Unrestricted Factor Analysis Research Articles

A simulation-based scaled test statistic for assessing model-data fit in least-squares unrestricted factor-analysis solutions

A shortcoming of least-squares unrestricted factor analysis (UFA) procedures, which are widely used in psychometric applications is that a test statistic for assessing model-data fit cannot be easily derived from the minimum fit function value. This paper proposes a chi-square type goodness-of-fit test statistic intended for the principal-axis, MINRES, and minimum-rank UFA procedures. The statistic is empirically obtained via intensive simulation based on a two-stage approach. First, a distribution of minimum fit function values is obtained from a scenario in which the null hypothesis of perfect model-data fit holds. Second, the obtained statistic is non-linearly transformed so that it has its first four moments equal to those of the theoretical reference chi-square distribution with the appropriate degrees of freedom. Extensions of the basic statistic are next proposed that include comparative and relative indexes based on it. Tests of close-fit and power assessment derived from the basic statistic are also proposed.

VICARIOUS EMBARRASSMENT SCALE: MORE OF CULTURE THAN EMPATHY

Traditionally, the vicarious embarrassment scale (VES) is developed by involving a protagonist with no relationship with the observer. This condition becomes problematic, especially in collectivistic contexts with interdependence in personal social relations. The protagonists of the original VES were modified from strangers to friends and family and were compared their psychometric properties and associations with empathy and self-construals. A total of 112 university students in Yogyakarta, Indonesia, filled out the online questionnaires voluntarily. Tests with Unrestricted Factor Analysis showed the retrieved eigenvalues of VES Other, VES Friend, and VES Family accounted for 61.54, 68.29, and 77.05, respectively. All VES were unidimensional, according to the parallel analysis with robust parallel using 500 random polychoric correlation matrices. Good internal consistency reliability was achieved, and fit criteria were met. This study supported previous findings of VES disassociation with empathy. The importance of cultural values reflected in self-construal showed interdependent self-construal relations with different protagonists with all VE scales. In contrast, independent self-construal was associated only with vicarious embarrassment with an unknown protagonist.

Cross-cultural Study of the Personality Inventory for the DSM-5 (PID-5) across the Portuguese and the United Arab Emirates (UAE) Community and Clinical Populations.

The present paper focused on compare the PID-5 mean score levels across two matched community and clinical samples of Portugal and the UAE. The generalizability and universality of the Alternative Model of Personality Disorders has been thoroughly studied through the Personality Inventory for DSM-5 (PID-5) across countries and languages. However, studies comparing Western and Middle Eastern countries are still limited, in particular those who assess the PID-5 measurement invariance. We examined measurement invariance of the PID-5 scales across matched Emirati and Portuguese clinical and nonclinical groups, as well as compare and contrast the PID-5 mean score levels across both countries and samples. The Arabic and the Portuguese versions of the PID-5 was administered to Emirati community participants (N = 300, 80% women and 20% men, Mage = 27.95) which were matched with Portuguese community participants (N = 300, 80.3% women and 19.7% men, Mage = 28.96), as well as clinical participants of the UAE (N = 150, 61.3% women and 38.7% men, Mage = 31.29) and Portugal (N = 150, 52% men and 48% women, Mage = 44.97). We examined measurement invariance through an unrestricted Factor Analysis based program, and mean scores levels were compared and analyzed. Our findings supported the PID-5 measurement invariance across the Emirati and Portuguese clinical samples pointing to the universality and generalizability of the Alternative Model of Personality Disorders. The Emirati psychiatric sample exhibited somehow higher results than the Portuguese psychiatric participants, albeit the small effect size for most of the PID-5 scales. Further research is needed to examine the applicability of the PID-5 across non-clinical representative samples of Portugal and the UAE, and other Middle Eastern countries.

Unrestricted factor analysis: A powerful alternative to confirmatory factor analysis

Unrestricted factor analysis: A powerful alternative to confirmatory factor analysis

GHQ-12 in adolescents: contributions to the controversial factorial validity

Objective: The GHQ-12 is one of the most widely used questionnaires in the adult population, but there are not as many studies exploring its applicability in adolescents. The main problem is the diversity of results on its factorial structure, as different studies have shown one, two or three dimensions. The purpose of this study was to explore the GHQ-12 factorial structure for adolescents. Method: An observational multicenter cross-sectional descriptive study was designed for schools in the city of Madrid. A random sample of n=2,171, 14-16-year-olds was stratified by the school’s development level and funding (public, private or mixed). Unrestricted factor analysis was applied based on the polychoric or tetrachoric correlations matrix (depending on the test scoring method). Results: The optimized parallel analysis provided an unequivocal one-factor structure, confirmed by unidimensionality assessment. Around 30% of male and 42% of female adolescents were found to be at risk of developing mental health problems. Conclusions: The GHQ-12 is a one-dimensional test for screening psychological distress, with excellent psychometric properties for its application in an adolescent population. The use of adequate statistical methods can overcome old controversies and promote proper application and interpretation of the results provided by the test.

Unrestricted factor analysis of multidimensional test items based on an objectively refined target matrix.

A common difficulty in the factor analysis of items designed to measure psychological constructs is that the factor structures obtained using exploratory factor analysis tend to be rejected if they are tested statistically with a confirmatory factor model. An alternative to confirmatory factor analysis is unrestricted factor analysis based on Procrustes rotation, which minimizes the distance from a target matrix proposed by the researcher. In the present article, we focus on the situation in which researchers propose a partially specified target matrix but are prepared to allow their initial target to be refined. Here we discuss RETAM as a new procedure for objectively refining target matrices. To date, it has been recommended that this kind of refinement be guided by human judgment. However, our approach is objective, because the threshold value is computed automatically (not decided on by the researcher) and there is no need to manually compute a number of factor rotations every time. The new procedure was tested in an extensive simulation study, and the results suggest that it may be a useful procedure in factor analysis applications based on incomplete measurement theory. Its feasibility in practice is illustrated with an empirical example from the personality domain. Finally, RETAM is implemented in a well-known noncommercial program for performing unrestricted factor analysis.

About feeding children: factor structure and internal reliability of a survey to assess mealtime strategies and beliefs of early childhood education teachers

BackgroundChildren spend a substantial amount of time in early care and education (ECE) settings and may eat a majority of their diet in this setting. While there are several instruments focused on measuring factors of the ECE environment that may influence diet and weight outcomes, there are few comprehensive, valid, and reliable measures for collecting self-report of ECE providers’ feeding practices. The purpose of this study was to establish the factor structure and internal reliability of a survey developed to measure practices and beliefs of ECE providers relative to feeding children.MethodsLicensed ECE centers from CA, CO, ID and NV were included in this cross-sectional survey study. The sample was stratified by states and census regions to yield equal numbers of centers from each category. The total sample distribution included 1600 randomly selected centers and up to 8000 staff members (who represented teachers, aides, assistants, or cooks); 1178 surveys were completed. We conducted an exploratory, unrestricted factor analysis as well as parallel analyses to inform the number of factors to be extracted.ResultsFactors within Structural Mealtime Strategies included Adult Control of Foods Consumed (Kuder-Richardson [KR] = 0.67), Bribing with Sweet Foods (KR = 0.70), and Supportive Adult Roles at Mealtime (KR = 0.55). Factors in Verbal Mealtime Strategies included Supporting Children’s Eating Self-regulation (KR =0.61), Pressure to Eat (KR = 0.58), and Social Comparisons (KR = 0.59). Beliefs about Mealtime factors were Autonomy Promoting (α = 0.64), Coercive Beliefs (α = 0.77), and Concern-Based Control (α = 0.60).ConclusionsThe AFC Strategies and Beliefs Survey provides a promising self-report instrument with a strong factor structure consistent with the extant literature to measure practices and beliefs related to feeding and mealtimes in the ECE setting. Feeding young children in group settings differs in many ways from feeding in a family setting; hence it is important that measures such as the AFC Strategies and Beliefs Survey capture unique aspects of the ECE feeding environment.

A Psychometric Examination of the Anagram Persistence Task: More Than Two Unsolvable Anagrams May Not Be Better.

The purpose of this investigation was to examine a single-anagram, a double-anagram, and multi-anagram versions of the Anagram Persistence Task (APT) for factorial validity, reliability, and convergent validity. Additionally, a battery of intelligence tests was administered to examine convergent validity. Based on an unrestricted factor analysis, two factors were uncovered from the 14 anagram (seven very difficult and seven very easy) response times: test-taking persistence and verbal processing speed. The internal consistency reliabilities for the single-anagram, double-anagram, and multi-anagram (seven difficult anagrams) measures were .42, .85, and .86, respectively. Furthermore, all three versions of the APT correlated positively with intelligence test performance (r ≈ .22). However, the double-anagram and multi-anagram versions also evidenced negative, nonlinear effects with intelligence test performance (r ≈ -.15), which suggested the possibility of testee adaptation. Taking psychometrics and administration time into consideration, simultaneously, the double-anagram version of the APT may be regarded as preferred.

Psychometric Evaluation of the interRAI Child and Youth Mental Health Disruptive/Aggression Behaviour Scale (DABS) and Hyperactive/Distraction Scale (HDS).

The present study aims to validate the interRAI Child and Youth Mental Health (interRAI ChYMH), Disruptive/Aggression Behaviour Scale (DABS) and Hyperactive/Distraction Scale (HDS). Data were collected from children/youth aged 4-18 (N = 3464) across 39 mental health agencies in Ontario, Canada. Unrestricted factor analysis using polychoric correlation matrices and Samejima's graded item response theory (IRT) parameterizations were conducted for both measures. Scores on the HDS and DABS were also compared amongst children/youth diagnosed with attention-deficit hyperactivity disorder (ADHD) and disruptive behaviour disorder (DBD) respectively using DSM-IV criteria. Results from the factor analysis and IRT analysis demonstrated good measurement properties. Using a receiver operating characteristics curve, the area under the curve (AUC) for the HDS and DABS is 0.79 and 0.75 for a diagnosis of ADHD and DBD respectively. Overall, converging results suggest that the interRAI HDS and DABS may serve as effective measures that detect externalizing mental health indicators.

COOP/WONCA: fiabilidad y validez de la prueba administrada telefónicamente

AimThe COOP/WONCA test was initially proposed as a self-report in which the answers were supported by drawings illustrating the state investigated. Subsequent studies have confirmed its usefulness as a mere verbal self-report face-to-face administered. No data have been found about its useful when administered by telephone interview. The aim of this study was to determine the psychometric properties of the COOP / WONCA test to measure Related Quality of Life (HRQoL) administered by telephone and compare them with those obtained in other forms of prior administration. DesignCross-sectional study on a random. SettingCity of Madrid. ParticipantsRandom sample of 802 adult subjects, representative of the adult population in Madrid, obtained by stratification from the population census. Main measurementsQuestionnaire COOP/WONCA with 9 ítems included in a broader battery, administered by telephone interview. ResultsThe unrestricted factor analysis points to the unifactoriality of the scale, which measures a single latent construct (HRQOL), showing high internal consistency, not significantly different from those found by face-to-face administration, ruling out the existence of biases in the phone modality. ConclusionsThe COOP/WONCA test appears as a reliable and valid measure of HRQOL and telephonic administration allows to assume no changes in the results, which can reduce costs in population studies, increasing efficiency without loss of quality in the information collected.

Likelihood-Based Confidence Intervals in Exploratory Factor Analysis

In exploratory or unrestricted factor analysis, all factor loadings are free to be estimated. In oblique solutions, the correlations between common factors are free to be estimated as well. The purpose of this article is to show how likelihood-based confidence intervals can be obtained for rotated factor loadings and factor correlations, by applying maximum likelihood factor analysis subject to scaling and rotation constraints. As an illustrative example, an oblique 5-factor model will be fitted to the variance-covariance matrix of the 30 personality facets measured by the Revised NEO Personality Inventory, and confidence intervals will be estimated for all factor loadings and factor correlations, as well as for the associated reliability and validity coefficients.

Agitation in Dutch Institutionalized Patients with Dementia: Factor Analysis of the Dutch Version of the Cohen-Mansfield Agitation Inventory

Background/Aims: To establish the construct validity of the Dutch version of the Cohen-Mansfield Agitation Inventory (CMAI-D) in institutionalized patients with dementia. Methods: The CMAI-D was administered to a large sample of 1,437 patients with moderate to severe dementia, receiving nursing home or outreaching nursing home care. Exploratory factor analysis was used to examine the behavioral dimensions underlying CMAI-D observations. Results: A restricted 3-factor solution showed 3 factors, i.e. physical aggression, physically nonaggressive behavior and verbally agitated behavior, with prevalences of 62, 67 and 62%, respectively. An unrestricted factor solution revealed 3 additional behavioral dimensions: hiding/hoarding, vocal agitation and a factor of miscellaneous items (i.e. repetitious mannerisms, spitting), which occurred in 30, 28 and 35% of the patients, respectively. Conclusion: The 3-factor solution of physical aggression, physically nonaggressive behavior and verbally agitated behavior corroborates earlier findings in other patient samples and therefore establishes the construct validity in institutionalized patients with severe dementia. The robustness of these findings across different care settings suggests that agitated behaviors have a common basis. In addition, unrestricted factor analysis showed 3 other important independent behavioral symptoms in dementia, but they are in fact too small to be used as a subscale. These findings might add to the taxonomy of agitation and aggression in dementia.

Acquiescent Responding in Balanced Multidimensional Scales and Exploratory Factor Analysis

Personality tests often consist of a set of dichotomous or Likert items. These response formats are known to be susceptible to an agreeing-response bias called acquiescence. The common assumption in balanced scales is that the sum of appropriately reversed responses should be reasonably free of acquiescence. However, inter-item correlation (or covariance) matrices can still be affected by the presence of variance due to acquiescence. To analyse these correlation matrices, we propose a method that is based on an unrestricted factor analysis and can be applied to multidimensional scales. This method obtains a factor solution in which acquiescence response variance is isolated in an independent factor. It is therefore possible, without the potentially confounding effect of acquiescence, to: (a) examine the dominant factors related to content latent variables; and (b) estimate participants’ factor scores on content latent variables. This method, which is illustrated by two empirical data examples, has proved to be useful for improving the simplicity of the factor structure.

Imince: an unrestricted factor-analysis-based program for assessing measurement invariance.

In this article, a Windows program for analyzing measurement invariance in two different populations is described. Factor analysis is a common way of assessing measurement invariance, and restricted factor analysis is now the most popular method. However, applied researchers have usually found that the theoretical advantages of restricted factor analysis do not always apply in practical situations. For example, when the participant sample is large, as is the case in Internet-based questionnaires, the available software for restricted factor analysis might fail to converge on a solution. Our program is based on unrestricted factor analysis and considers the three parameters that define factor invariance: difficulties, discriminations, and residual variances. The statistical significance of the tests for evaluating invariance is obtained using Bootstrap resampling procedures. A real-life example demonstrates the usefulness of the program.

Applications of standard error estimates in unrestricted factor analysis: significance tests for factor loadings and correlations.

Estimates of standard errors of factor loadings and factor correlations in the unrestricted factor analysis model can be computed for oblique or orthogonal solutions under maximum likelihood. This information can be used to test individual coefficients for significance, to evaluate whether an orthogonal or oblique structure is most consistent with sample data, or to compute confidence intervals for single parameters or confidence regions for arbitrary groups of coefficients. Because the number of parameters estimated in factor analysis is approximately the product of number of variables multiplied by number of factors, a Bonferroni correction for the critical point of the individual test statistics is recommended to control the probability of a Type I error. Several examples are presented.

Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations.

Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations.

Circumplex models for correlation matrices

Structural models that yield circumplex inequality patterns for the elements of correlation matrices are reviewed. Particular attention is given to a stochastic process defined on the circle proposed by T. W. Anderson. It is shown that the Anderson circumplex contains the Markov Process model for a simplex as a limiting case when a parameter tends to infinity. Anderson's model is intended for correlation matrices with positive elements. A replacement for Anderson's correlation function that permits negative correlations is suggested. It is shown that the resulting model may be reparametrzed as a factor analysis model with nonlinear constraints on the factor loadings. An unrestricted factor analysis, followed by an appropriate rotation, is employed to obtain parameter estimates. These estimates may be used as initial approximations in an iterative procedure to obtain minimum discrepancy estimates. Practical applications are reported.

Noniterative Factor Analysis Estimators, With Algorithms for Subset and Instrumental Variable Selection

Noniterative estimators of the unrestricted factor analysis model have been developed by, among others, Hägglund (1982) and Ihara and Kano (1986) that are consistent and very efficient computationally. Whereas each of these methods has several desirable properties, both require a subjective decision regarding the selection of subsets of variables that are needed to compute estimates of the parameters. An algorithm called PACE, based on an application of the sweep operator, is presented that automatically selects subsets of variables used for the Ihara-Kano estimator. A second algorithm initially presented by Du Toit (1986) is also described that automatically selects reference variables used in Hägglund’s Fabin estimators. A Monte Carlo experiment is reviewed that compares the relative performance of these estimators in addition to several others. Both new methods performed well in this experiment. Their relative merits on other criteria are discussed.

Robustness of Statistical Inference in Factor Analysis and Related Models

A class of latent variable models which includes the unrestricted factor analysis model is considered. It is shown that minimum discrepancy test statistics and estimators derived under normality assumptions retain their asymptotic properties when the common factors are not normally distributed but the unique factors do have a multivariate normal distribution. The minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic and maximum likelihood estimators.

Robustness of statistical inference in factor analysis and related models

SUMMARY A class of latent variable models which includes the unrestricted factor analysis model is considered. It is shown that minimum discrepancy test statistics and estimators derived under normality assumptions retain their asymptotic properties when the common factors are not normally distributed but the unique factors do have a multivariate normal distribution. The minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic and maximum likelihood estimators.