Measuring the menu, not the food: "psychometric" data may instead measure "lingometrics" (and miss its greatest potential).

This is a review of a range of empirical studies that use digital text algorithms to predict and model response patterns from humans to Likert-scale items, using texts only as inputs. The studies show that statistics used in construct validation is predictable on sample and individual levels, that this happens across languages and cultures, and that the relationship between variables are often semantic instead of empirical. That is, the relationships among variables are given a priori and evidently computable as such. We explain this by replacing the idea of "nomological networks" with "semantic networks" to designate computable relationships between abstract concepts. Understanding constructs as nodes in semantic networks makes it clear why psychological research has produced constant average explained variance at 42% since 1956. Together, these findings shed new light on the formidable capability of human minds to operate with fast and intersubjectively similar semantic processing. Our review identifies a categorical error present in much psychological research, measuring representations instead of the purportedly represented. We discuss how this has grave consequences for the empirical truth in research using traditional psychometric methods.

A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix.

We present and investigate a simple way to generate nonnormal data using linear combinations of independent generator (IG) variables. The simulated data have prespecified univariate skewness and kurtosis and a given covariance matrix. In contrast to the widely used Vale-Maurelli (VM) transform, the obtained data are shown to have a non-Gaussian copula. We analytically obtain asymptotic robustness conditions for the IG distribution. We show empirically that popular test statistics in covariance analysis tend to reject true models more often under the IG transform than under the VM transform. This implies that overly optimistic evaluations of estimators and fit statistics in covariance structure analysis may be tempered by including the IG transform for nonnormal data generation. We provide an implementation of the IG transform in the R environment.

Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections.

This simulation study investigates the performance of three test statistics, T1, T2, and T3, used to evaluate structural equation model fit under non normal data conditions. T1 is the well-known mean-adjusted statistic of Satorra and Bentler. T2 is the mean-and-variance adjusted statistic of Sattertwaithe type where the degrees of freedom is manipulated. T3 is a recently proposed version of T2 that does not manipulate degrees of freedom. Discrepancies between these statistics and their nominal chi-square distribution in terms of errors of Type I and Type II are investigated. All statistics are shown to be sensitive to increasing kurtosis in the data, with Type I error rates often far off the nominal level. Under excess kurtosis true models are generally over-rejected by T1 and under-rejected by T2 and T3, which have similar performance in all conditions. Under misspecification there is a loss of power with increasing kurtosis, especially for T2 and T3. The coefficient of variation of the nonzero eigenvalues of a certain matrix is shown to be a reliable indicator for the adequacy of these statistics.

The effect of kurtosis on the power of two test statistics in covariance structure analysis.

We study the effect of excess kurtosis on the non-centrality parameters of the rescaled and the residual-based test statistics for covariance structure models. The analysis is based on population matrices and parameters, which eliminates the sampling variability inherent in simulation studies. We show that the non-centrality parameters, and consequently the asymptotic power, decrease as kurtosis in the data increases. Examples are provided to compare this decrease for the two test statistics, and to illustrate how substantial it is.

Does the ADF fit function decrease when the kurtosis increases?

In this study we demonstrate how the asymptotically distribution-free (ADF) fit function is affected by (excessive) kurtosis in the observed data. More specifically, we address how different levels of univariate kurtosis affect fit values (and therefore fit indices) for misspecified factor models. By using numerical calculation, we show (for 13 factor models) that the probability limit F(0) of F empty set for the ADF fit function decreases considerably as the kurtosis increases. We also give a formal proof that the value of F(0) decreases monotonically with the kurtosis for a whole class of structural equation models.