On the ambiguity of interaction and nonlinear main effects in a regime of dependent covariates
- 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 naturalThe 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.…
| Author details: | Hannes MatuschekORCiDGND, Reinhold KlieglORCiDGND |
|---|---|
| DOI: | https://doi.org/10.3758/s13428-017-0956-9 |
| ISSN: | 1554-351X |
| ISSN: | 1554-3528 |
| Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/28917056 |
| Title of parent work (English): | Behavior research methods : a journal of the Psychonomic Society |
| Publisher: | Springer |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2017/09/15 |
| Publication year: | 2017 |
| Release date: | 2021/09/21 |
| Tag: | Additive mixed models; Interaction effects; Mixed models; Non-parametric curve estimation; Regression splines |
| Volume: | 50 |
| Issue: | 5 |
| Number of pages: | 13 |
| First page: | 1882 |
| Last Page: | 1894 |
| Funding institution: | Deutsche Forschungsgemeinschaft for Research Group 868 Computational Modeling of Behavioral, Cognitive, and Neural DynamicsGerman Research Foundation (DFG) [KL 955/14] |
| Organizational units: | Humanwissenschaftliche Fakultät / Strukturbereich Kognitionswissenschaften / Department Psychologie |
| DDC classification: | 1 Philosophie und Psychologie / 15 Psychologie / 150 Psychologie |
| Peer review: | Referiert |
| Publishing method: | Open Access / Bronze Open-Access |
