequency and severity amongst a sample of 1,200 (652 females) participants aged 22–37 years from the Human Connectome Project. Substance use behaviour across eight classes (alcohol, tobacco, marijuana, sedatives, hallucinogens, cocaine, stimulants, opiates) was measured using the Semi-Structured Assessment for the Genetics of Alcoholism. We explored the latent organization of substance use behaviour using a combination of exploratory structural equation modelling, latent class analysis, and factor mixture modelling to reveal a unidimensional continuum of substance use behaviour. Participants could be rank ordered along a unitary severity spectrum encompassing frequency of use of all eight substance classes, with factor score estimates generated to represent each participant’s substance use severity. Factor score estimates and delay discounting scores were compared with functional connectivity in 650 participants with imaging data using the Network-based Statistic. This neuroimaging cohort excludes participants aged 31 and over. We identified brain regions and connections correlated with impulsive decision-making and poly-substance use, with the medial orbitofrontal, lateral prefrontal and posterior parietal cortices emerging as key hubs. Functional connectivity of these networks could serve as susceptibility biomarkers for substance use disorders, informing earlier identification and treatment.

ELDER MISTREATMENT AND RELATIONSHIP QUALITY: SECONDARY DATA ANALYSIS USING DATA FROM THE NSHAP

Abstract As social networks shrink with age, older adults value the importance of interpersonal relationships with close others, such as partners, family and friends. Previous studies focused on perpetrators' and victims' characteristics; however, few studies examined the relationships with close others and the incidence of elder mistreatment. This study used the National Social Life, Health, and Aging Project Wave 1 data (2005-06) to examine the correlations between relationship quality with close others and the occurrence of mistreatment among older adults (N = 3005). Based on spousal relationship literature using the NSHAP data, factor analysis was used to estimate factor scores conceptualizing two domains of relationship quality: relationship support (positive dimensions of relationship), and relationship strain (negative dimensions of the relationship). Logistic regression models were used to test the relationship between the relationship quality factor scores and the likelihood of each mistreatment type while controlling for gender, education, age, and race. Psychological abuse was more likely for older adults experiencing relationship strain with spouse (OR=1.82, p&amp;lt;.001), family (OR=1.75, p&amp;lt;.001), and/or friends (OR=1.67, p&amp;lt; 0.001). Financial abuse was more likely for those experiencing poor relationship support with family (OR=1.34, p&amp;lt;.05) and those experiencing relationship strain with friends (OR=1.47, p&amp;lt;.01). However, relationship quality was not correlated with likelihood of physical abuse. Interpersonal relationships with close others could provide stronger support and care, but relationship strain might contribute to mistreatment. When determining safeguarding gatekeepers to protect older adults from potential mistreatment, interventions should consider the quality and composition of interpersonal relationships with close others.

Latent Variable Estimation in Factor Analysis and Item Response Theory

This essay sketches the historical development of latent variable scoring procedures in the item response theory (IRT) and factor analysis literatures, observing that the most commonly used score estimates in both traditions are fundamentally the same; only methods of calculation differ. Different procedures have been used to derive factor score estimates and latent variable estimates in IRT, and different computational procedures have been the result. Due to differences in the context of score usage, challenges have led to different solutions in the IRT and factor analytic traditions. The needs for bias corrections differ, as do the corrections that have been proposed. While the standard factor analysis model has naturally Gaussian likelihoods, IRT does not, but in IRT normal approximations have been used in various contexts to make the IRT computations more like those of factor analysis. Finally, factor analysis alone has been the home of decades of controversy over factor score indeterminacy, while IRT has not, even though the scores in question are the same. That is an artifact of history and the ways the models have been written in the IRT and factor analytic literatures. IRT has never been plagued with questions of indeterminacy, which helps to clarify the position that what is referred to as indeterminacy is not a problem.

Informing Harmonization Decisions in Integrative Data Analysis: Exploring the Measurement Multiverse.

Combining datasets in an integrative data analysis (IDA) requires researchers to make a number of decisions about how best to harmonize item responses across datasets. This entails two sets of steps: logical harmonization, which involves combining items which appear similar across datasets, and analytic harmonization, which involves using psychometric models to find and account for cross-study differences in measurement. Embedded in logical and analytic harmonization are many decisions, from deciding whether items can be combined prima facie to how best to find covariate effects on specific items. Researchers may not have specific hypotheses about these decisions, and each individual choice may seem arbitrary, but the cumulative effects of these decisions are unknown. In the current study, we conducted an IDA of the relationship between alcohol use and delinquency using three datasets (total N = 2245). For analytic harmonization, we used moderated nonlinear factor analysis (MNLFA) to generate factor scores for delinquency. We conducted both logical and analytic harmonization 72 times, each time making a different set of decisions. We assessed the cumulative influence of these decisions on MNLFA parameter estimates, factor scores, and estimates of the relationship between delinquency and alcohol use. There were differences across paths in MNLFA parameter estimates, but fewer differences in estimates of factor scores and regression parameters linking delinquency to alcohol use. These results suggest that factor scores may be relatively robust to subtly different decisions in data harmonization, and measurement model parameters are less so.

Application of 2‑gram and 3‑gram to Obtain Factor Scores of Statements Posted at Q&A Sites

With a view to solving the mismatches between the ideas of questioners and respondents of Question and Answer (Q&A) sites, impression evaluation experiments have resulted in obtaining nine factors of impressions. Then through multiple regression analysis factor scores have been estimated by utilizing the feature values of statements, such as syntactic information, etc. Those factor scores calculated were subsequently employed for inspecting their potential to detect respondents who are expected and likely to appropriately answer a newly posted question. Nevertheless, our method so far has largely depended on the syntactic information extracted through morphological analysis. Moreover, the number of explanatory variables utilized for obtaining factor scores has been appreciably extravagant and complex. Thus, instead of morphological analysis, 2-gram was applied to the explanatory variables to estimate factor scores. The analysis result with the application of 2-gram has led to greater estimation accuracy than the case of morphological analysis for all nine factors. For further perception and comparison, in this paper, 3-gram was applied to the feature values in place of 2-gram or morphological analysis, in a similar fashion as the previous analysis using 2-gram. Further analysis has shown that 2-gram and 3-gram outperform morphological analysis in terms of estimation accuracy. Comparing the results for the nine factors, 2-gram showed the best results. It could also be suggested that a mere 2-gram or 3-gram would be sufficient in applying N-gram as syntactic information of the feature values to estimate factor scores.

Structured Factor Analysis: A Data Matrix-Based Alternative Approach to Structural Equation Modeling

Jöreskog’s covariance-based approach (JCA) has been considered a standard method for structural equation modeling. However, JCA is prone to the occurrence of improper solutions and cannot make probabilistic inferences about the true factor scores. To address the enduring issues of JCA, we propose a data matrix-based alternative, termed structured factor analysis (SFA). Given a data matrix of indicators, SFA begins by estimating both measurement model parameters and factor scores by minimizing a single cost function via an alternating least squares algorithm, which mathematically guarantees convergence to proper solutions. It then employs the factor score estimates to estimate structural model parameters. Once all parameters are estimated, SFA further estimates the probability distribution of the factor scores that can generate the data matrix of indicators, which can be used for probabilistic inferences about the true factor scores. We investigate SFA’s performance and empirical utility through simulated and real data analyses.

Parallel Process Latent Growth Modeling with Multivariate Confounders/Suppressors

A parallel process growth model is often limited to the developments of two main trends due to model complexity. Two major parallel processes are only modeled to examine how the changes in two longitudinal processes might be related without considering other growth models possibly related to the two main processes. However, the exclusion of a third LGM risks introducing bias into key associations while capturing the relations between only two growth processes, since they are not controlled. This study presents a method to address the effect of spurious relationship while minimizing convergence issues when other processes are not considered. The suggested method utilizes the factor score estimates for other relevant growth models to control the spurious effect. Results revealed the superiority of the parallel process model using the factor scores over the typical parallel process model and illustrated the importance of considering growth models relevant to the parallel process model.

Working memory and reaction time variability mediate the relationship between polygenic risk and ADHD traits in a general population sample

Endophenotypes are heritable and quantifiable traits indexing genetic liability for a disorder. Here, we examined three potential endophenotypes, working memory function, response inhibition, and reaction time variability, for attention-deficit hyperactivity disorder (ADHD) measured as a dimensional latent trait in a large general population sample derived from the Adolescent Brain Cognitive DevelopmentSM Study. The genetic risk for ADHD was estimated using polygenic risk scores (PRS) whereas ADHD traits were quantified as a dimensional continuum using Bartlett factor score estimates, derived from Attention Problems items from the Child Behaviour Checklist and Effortful Control items from the Early Adolescent Temperament Questionnaire-Revised. The three candidate cognitive endophenotypes were quantified using task-based performance measures. Higher ADHD PRSs were associated with higher ADHD traits, as well as poorer working memory performance and increased reaction time variability. Lower working memory performance, poorer response inhibition, and increased reaction time variability were associated with more pronounced ADHD traits. Working memory and reaction time variability partially statistically mediated the relationship between ADHD PRS and ADHD traits, explaining 14% and 16% of the association, respectively. The mediation effect was specific to the genetic risk for ADHD and did not generalise to genetic risk for four other major psychiatric disorders. Together, these findings provide robust evidence from a large general population sample that working memory and reaction time variability can be considered endophenotypes for ADHD that mediate the relationship between ADHD PRS and ADHD traits.