Exploratory factor analysis (EFA) is a multivariate statistical method that has become a fundamental tool in the development and validation of psychological theories and measurements. However, researchers must make several thoughtful and evidence-based methodological decisions while conducting an EFA, and there are a number of options available at each decision point, some better than others. Reviews of the professional literature have consistently found that many applications of EFA are marked by an injudicious choice of methods and incomplete reports. This article provides a systematic, evidence-based guide to the conduct of EFA studies that can be followed by researchers with modest statistical training, supplemented with an example to illustrate its application.

Objective: To demonstrate that Coefficient omega, a model-based estimate, is more a more appropriate index of reliability than coefficient alpha for the multidimensional scales that are commonly employed by neuropsychologists. Method: As an illustration, a structural model of an overarching general factor and four first-order factors for the WAIS-IV based on the standardization sample of 2200 participants was identified and omega coefficients were subsequently computed for WAIS-IV composite scores. Results: Alpha coefficients were ≥ .90 and omega coefficients ranged from .75 to .88 for WAIS-IV factor index scores, indicating that the blend of general and group factor variance in each index score created a reliable multidimensional composite. However, the amalgam of variance from general and group factors did not allow the precision of Full Scale IQ (FSIQ) and factor index scores to be disentangled. In contrast, omega hierarchical coefficients were low for all four factor index scores (.10–.41), indicating that most of the reliable variance of each factor index score was due to the general intelligence factor. In contrast, the omega hierarchical coefficient for the FSIQ score was .84. Conclusions: Meaningful interpretation of WAIS-IV factor index scores as unambiguous indicators of group factors is imprecise, thereby fostering unreliable identification of neurocognitive strengths and weaknesses, whereas the WAIS-IV FSIQ score can be interpreted as a reliable measure of general intelligence. It was concluded that neuropsychologists should base their clinical decisions on reliable scores as indexed by coefficient omega.

Comprehensive assessment of attention-deficit/hyperactivity disorder (ADHD) symptoms includes parent and teacher questionnaires. The ADHD Rating Scale-5 was developed to incorporate changes for the Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-5; American Psychiatric Association, 2013). This study examined the fit of a correlated, 2-factor structure of ADHD (i.e., DSM-5 conceptual model) and alternative models; determined whether ADHD symptom ratings varied across teacher and child demographic characteristics; and presented normative data. Two samples were included: (a) 2,079 parents and guardians (1,131 female, 948 male) completed ADHD symptom ratings for children (N = 2,079; 1,037 males, 1,042 females) between 5 and 17 years old (M = 10.68; SD = 3.75) and (b) 1,070 teachers (766 female, 304 male) completed ADHD symptom ratings for students (N = 2,140; 1,070 males, 1,070 females) between 5 and 17 years old (M = 11.53; SD = 3.54) who attended kindergarten through 12th grade. The 2-factor structure was confirmed for both parent and teacher ratings and was invariant across child gender, age, informant, informant gender, and language. In general, boys were higher in symptom frequency than girls; older children were rated lower than younger children, especially for hyperactivity-impulsivity; and non-Hispanic children were rated higher than Hispanic children. Teachers also rated non-Hispanic African American children higher than non-Hispanic White, Asian, and Hispanic children. Non-Hispanic White teachers provided lower hyperactivity-impulsivity ratings than non-Hispanic, African American, and Hispanic teachers. Normative data are reported separately for parent and teacher ratings by child gender and age. The merits of using the ADHD Rating Scale-5 in a multimodal assessment protocol are discussed. (PsycINFO Database Record

Previous confirmatory factor analytic research that has examined the factor structure of the Wechsler Adult Intelligence Scale–Fourth Edition (WAIS-IV) has endorsed either higher order models or oblique factor models that tend to amalgamate both general factor and index factor sources of systematic variance. An alternative model that has not yet been examined for the WAIS-IV is the bifactor model. Bifactor models allow all subtests to load onto both the general factor and their respective index factor directly. Bifactor models are also particularly amenable to the estimation of model-based reliabilities for both global composite scores (ω _h ) and subscale/index scores (ω _s ). Based on the WAIS-IV normative sample correlation matrices, a bifactor model that did not include any index factor cross loadings or correlated residuals was found to be better fitting than the conventional higher order and oblique factor models. Although the ω _h estimate associated with the full scale intelligence quotient (FSIQ) scores was respectably high (.86), the ω _s estimates associated with the WAIS-IV index scores were very low (.13 to .47). The results are interpreted in the context of the benefits of a bifactor modeling approach. Additionally, in light of the very low levels of unique internal consistency reliabilities associated with the index scores, it is contended that clinical index score interpretations are probably not justifiable.

Bi-factor confirmatory factor models have been influential in research on cognitive abilities because they often better fit the data than correlated factors and higher-order models. They also instantiate a perspective that differs from that offered by other models. Motivated by previous work that hypothesized an inherent statistical bias of fit indices favoring the bi-factor model, we compared the fit of correlated factors, higher-order, and bi-factor models via Monte Carlo methods. When data were sampled from a true bi-factor structure, each of the approximate fit indices was more likely than not to identify the bi-factor solution as the best fitting. When samples were selected from a true multiple correlated factors structure, approximate fit indices were more likely overall to identify the correlated factors solution as the best fitting. In contrast, when samples were generated from a true higher-order structure, approximate fit indices tended to identify the bi-factor solution as best fitting. There was extensive overlap of fit values across the models regardless of true structure. Although one model may fit a given dataset best relative to the other models, each of the models tended to fit the data well in absolute terms. Given this variability, models must also be judged on substantive and conceptual grounds.