We created a shorter and more refined item set from the Almost Perfect Scale-Revised (APS-R; Slaney, Mobley, Trippi, Ashby, & Johnson, 1996; Slaney, Rice, Mobley, Trippi, & Ashby, 2001) to measure 2 major dimensions of perfectionism: standards (high performance expectations) and discrepancy (self-critical performance evaluations). In Study 1, after testing the internal structure of the measure (N = 749), a subset of the current APS-R items was derived (Short Almost Perfect Scale [SAPS]) that possessed good psychometric features, such as strong item-factor loadings, score reliability, measurement invariance between women and men, and criterion-related validity through associations with neuroticism, conscientiousness, academic performance, and depression. Controlling for neuroticism and conscientiousness, factor mixture modeling supported a 2-factor, 3-class model of perfectionism, and results were consistent with labeling the classes as nonperfectionists and adaptive and maladaptive perfectionists. Measurement results were cross-validated in a separate sample (N = 335). Study 2 also provided substantial evidence for the convergent, discriminant, and criterion-related validity of SAPS scores. Both studies supported the SAPS as a brief and psychometrically strong measure of major perfectionism factors and classes of perfectionists.

Structural Equation Mixture Models(SEMMs) are latent class models that permit the estimation of a structural equation model within each class. Fitting SEMMs is illustrated using data from one wave of the Notre Dame Longitudinal Study of Aging. Based on the model used in the illustration, SEMM parameter estimation and correct class assignment are investigated in a large scale simulation study. Design factors of the simulation study are (im)balanced class proportions, (im)balanced factor variances, sample size, and class separation. We compare the fit of models with correct and misspecified within-class structural relations. In addition, we investigate the potential to fit SEMMs with binary indicators. The structure of within-class distributions can be recovered under a wide variety of conditions, indicating the general potential and flexibility of SEMMs to test complex within-class models. Correct class assignment is limited.

When analyzing survey data the decision to weight variables or not can have serious implications. Sample selection probabilities might be unequal by design or as a result of frame errors, nonresponse or other data collection problems. If we do not weight when appropriate, we run the risk of having biased coefficient estimates and poor inferences. Alternatively, when we unnecessarily apply weights, we can create an inefficient estimator with reduced statistical power and no gain in accuracy. Yet in practice it is rare to see researchers testing whether weighting is necessary. One reason for this is that researchers are sometimes guided more by the current practice in their field than by scientific evidence. Another reason is that the statistical tests for weighting are neither widely known nor widely available in major statistical software packages. This is further complicated by the broad array of tests with little guidance on which has optimal properties under which conditions. This paper reviews a wide variety of empirical tests to determine whether weighted analyses are justified. Our focus is on regression models, though the implications of our review extend beyond regression. Even with this focus, there are a half-dozen or more diagnostic tests that are a source of confusion for analysts. Our review demonstrates that nearly all such tests are classifiable into two categories that we refer to as Hausman-type Tests and Weight Association Tests. We describe the distinguishing features of each category, present the known properties of the tests, and how they are related to each other. We also review the limited simulation evidence that has investigated the sampling properties of these tests in finite samples. Finally, we highlight the unanswered theoretical and practical questions that surround these tests and that deserve further statistical research.

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Taxometric procedures such as MAXEIG and factor mixture modeling (FMM) are used in latent class clustering, but they have very different sets of strengths and weaknesses. Taxometric procedures, popular in psychiatric and psychopathology applications, do not rely on distributional assumptions. Their sole purpose is to detect the presence of latent classes. The procedures capitalize on the assumption that, due to mean differences between two classes, item covariances within class are smaller than item covariances between the classes. FMM goes beyond class detection and permits the specification of hypothesis-based within-class covariance structures ranging from local independence to multidimensional within-class factor models. In principle, FMM permits the comparison of alternative models using likelihood-based indexes. These advantages come at the price of distributional assumptions. In addition, models are often highly parameterized and susceptible to misspecifications of the within-class covariance structure. Following an illustration with an empirical data set of binary depression items, the MAXEIG procedure and FMM are compared in a simulation study focusing on class detection and the assignment of subjects to the latent classes. FMM generally outperformed MAXEIG in terms of class detection and class assignment. Substantially different class sizes negatively impacted the performance of both approaches, whereas low class separation was much more problematic for MAXEIG than for the FMM.