Assessing gene-environment interaction in case of heterogeneous measurement error

Recently, the Dutch Bureau for Economic Policy published a report stating that Dutch students are underperforming when compared internationally. Overall performance was not bad, but strikingly, the Dutch best performing students were ranked lower than were the average and poor performing students when compared internationally within their respective performance groups. Arguably, this suggest that Holland’s most gifted students are not nurtured to their maximum potential. Our project aims at assessing whether this hypothesis is true using twin data on school performance.
Many methods to study gene-environment interaction are directly or indirectly based on relationships between absolute differences in the twins’ phenotypic scores and the sum of their scores. However, difference scores not only indicate the influence of non-genetic factors, but also possibly reflect measurement error. While existing tests generally show lower measurement error variance for average students, scale scores may be very unreliable for high performing students due to the relatively little information provided by only a few very difficult items. If differences in measurement precision across the scale is ignored, this may lead to bias in the assessment of gene-environment influences.
In a simulation study it is illustrated by means of Item Response Theory (IRT) that standard errors of measurement are not constant across the entire performance range. In addition it is shown that potential bias can be remedied by incorporating a measurement model when assessing gene-environment interaction.