# Method-Toolbox

## Ant Colony Optimization (ACO)

Ant Colony Optimization (ACO) mimics the foraging behavior of ants and is a popular optimization algorithm in computational science. Ants use pheromone trails to find the shortest route from the nest to the food source, with pheromones generally accumulating faster on shorter routes, which in turn attract more ants. The routes are constantly optimized until an efficient route is found. ACO has been widely used to construct psychometrically sound and efficient short scales (Schroeders et al., 2016a). However, due to the great flexibility of the algorithm, ACO can be applied to many combinatorial optimization problems in psychological assessment.

We have used ACO to construct measures that balance between reliability and validity (Schroeders et al., 2016; Steger et al., 2023), to balance between categorical and dimensional assessment (Achaa-Amankwaa et al., 2024), to compile short scales in combination with meta-analysis (Schroeders et al., 2023), to assemble parallel test versions (Zimny et al., 2023), to construct measurement invariant scales across cultures (Jankowsky et al., 2020) or age groups (Olaru et al., 2018), but also to amplify differences between groups to learn more about the influence of item sampling on the construct, specifically age differences in personality (Olaru et al., 2019) and gender differences in declarative knowledge (Schroeders et al., 2016).

↗ Recent ACO script

↗ Key publication

## Bee Swarm Optimization (BSO)

Bee Swarm Optimization (BSO) mimics the foraging and complex communication of honey bees. In nature, scout bees explore new food sources, while onlooker bees search for food in the vicinity of previously explored, promising food sources. These principles can also be used to find the optimal factor structure of measures, which is a common optimization problem in test or questionnaire development. We have developed a novel BSO algorithm and described its functionality in a proof-of-concept study: Schroeders, Scharf, et al. (2023). The main idea in model specification search is that scout bees initiate rather global model revisions (e.g., removal of a factor), whereas onlooker bees investigate alternative models at a finer-grained level (e.g., reassignment of a single item).

↗ Recent BSO script

↗ Key publication

## Multigroup measurement invariance testing

Measurement invariance (MI) is a key concept in psychological assessment and a fundamental prerequisite for meaningful comparisons across groups. In the prevalent approach, multi-group confirmatory factor analysis (MGCFA), specific measurement parameters are constrained to equality across groups, to test for (a) configural MI, (b) metric MI, (c) scalar MI, and (d) strict MI. In the online supplement to Schroeders & Gnambs (2018), we provide example syntax for all steps of MI in lavaan and Mplus for different ways of scaling latent variables: Identification by (a) marker variable, (b) reference group, and (c) effects coding. We welcome the recent effort of journals in psychology to include soundness checks on manuscript submission to improve the accuracy of statistical reporting. Thus, we encourage authors and reviewers to routinely use our online tool to double-check the degrees of freedom of your reported models. You only have to enter the number of indicators, latent variables, groups, cross-loadings, etc. and you wil get the df for the different measurement invariant steps in a single- or multi-group confirmatory factor analysis.