The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.
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From the literature three types of predictors for factor scores are available. These are characterized by the constraints: linear, linear conditionally unbiased, and linear correlation preserving. Each of these constraints generates a class of predictors. Best predictors are defined in terms of L?wner's partial matrix order applied to matrices of mean square error of prediction. It is shown that within the first two classes a best predictor exists and that it does not exist in the third. Copyright ? 1996 by Marcel Dekker, Inc.
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A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that B. F. Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are "correctly" selected by the best linear factor predictor. (PsycINFO Database Record (c) 2009 APA, all rights reserved)
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Anderson and Rubin and McDonald have proposed a correlation-preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables. Green has proposed a correlation-preserving method which minimizes the trace of a residual covariance matrix for factors. Krijnen, Wansbeek and Ten Berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix, and offered an iterative procedure to that effect. In the present paper it is shown that the iterative procedure can be replaced by a closed-form solution. When all unique variances are strictly positive, this solution is the same as McDonald's. The solution coincides with Green's solution in certain special cases, for instance, when the factors are orthogonal.
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A previous study found a variety of unusual sexual interests to cluster in a five-factor structure, namely submission/masochism, forbidden sexual activities, dominance / sadism, mysophilia, and fetishism (Schippers et al., 2021). The current study was an empirical replication to examine whether these findings generalized to a representative population sample. An online, anonymous sample (N = 256) representative of the Dutch adult male population rated 32 unusual sexual interests on a scale from 1 (very unappealing) to 7 (very appealing). An exploratory factor analysis assessed whether similar factors would emerge as in the original study. A subsequent confirmatory factor analysis served to confirm the factor structure. Four slightly different factors of sexual interest were found: extreme, illegal and mysophilic sexual activities; light BDSM without real pain or suffering; heavy BDSM that may include pain or suffering; and illegal but lower-sentenced and fetishistic sexual activities. The model fit was acceptable. The representative replication sample was more sexually conservative and showed less sexual engagement than the original convenience sample. On a fundamental level, sexual interest in light BDSM activities and extreme, forbidden, and mysophilic activities seem to be relatively separate constructs.
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BACKGROUND: Prediction models and prognostic scores have been increasingly popular in both clinical practice and clinical research settings, for example to aid in risk-based decision making or control for confounding. In many medical fields, a large number of prognostic scores are available, but practitioners may find it difficult to choose between them due to lack of external validation as well as lack of comparisons between them.METHODS: Borrowing methodology from network meta-analysis, we describe an approach to Multiple Score Comparison meta-analysis (MSC) which permits concurrent external validation and comparisons of prognostic scores using individual patient data (IPD) arising from a large-scale international collaboration. We describe the challenges in adapting network meta-analysis to the MSC setting, for instance the need to explicitly include correlations between the scores on a cohort level, and how to deal with many multi-score studies. We propose first using IPD to make cohort-level aggregate discrimination or calibration scores, comparing all to a common comparator. Then, standard network meta-analysis techniques can be applied, taking care to consider correlation structures in cohorts with multiple scores. Transitivity, consistency and heterogeneity are also examined.RESULTS: We provide a clinical application, comparing prognostic scores for 3-year mortality in patients with chronic obstructive pulmonary disease using data from a large-scale collaborative initiative. We focus on the discriminative properties of the prognostic scores. Our results show clear differences in performance, with ADO and eBODE showing higher discrimination with respect to mortality than other considered scores. The assumptions of transitivity and local and global consistency were not violated. Heterogeneity was small.CONCLUSIONS: We applied a network meta-analytic methodology to externally validate and concurrently compare the prognostic properties of clinical scores. Our large-scale external validation indicates that the scores with the best discriminative properties to predict 3 year mortality in patients with COPD are ADO and eBODE.
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We show how to estimate a Cronbach's alpha reliability coefficient in Stata after running a principal component or factor analysis. Alpha evaluates to what extent items measure the same underlying content when the items are combined into a scale or used for latent variable. Stata allows for testing the reliability coefficient (alpha) of a scale only when all items receive homogenous weights. We present a user-written program that computes reliability coefficients when implementation of principal component or factor analysis shows heterogeneous item loadings. We use data on management practices from Bloom and Van Reenen (2010) to explain how to implement and interpret the adjusted internal consistency measure using afa.
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Estimation of the factor model by unweighted least squares (ULS) is distribution free, yields consistent estimates, and is computationally fast if the Minimum Residuals (MinRes) algorithm is employed. MinRes algorithms produce a converging sequence of monotonically decreasing ULS function values. Various suggestions for algorithms of the MinRes type are made for confirmatory as well as for exploratory factor analysis. These suggestions include the implementation of inequality constraints and the prevention of Heywood cases. A simulation study, comparing the bootstrap standard deviations for the parameters with the standard errors from maximum likelihood, indicates that these are virtually equal when the score vectors are sampled from the normal distribution. Two empirical examples demonstrate the usefulness of constrained exploratory and confirmatory factor analysis by ULS used in conjunction with the bootstrap method.
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In this study we use aggregated weighted scores of environmental effects to study environmental influences on well-being and happiness. To this end, we split a sample of Netherlands Twin Register (NTR) participants into a training (N =4857) and test (N =2077) sample. In the training sample, we use elastic net regression to estimate effect sizes for associations between life satisfaction and two sets of environmental variables: one based on self- report socioenvironmental data, and one based on objective physical environmental data. Based on these effect sizes, we create two poly-environmental scores (PES-S and PES-O, for self-reports and objective data respectively). In the test sample, we perform association analyses between different measures of well-being and the two PESs. We find that the PES-S explains ~36% of the variance in well-being, while the PES-O does not significantly contribute to the model. Variance in other well-being measures (i.e., different life satisfaction domains, subjective happiness, quality of life, flourishing, psychological well-being, self-rated health, depressive problems, and loneliness) are explained to varying extents by the PESs, ranging from 6.36% (self-rated health) to 36.66% (loneliness). These predictive values did not change during the COVID-19 pandemic (N =3214). Validating the PES-S in the UK biobank (N =40,614), we find that the UK biobank PES-S explains about ~12% of the variance in happiness. Lastly, we examine if there is any indication for gene-environment correlation (rGE), the phenomenon where one’s genetic predisposition influences exposure to the environment, by associating the PESs with polygenic scores (PGS) in a sample of Netherlands Twin Register (NTR) and UK Biobank participants. While the PES and PGS were not correlated in the NTR sample, they were correlated in the larger UK biobank sample, indicating the potential presence of rGE. We discuss several limitations pertaining to our dataset, such as a potential influence of common method bias, and reflect on how PESs might be used in future research.
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Objective: To examine the underlying factor structure and psychometric properties of the Assessment of Self-management in Anxiety and Depression (ASAD) questionnaire, which was specifically designed for patients with (chronic) anxiety and depressive disorders. Moreover, this study assesses whether the number of items in the ASAD can be reduced without significantly reducing its precision. Methods: The ASAD questionnaire was completed by 171 participants across two samples: one sample comprised patients with residual anxiety or depressive symptoms, while the other consisted of patients who have been formally diagnosed with a chronic anxiety or depressive disorder. All participants had previously undergone treatment. Both exploratory (EFA) and confirmatory factor analyses (CFA) were conducted. Internal consistency and test–retest reliability were also assessed. Results: Both EFA and CFA indicated three solid factors: Seeking support, Daily life strategies and Taking ownership [Comparative Fit Index = 0.80, Tucker Lewis Index = 0.78, Root Mean Square Error of Approximation = 0.09 (CI 0.08–1.00), Standardized Root Mean Square Residual = 0.09 ($2 = 439.35, df = 168)]. The ASAD was thus reduced from 45 items to 21 items, which resulted in the ASAD-Short Form (SF). All sub-scales had a high level of internal consistency (> a = 0.75) and test–retest reliability (ICC > 0.75). Discussion: The first statistical evaluation of the ASAD indicated a high level of internal consistency and test–retest reliability, and identified three distinctive factors. This could aid patients and professionals’ assessment of types of self-management used by the patient. Given that this study indicated that the 21-item ASAD-SF is appropriate, this version should be further explored and validated among a sample of patients with (chronic or partially remitted) anxiety and depressive disorders. Alongside this, to increase generalizability, more studies are required to examine the English version of the ASAD within other settings and countries.
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