Bee Swarm Optimization (BSO)

“Bees are amazing, little creatures” (Richardson, 2017) – I agree. Bees have fascinated people since time immemorial, and yet even today there are still novel and fascinating discoveries (see the PLOS collection for some mind-boggling facts). Although bees as an insect species might seem as the prime example of state-building insects, highly social forms of community are the exception among bees. The large majority of all bee species are solitary bees or cuckoo bees that do not form insect states.

Honey bees, however, are known for their social life, their division of labor and sophisticated ways of communication. Scout bees search the surroundings of the hive for profitable food sources. After collecting the nectar, they return to the hive and hand over samples to taster bees, which evaluate the quality of the food source. In case of a positive evaluation, the scouts are requested to pass on additional information to the onlooker bees. Information on the type and quality of the material and, for more distant sources, the distance and direction are communicated through dances. As a consequence, onlooker bees are directed near the indicated food sources to exploit the profitable food sources. But what has the waggle dance to do with psychological assessment. Let me explain.

Structure finding and item selection

BSO algorithms have been applied in the computational sciences to solve various problems (for an overview see Karaboga & Akay, 2009; Karaboga et al., 2012). In a new paper, we transfer BSO to psychological assessment to tackle a prevalent issue: In test or questionnaire development, finding the optimal factor structure while selecting appropriate items represents a complex optimization problem. The default procedure is to run an Exploratory Factor Analysis (EFA; Fabrigar & Wegener, 2011) in combination with some item selection (Kruyen et al., 2013; Steger et al., 2022). This approach includes a number of individual decisions for the EFA part, such as deciding on the estimator (Preacher & MacCallum, 2003), choosing a rotation method (Schmitt & Sass, 2011), and determining the number of factors to be extracted (Preacher et al., 2013). Subsequently, items with substantial cross-loadings are excluded, and the steps are repeated until a robust and interpretable solution is found. This might seem like a straightforward procedure, but it is not. In each iteration of the procedure, there are multiple options. For example, several methods have been suggested to determine how many factors should be retained, but without clear recommendations as to when they should be used (Auerswald & Moshagen, 2019). Thus, item selection with a simultaneous assignment of items to factors is a formidable optimization problem with many researchers’ degrees of freedom (Nelson et al., 2018; Simmons et al., 2011).

The blueprint of BSO

This is where BSO might help, because the principles how bees organize their foraging behavior can be translated to the issue of finding the core structure and of measure. What do I mean with core structure? Finding important dimensions of a measure and conducting item selection simultaneously. The main idea is that there is also a kind of division of labor in model specification search. In short, scout bees introduce major changes to a model (i.e., handling of factors), whereas onlooker bees investigate alternative models at a more fine-grained level (i.e., re-assigning a single item). In the manuscript the baseline model is a bifactor model (or bee factor model, because of the pun alone), but in principle the mechanisms presented are easily transferable to other measurement models.

Each model is considered a location in the area and a potential food source that is visited by a bee. All models are evaluated by a pre-defined optimization function including multiple criteria (e.g., model fit and factor saturation) and sorted accordingly. The better a model is evaluated, the more bees are requested to follow and investigate alternative solutions similar to this model. Scout bees take the best model of previous iterations and (a) add a nested factor, (b) split a nested factor, (c) remove a nested factor completely, or (d) merge two nested factors. In contrast, onlooker bees introduce minor changes to the model, that is, (a) add an item to a nested factor (if it was not assigned to a nested factor previously), (b) remove an item from a nested factor (so that it only loads on the general factor), (c) swap an item between nested factors, or (d) completely remove an item from the pool. Model search is an iterative, that is, after each iteration, the list of best models is updated and used as a starting point by both scout and onlooker bees in the next iteration.

Model specification searches using BSO

We have developed this new BSO algorithm and described its functionality in a preprint: Schroeders et al. (2022). With this proof-of-concept study, we follow two aims: First, we systematically study the influence of different hyperparameters such as the number of scout bees and onlooker bees, respectively, on the convergence and the quality of the provided solutions. For this purpose, we used the well-known Holzinger-Swineford data set (Holzinger & Swineford, 1939). Second, we study the usability and applicability of BSO in another data set featuring a short dark triad questionnaire (SD3, Jones & Paulhus, 2014). We took the questionnaire as an example to showcase how to derive essentially equivalent models that all satisfy the predefined psychometric criteria. Thus, BSO enables researchers to examine the variation of possible and feasible solutions, quite similar to a Multiverse Analysis (Steegen et al., 2016) at the level of a measurement model.

If you are interest you can find the complete Bee Swarm Optimization script on GitHub. If you have further questions, what the algorithm can and cannot do, drop me a line.