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Testing Systematic Genotype by Environment Interactions Using Item Level Data

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Abstract

Investigating genotype by environment interactions (GxE) is generally considered challenging due to the scale dependency of the interaction effect. The present paper illustrates the problems associated with testing for GxEs on summed item scores within the well-known ACE model. That is, it is shown how genuine GxEs may be masked and how spurious interactions can arise from scaling issues in the data. A solution is proposed which explicitly distinguishes between a measurement model for the ordinal item responses and a biometric model in which the GxE effects are investigated. The new approach is studied in a simulation study using both a scenario in which the measurement instrument suffers from mild scaling problems and a scenario in which the measurement instrument suffers from severe scaling problems. Results indicate that the severity of the scale problems affects the power to detect GxE, but it rarely results in false positives. We illustrate the new approach on a real dataset concerning affect.

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Notes

  1. The work by Schwabe and van den Berg (2014) was conducted parallel to—but independent from—the present undertaking. Only at a late stage did we learn about each others work on this topic.

  2. The cumulative standard normal distribution function, Φ(.), in Eq. 5 assumes unit polychoric variances of the item scores conditional on θp1 and θp2. Due to the presence of δpi, the conditional polychoric variance will depart from 1 if r i ≠ 0. Therefore, to prevent parameter bias, the scaling term is added to ensure that the conditional polychoric variance will be equal to 1.

  3. The opinions expressed in this article are those of the authors and do not necessarily reflect the views of the ICPSR.

  4. Because we used a Bayesian model fit approach, we omitted the term ‘power’ in discussion of the results and spoke of ‘hit rate’ instead. However, to be able to compare results of the frequentist results we take the ‘hit rate’ as found in present study as an indication for what the ‘power’ would have been when we would have implemented present model in a frequentist framework.

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Acknowledgment

Conor V. Dolan is supported by the European Research Council (Genetics of Mental Illness; Grant number: ERC-230374).

Conflict of Interest

Dylan Molenaar and Conor V. Dolan declare that they have no conflict of interest.

Human and Animal Rights and Informed Consent

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000 (5). Informed consent was obtained from all patients for being included in the study. As we analyse data that was administered in the National Survey of Midlife Development in the United States (MIDUS) in 1995–1996 under the auspices of the Inter-university Consortium for Political and Social Research (ICPSR), we kindly refer to this source for details concerning ethical procedures and informed consent.

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Authors and Affiliations

  1. Psychological Methods, Department of Psychology, University of Amsterdam, Weesperplein 4, 1018 XA, Amsterdam, The Netherlands

    Dylan Molenaar

  2. Department of Biological Psychology, VU University, Amsterdam, The Netherlands

    Conor V. Dolan

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  1. Dylan Molenaar
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  2. Conor V. Dolan
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Correspondence to Dylan Molenaar.

Appendices

Appendix A: OpenBUGS code to fit the model in case of dichotomous item scores

Appendix B: OpenBUGS code to fit the model in case of Likert item scores

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Molenaar, D., Dolan, C.V. Testing Systematic Genotype by Environment Interactions Using Item Level Data. Behav Genet 44, 212–231 (2014). https://doi.org/10.1007/s10519-014-9647-9

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