TY  - JOUR
A1  - Matuschek, Hannes
A1  - Kliegl, Reinhold
T1  - On the ambiguity of interaction and nonlinear main effects in a regime of dependent covariates
JF  - Behavior research methods : a journal of the Psychonomic Society
N2  - The analysis of large experimental datasets frequently reveals significant interactions that are difficult to interpret within the theoretical framework guiding the research. Some of these interactions actually arise from the presence of unspecified nonlinear main effects and statistically dependent covariates in the statistical model. Importantly, such nonlinear main effects may be compatible (or, at least, not incompatible) with the current theoretical framework. In the present literature, this issue has only been studied in terms of correlated (linearly dependent) covariates. Here we generalize to nonlinear main effects (i.e., main effects of arbitrary shape) and dependent covariates. We propose a novel nonparametric method to test for ambiguous interactions where present parametric methods fail. We illustrate the method with a set of simulations and with reanalyses (a) of effects of parental education on their children’s educational expectations and (b) of effects of word properties on fixation locations during reading of natural sentences, specifically of effects of length and morphological complexity of the word to be fixated next. The resolution of such ambiguities facilitates theoretical progress.
KW  - Interaction effects
KW  - Mixed models
KW  - Additive mixed models
KW  - Regression splines
KW  - Non-parametric curve estimation
Y1  - 2017
U6  - https://doi.org/10.3758/s13428-017-0956-9
SN  - 1554-351X
SN  - 1554-3528
VL  - 50
IS  - 5
SP  - 1882
EP  - 1894
PB  - Springer
CY  - New York
ER  -