Experimental effects and individual differences in Linear Mixed Models: Estimating the relationship between spatial, object, and attraction effects in visual attention

<strong>Paper package (preprint PDF, data, R scripts) for:</strong> Kliegl, R., Wei, P., Dambacher, M., Yan, M., &amp; Zhou, X. (2011). Experimental effects and individual differences in Linear Mixed Models: Estimating the relationship between spatial, object, and attraction effects in visual attention. <em>Frontiers in Quantitative Psychology and Measurement, 1.</em> <strong>Abstract</strong>. Linear mixed models (LMMs) provide a still underused methodological perspective on combining experimental and individual-differences research. Here we illustrate this approach with two-rectangle cueing in visual attention (Egly, Driver, &amp; Rafal, 1994). We replicated previous experimental cue-validity effects relating to a spatial shift of attention within an object (spatial effect), to attention switch between objects (object effect), and to the attraction of attention towards the display centroid (attraction effect), taking also into account the design-inherent imbalance of valid and other trials. We simultaneously estimated variance/covariance components of subject-related random effects for these spatial, object, and attraction effects in addition to their mean RTs. The spatial effect showed a strong positive correlation with mean RT and a strong negative correlation with the attraction effect. The analysis of individual differences suggests that slow subjects engage attention more strongly at the cued location than fast subjects. We compare this joint LMM analysis of experimental effects and associated subject-related variances and correlations with two frequently used alternative statistical procedures. <strong>Corrections.</strong> Titus von der Malsburg pointed out two errors in the publication relating to AIC and BIC values reported on page 7: (1) The AIC-value for the model m2 was reported as 328540; the correct value is 325840. This was a transposition typo ("85" instead of "58"). (2) The BIC-value for model m1 (325941) is actually smaller than the BIC-value for model m2 (325964). Thus, for BIC, the fit of model m2 is not better than the one for model m1. 5 Jan 2011, R. Kliegl <strong>Update.</strong> KWDYZ.FQPM.v5.R is compatible with ggplot2 (0.9.0). 21 April 2012, R. Kliegl