Determining Sample Size Requirements in EFA Solutions: A Simple Empirical Proposal.

In unrestricted or exploratory factor analysis (EFA), there is a wide range of recommendations about the size samples should be to attain correct and stable solutions. In general, however, these recommendations are either rules of thumb or based on simulation results. As it is hard to establish the extent to which a particular data set suits the conditions used in a simulation study, the advice produced by simulation studies is not direct enough to be of practical use. Instead of trying to provide general and complex recommendations, in this article, we propose to estimate the sample size that is needed to analyze a data set at hand. The estimation takes into account the specified EFA model. The proposal is based on an intensive simulation process in which the sample correlation matrix is used as a basis for generating data sets from a pseudo-population in which the parent correlation holds exactly, and the criterion for determining the size required is a threshold that quantifies the closeness between the pseudo-population and the sample reproduced correlation matrices. The simulation results suggest that the proposal works well and that the determinants identified agree with those in the literature.

Personality Traits in Latin America: A Cross-Cultural Study of the Big Five Factor Structure and its Relationship with Self-Reported Daily Behaviors.

The Big Five factors model of personality is one of the most internationally studied and applied since it has been replicated in multiple investigations in different countries and cultures. This five-dimensional structure has evidence from studies carrying out factor analyses in different versions and adaptations of personality measurement instruments under these theoretical assumptions, and cross-cultural studies reveal its universality. However, no research has investigated how this structure is replicated in Latin American countries yet. This study aimed to carry out a cross-cultural study evaluating the factorial congruence of the Revised International Personality Item Pool in Latin American countries. The validity was also analyzed assessing relationships with gender, age, and self-reported activities of daily living. The five-dimensional structure was supported by evidence in the different samples that participated in this study, preserving the individual differences that characterize each country. Differences according to gender and age were found in different personality factors, as well as relationships with recreational activities. It is concluded that the five-factor structure of the scale is replicated in Latin American samples and that the psychometric properties of the instrument are consistent. Limitations and future lines of research are discussed.

Psychometric properties of the Spanish version of the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire (EORTC QLQ-C30).

PURPOSE: The aim of this study was to analyze the internal structure of the EORTC QLQ-C30, to examine the validity and normative data for cancer patients. METHOD: Exploratory and Confirmatory factor analyses were conducted to explore the scale's dimensionality and test for strong measurement invariance across sex and tumor site. All the analyses were based on a multicenter cohort of 931 patients who completed the Brief Symptom Inventory (BSI-18) and the EORTC QLQ-C30. RESULTS: Our findings indicate that the EORTC QLQ-C30 has acceptable psychometric properties and an internal structure that is well accounted for a bifactor model: a general factor that evaluates quality of life and a group factor that would analyze physical health that would be defined by physical function, role function, and fatigue. The result of the multi-group CFA revealed a strong invariance according to sex, tumor, and over time. Reliability of the EORTC exceeding 0.86 and the simple sum of the items of the scale was a good indicator of oncology patients' quality of life. Both factors correlate closely with depression, anxiety, and psychological distress and are sensitive to change, especially the quality of life, with a significant decrease in the post-test. CONCLUSION: The Spanish version of the EORTC QLQ-C30 proved to be a valid, reliable instrument to appraise quality of life in cancer patients. The normative data collected from this study may be useful for the early detection of initial symptoms of deterioration of quality of life in oncology patients.

SOLOMON: a method for splitting a sample into equivalent subsamples in factor analysis.

Nowadays, exploratory and confirmatory factor analyses are two important consecutive steps in an overall analysis process. The overall analysis should start with an exploratory factor analysis that explores the data and establishes a hypothesis for the factor model in the population. Then, the analysis process should be continued with a confirmatory factor analysis to assess whether the hypothesis proposed in the exploratory step is plausible in the population. To carry out the analysis, researchers usually collect a single sample, and then split it into two halves. As no specific splitting methods have been proposed to date in the context of factor analysis, researchers use a random split approach. In this paper we propose a method to split samples into equivalent subsamples similar to one that has already been proposed in the context of multivariate regression analysis. The method was tested in simulation studies and in real datasets.

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.

Psychometric properties and factorial analysis of invariance of the Satisfaction with Life Scale (SWLS) in cancer patients.

PURPOSE: The purpose of this study was to assess the psychometric properties of the Satisfaction with Life Scale (SWLS), evaluate the measurement invariance with respect to sex, age, and tumor location, as well as analyze associations between life satisfaction and socio-demographic and clinical variables among individuals with resected, non-advanced cancer. METHODS: A confirmatory factor analysis was conducted to explore the dimensionality of the scale and test invariance across gender, age, and tumor localization in a prospective, multicenter cohort of 713 patients who completed the following scales: SWLS, Health-related Quality of Life Questionnaire (EORTC QLQ-C30), Brief Symptom Inventory (BSI-18). RESULTS: Confirmatory factor analysis results indicated that the SWLS is an essentially unidimensional instrument, providing accurate scores: both McDonald's omega and Cronbach's alpha estimates were 0.91. Strong measurement invariance was found to hold across gender, age, and tumor localization. Low satisfaction with life was associated with psychological symptoms (anxiety, depression, and somatization), and decreased quality of life (malfunction, symptoms, poor global QoL). CONCLUSION: The SWLS is a reliable, valid satisfaction with life measurement among people with cancer and should be recommended as an indicator of psychological adjustment in oncological patients.

A General Approach for Fitting Pure Exploratory Bifactor Models.

This article proposes a procedure for fitting a pure exploratory bifactor solution in which the general factor is orthogonal to the group factors, but the loadings on the group factors can satisfy any orthogonal or oblique rotation criterion. The proposal combines orthogonal Procrustes rotations with analytical rotations and consists of a sequence of four steps. The basic input is a semispecified target matrix that can be (a) defined by the user, (b) obtained by using Schmid-Leiman orthogonalization, or (c) automatically built from a conventional unrestricted solution based on a prescribed number of factors. The relevance of the proposal and its advantages over existing procedures is discussed and assessed via simulation. Its feasibility in practice is illustrated with two empirical examples in the personality domain.

The mediating role of spirituality (meaning, peace, faith) between psychological distress and mental adjustment in cancer patients.

OBJECTIVE: The objectives of this study were (a) to determine the psychometric properties of the Functional Assessment of Chronic Illness Therapy-Spiritual Well-Being (FACIT-Sp) scale and (b) to provide that FACIT scores behave one-dimensional to establish the mediating role of spiritual well-being in psychological distress and mental adjustment in a sample of patients with non-metastatic, resected cancer. METHOD: A total of 504 consecutive patients completed the FACIT-Sp, Brief Symptom Inventory, and Mini-Mental Adjustment to Cancer scales. The dimensionality and structure of the scale were assessed by semi-confirmatory factor analysis; the reliability of the derived scale scores was evaluated using the omega coefficient, and regression analysis appraised the FACIT-Sp's mediating role between psychological distress and mental adjustment. RESULTS: A clear and theoretically interpretable solution in two factors that agreed generally with solutions reported in other languages was obtained for the FACIT item scores and omega reliabilities of the derived Meaning/Peace (0.85) and Faith (0.86) scales were acceptable. The oblique solution in two factors was compatible with an essentially unidimensional solution of general well-being and associated strongly with psychological distress and mental adjustment. Spiritual well-being acted as a partial mediator between psychological distress and mental adjustment strategies, such as fighting spirit, hope, and cognitive avoidance. CONCLUSIONS: The Spanish version of the FACIT-Sp scale is a reliable and valid clinical evaluation tool, and further highlights the potential clinical implications of spirituality for improving quality of life and adjustment to cancer.

POLYMAT-C: a comprehensive SPSS program for computing the polychoric correlation matrix.

We provide a free noncommercial SPSS program that implements procedures for (a) obtaining the polychoric correlation matrix between a set of ordered categorical measures, so that it can be used as input for the SPSS factor analysis (FA) program; (b) testing the null hypothesis of zero population correlation for each element of the matrix by using appropriate simulation procedures; (c) obtaining valid and accurate confidence intervals via bootstrap resampling for those correlations found to be significant; and (d) performing, if necessary, a smoothing procedure that makes the matrix amenable to any FA estimation procedure. For the main purpose (a), the program uses a robust unified procedure that allows four different types of estimates to be obtained at the user's choice. Overall, we hope the program will be a very useful tool for the applied researcher, not only because it provides an appropriate input matrix for FA, but also because it allows the researcher to carefully check the appropriateness of the matrix for this purpose. The SPSS syntax, a short manual, and data files related to this article are available as Supplemental materials that are available for download with this article.

Psychometric Properties and Measurement Invariance of the Herth Hope Index in Spanish Cancer Patients.

BACKGROUND: The aim of this study was to evaluate the psychometric properties, differential item functioning, factorial invariance, and convergent validity of the Spanish version of the Herth Hope Index (HHI) in patients with cancer. METHOD: Exploratory and confirmatory factor analyses were conducted to explore the scale, dimensionality, functioning of items, test for strong measurement invariance across sex, age, tumor site, and expected survival, and an extended structural equation model to assess external validity in a cross-sectional, multicenter, prospective study of 863 cancer patients from 15 Spanish hospitals. RESULTS: The results do not support the original 3-factor scale but instead suggest a one-factor structure, which explained 62% of the common variance. Scores from the unidimensional structure exhibited satisfactory reliability (ω = .88). A strong invariance solution demonstrated excellent fit across sex, age, tumor site, and survival. HHI exhibited substantial associations with resilience coping strategies and spiritual well-being. CONCLUSIONS: The findings of our study contribute to the diversity of earlier empirical findings regarding the construct of hope. Despite this, our results indicate that the Spanish version of the HHI is a short, easy-to-administer, valid, reliable tool for evaluating cancer patients' levels of hope.

Gulliksen's pool: A quick tool for preliminary detection of problematic items in item factor analysis.

Exploratory factor analysis is widely used for item analysis in the earlier stages of scale development, usually with large pools of items. In this scenario, the presence of inappropriate or ineffective items can hamper the process of analysis, making it very difficult to correctly assess dimensionality and structure. To minimize, this (quite frequent) problem, we propose and implement a simple procedure designed to flag potentially problematic items before we specify any particular factorial solution. The procedure defines regions of item appropriateness and efficiency based on the combined impact of two prior item features: extremeness and consistency. The general proposal is related to the most widely used frameworks for item analysis. The limits of the appropriateness regions are obtained by extensive simulation in conditions that mimic those found in applications. An Item Response Theory index of prior item efficiency is then defined, and a combined approach for selecting the most effective and problem-free item sub-set is proposed. The proposal is useful to normal-range measures, such as questionnaire surveys that elicit reports about non-extreme attitudes, facts, beliefs or states, or personality questionnaires that measure normal-range constructs. The procedure is implemented in a freeware software.

TETRA-COM: a comprehensive SPSS program for estimating the tetrachoric correlation.

We provide an SPSS program that implements descriptive and inferential procedures for estimating tetrachoric correlations. These procedures have two main purposes: (1) bivariate estimation in contingency tables and (2) constructing a correlation matrix to be used as input for factor analysis (in particular, the SPSS FACTOR procedure). In both cases, the program computes accurate point estimates, as well as standard errors and confidence intervals that are correct for any population value. For purpose (1), the program computes the contingency table together with five other measures of association. For purpose (2), the program checks the positive definiteness of the matrix, and if it is found not to be Gramian, performs a nonlinear smoothing procedure at the user's request. The SPSS syntax, a short manual, and data files related to this article are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.

Development of a Revised Version of the Statistical Anxiety Scale.

BACKGROUND: Statistics anxiety is a common problem in students taking statistics courses in the social sciences. It is most widely measured by the statistical anxiety scale. The various adaptations of this instrument have shown certain problems in the replication of its factorial structure and do not have a system to control possible response bias effects. The objective of our study was to propose a short test to measure statistical anxiety that also includes a scale to control social desirability bias. METHOD: We developed a revised version of the statistical anxiety scale using procedures for controlling response biases and examined its factorial structure using exploratory and confirmatory analysis in a sample of 531 students. RESULTS: The revised version showed a clear four-factor structure in exploratory and confirmatory factor analyses with the expected three content factors plus one social desirability factor. The scales showed no acquiescence effects and moderate social desirability effects, and had a clear relationship with academic success. CONCLUSIONS: The revised version of the statistical anxiety scale improves on the psychometric properties of the original version and may overcome the problems detected in some adaptations of the previous version.

[Decalogue for the Factor Analysis of Test Items].

Decalogue for the Factor Analysis of Test Items. BACKGROUND: In the study of the psychometric properties of the items of a test, a fundamental aspect is the analysis of their dimensional structure. The objective of this work is to provide some guidelines that allow the factor analysis of the items to be carried out in a rigorous and systematic way. METHOD: A review of the recent psychometric literature was carried out to identify the fundamental steps to be followed in order to carry out an adequate factor analysis of the items of a test. RESULTS: Ten main recommendations were identified to carry out the factorial analysis of the items of a test: adequacy of the data and the sample, univariate statistics, justification of the analysis, selection of the analyzable items, type of model, most appropriate factorial solution, estimation of the parameters, adequacy of the factorial solution, substantive coherence of the model, and final version of the test. CONCLUSIONS: If the ten recommendations proposed in the current psychometric literature are systematically followed, it will be possible to optimize the quality of the tests and the decision-making based on the estimates of the scores obtained through them. These recommendations should be useful to both researchers and practitioners.

The forgotten role of absorption in music reward.

Interindividual differences in music-related reward have been characterized as involving five main facets: musical seeking, emotion evocation, mood regulation, social reward, and sensory-motor. An interesting concept related to how humans decode music as a rewarding experience is music transcendence or absorption (i.e., music-driven states of complete immersion, including momentary loss of self-consciousness or even time-space disorientation). Here, we investigated the relation between previously characterized facets of music reward and individual differences in music absorption. A first sample of participants (N = 370) completed both the Barcelona Music Reward Questionnaire (BMRQ) and the Absorption in Music Scale (AIMS). Results showed that both constructs were highly interrelated (r = 0.78, p < 0.001), indicating that higher music reward sensitivity is associated with a greater tendency to music-related absorption states. In addition, four items from the AIMS were identified as suitable to be added to an extended version of the BMRQ (eBMRQ). A second sample (N = 550) completed the eBMRQ for a validation study. Exploratory and confirmatory factor analyses on the whole sample (N = 920) showed the reliable psychometric properties of the eBMRQ and suggested that taking into account an absorption facet could contribute to a better characterization of individual differences in the sensitivity to experience music-related reward and pleasure.

Cultural adaptation, translation and validation of the Spanish version Debriefing Experience Scale.

Clinical simulation as a teaching methodology allows the student to train and learn technical abilities and/or non-technical abilities. One of the key elements of this teaching methodology is the debriefing, which consists of a conversation between several people, in which the participants go over a real or simulated event in order to analyze their actions and reflect on the role that thought processes, psychomotor skills and emotional states can play in maintaining, or improving their performance in the future. The Debriefing Experience Scale allows the experience of students in debriefing to be measured. The objective of this study is to translate the Debriefing Experience Scale (DES) into Spanish and analyze its reliability and validity to measure the experience of nursing students during the debriefing. The study was developed in two phases: One: the adaption of the instrument to Spanish, two: a transversal study carried out in a sample of 290 nursing students. The psychometric properties were analyzed in terms of reliability and construct validity using confirmatory factorial analysis (CFA). Cronbach's alpha was adequate for all the scales and for each one of the dimensions. The confirmatory factorial analysis showed that the 4-dimensional model is acceptable for both scales (experience and opinion). The Spanish version Debriefing Experience Scale questionnaire is useful, valid and reliable for use to measure the debriefing experience of university students in a simulation activity.

Measurement properties of the Spanish version of the brief resilient coping scale (BRCS) in cancer patients.

Background/Objective: Resilience is the capacity to adaptively confront stress. The aim of this study was to evaluate the psychometric properties, convergent validity, and factorial invariance of the Spanish version of the Brief Resilient Coping Scale (BRCS). Method: Exploratory and confirmatory factor analyses based on a cross-validation were conducted to explore the scale's dimensionality and test for strong (scalar) measurement invariance across gender, age, tumor site, and survival, by fitting multiple-group confirmatory solutions. An extended structural equation model was used to assess external validity. Prospective, multicenter cohort study of 636 patients who completed the BRCS, Satisfaction with Life Scale (SWLS), and Spiritual well-being (FACIT-sp) scales. Results: The data supported a unidimensional structure. The BRCS is a very short, narrow bandwidth measure, with items demonstrating high discriminating power. A strong invariance solution demonstrated excellent fit across gender, age, tumor site, and survival. Scores derived from the unidimensional structure exhibited satisfactory degrees of reliability (ω = .86) and determinacy (FDI = .94). BRCS revealed substantial associations with satisfaction with life and spirituality well-being (all p < .001), factors widely related to resilience, particularly in cancer patients. Conclusions: The Spanish version of the BRCS is a reliable, valid resilience measure in advanced cancer.

FIRE: an SPSS program for variable selection in multiple linear regression analysis via the relative importance of predictors.

We provide an SPSS program that implements currently recommended techniques and recent developments for selecting variables in multiple linear regression analysis via the relative importance of predictors. The approach consists of: (1) optimally splitting the data for cross-validation, (2) selecting the final set of predictors to be retained in the equation regression, and (3) assessing the behavior of the chosen model using standard indices and procedures. The SPSS syntax, a short manual, and data files related to this article are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.

The Appropriateness of Sum Scores as Estimates of Factor Scores in the Multiple Factor Analysis of Ordered-Categorical Responses.

Unit-weight sum scores (UWSSs) are routinely used as estimates of factor scores on the basis of solutions obtained with the nonlinear exploratory factor analysis (EFA) model for ordered-categorical responses. Theoretically, this practice results in a loss of information and accuracy, and is expected to lead to biased estimates. However, the practical relevance of these limitations is far from clear. In this article, we adopt an empirical view and propose indices and procedures (some of them new) for assessing the appropriateness of UWSSs in nonlinear EFA applications. A new automated approach for obtaining UWSSs that maximize fidelity and correlational accuracy is proposed. The appropriateness of UWSSs under different conditions and the behavior of the present proposal in comparison with other more common approaches are assessed with a simulation study. A tutorial for interested practitioners is presented using an illustrative example based on a well-known personality questionnaire. All the procedures proposed in the article have been implemented in a well-known noncommercial EFA program.

Is Correcting for Acquiescence Increasing the External Validity of Personality Test Scores?

BACKGROUND: Balanced scales control for acquiescence (ACQ) because the tendency of the respondent to agree with the positive items is cancelled out by the tendency to agree with opposite-pole items. When full balance is achieved, ACQ is not expected to affect external validity. Otherwise, attenuated estimates are expected to appear if no control methods such as Lorenzo-Seva & Ferrando's (2009) are used. METHOD: Expected results were derived analytically. Subsequently, a simulation was carried out to assess (a) how ACQ impacted external validity and (b) how validity estimates behaved when ACQ was corrected. Two illustrative examples are provided. RESULTS: A sizable number of items and/or high content loadings tended to decrease ACQ's impact on validity estimates, making the empirical coefficient closer to its structural value. Furthermore, when scales were well balanced, the controlled and uncorrected scores were close to each other, and led to unbiased validity estimates. When the scales were unbalanced and no corrections were used, attenuated empirical validity coefficients inevitably appeared. CONCLUSIONS: Designing a well-balanced test or correcting for ACQ are the best ways to minimize attenuation in external validity estimation.