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dealing with Numbers

FIGURE 18.4. Latent and observed variances of the seven method traits according to Model 8.

FIGURE 18.4. Latent and observed variances of the seven method traits according to Model 8.

parameters is 98. This seven-dimensional Rasch model has a log likelihood value of-12,129. Figure 18.5 shows the latent variances of the seven latent dimensions of this model. Compared to the variance estimates of the seven-dimensional LLTM, the estimates of the seven-dimensional Rasch model are generally higher. This is true for the latent as well as for the WLE variances. The latent variance estimates range from 0.725 for "convergent thinking" to 2.436 for "dealing with numbers," whereas the WLE variances vary from 1.285

for "mental model" to 2.540 for "dealing with numbers."

To interpret the 21 covariances of the 7 traits, a principal components analysis based on the latent correlations was calculated. Figure 18.6 shows the varimax rotation of the two-factor solution that explains 94.4% of the observed variance. With regard to the first two principal components, the cognitive competencies "dealing with graphical representations," "dealing with numbers," "employing mental models," and "convergent thinking" have

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