A note on computing Louis’ observed information matrix identity for IRT and cognitive diagnostic models

Using Louis’ formula, it is possible to obtain the observed information matrix and the corresponding large-sample standard error estimates after the expectation–maximization (EM) algorithm has converged. However, Louis’ formula is commonly de-emphasized due to its relatively complex integration representation, particularly when studying latent variable models. This paper provides a holistic overview that demonstrates how Louis’ formula can be applied efficiently to item response theory (IRT) models and other popular latent variable models, such as cognitive diagnostic models (CDMs). After presenting the algebraic components required for Louis’ formula, two real data analyses, with accompanying numerical illustrations, are presented. Next, a Monte Carlo simulation is presented to compare the computational efficiency of Louis’ formula with previously existing methods. Results from these presentations suggest that Louis’ formula should be adopted as a standard method when computing the observed information matrix for IRT models and CDMs fitted with the EM algorithm due to its computational efficiency and flexibility.     

Active or Inert? An Experimental Comparison of Creative Ideation across Incubation Periods

The primary objective of this study was to contribute to the growing research discipline investigating the effects of physical exercise on divergent thinking creativity performance. Thirty‐two students participated in this two‐visit, within‐subject intervention. Individuals consented to participate in two randomized, and counterbalanced, experimental conditions, consisting of 15 min of active treadmill walking and an inert, seated control incubation period. Creativity was assessed at baseline and post‐exercise (and control) via the Instances Creativity Task (ICT). Creativity scores for changes in fluency (F(1, 31) = 2.90, p = .10) were not statistically significant across the experimental conditions. Originality scores were higher at baseline and follow‐up when compared to the exercise condition (F(1, 31) = 6.82, p = .01). However, there was no statistically significant condition × time interaction effect (F(1, 31) = 1.78, p = .19). Further analyses demonstrated that there was no statistically significant difference between the experimental conditions on recall score (F(1, 31) = 1.04, p = .32). All models indicated statistically significant main effects for time: fluency (F(1, 31) = 131.17, p < .001); originality (F(1, 31) = 36.54, p < .001); and recall (F(1, 31) = 51.75, p < .001). These findings suggest that both active and inert creative incubation periods may similarly enhance subsequent divergent thinking performance.