Fig 1.
Illustration of the Genetic Algorithm.
In the first iteration, the Genetic Algorithm randomly selects four item sets, which are highlighted in color, from an initial pool of 10 item sets. Each two of these sets are used to produce a new item set based on two principles: 1) subsetting and recombination (= crossover) and 2) random changes to the item set (= mutation). The newly assembled short versions are evaluated and ordered according to an optimization function (= fitness evaluation). The ordering influences the selection probability of an item to be assembled in a short version in the next iteration.
Table 1.
Description of Cognitive and Motivational Measures.
Fig 2.
Distribution of Factor Loadings for the Original and Shortened Versions.
A boxplot covers the interquartile range; the solid line refers to the median. Letters indicate the item selection algorithm: S = Stepwise Confirmatory Factor Analysis; A = Ant Colony Optimization; G = Genetic Algorithm; Numbers refer to the number of items in the abridged version; 89 = Original version with 89 items.
Fig 3.
Distributions of the Item Difficulties of the Original and Shortened Versions.
A boxplot covers the interquartile range; the solid line within a boxplot refers to the median. The gray solid line points out the guessing probability; the gray dashed line refers to the optimum item difficulty of .625. Letters indicate the item selection algorithm: S = Stepwise Confirmatory Factor Analysis; A = Ant Colony Optimization; G = Genetic Algorithm; Numbers refer to the number of items in the abridged version; 89 = Original version with 89 items. The horizontal gray line indicates the guessing probability (P(x) = .25).
Fig 4.
Correlation of the Original and Shortened Versions to Covariates.
Letters indicate the item selection algorithm: S = Stepwise Confirmatory Factor Analysis; A = Ant Colony Optimization; G = Genetic Algorithm; Numbers refer to the number of items in the abridged version; 89 = Original version with 89 items.
Table 2.
Model Fit of Original and Shortened Versions.