OLS is AOK for ACE: A Regression-Based Approach to Synthesizing Political Science and Behavioral Genetics Models

It is important to note that some political scientists have been calling for just such a shift for more than 30 years (e.g., Somit 1972; Masters et al. 1984). With few exceptions, however, these calls were largely ignored by the discipline’s mainstream until relatively recently.

These are not the only assumptions of the model. Classically there is also an assumption of no gene–environment interaction (which would require adding a G × E term), though these are increasingly being explicitly modeled. The external validity of finding from twin studies also rests on the assumption that twins are representative of the general population. For a more extensive introduction to the logic and assumptions of twin studies see Medland and Hatemi (2009).

The original DF formulation presented here is still widely employed, even though a number of extensions and refinements have been proposed. The best known of the latter is probably Rodgers and Kohler’s (2005) reformulation, which is based on centering the data. Centering allows the R parameter and the intercept to be dropped, thus directly modeling P = A + C. One potential concern with DF models that might occur to some readers is the possibility that as regression coefficents the parameters representing A and C might be statistically significant yet greater than 1.0 or less than zero. While this is mathematically possible, it is an unlikely occurrence. More possible (though not particularly probable) are confidence intervals that would extend beyond the 1.0/zero boundaries. Such results would likely be caused when most of the variance in P is being driven by either A or C and/or when twins are systematically dissimilar on a trait (e.g., if twins who are liberal generally and systematically tended to have co-twins who are more conservative). In any case, in terms of substantive inference the story would almost certainly be the same as that taken from a maximum likelihood approach constraining estimates to the boundaries of 1.0 and zero, i.e., either all the variance (an estimate of 1.0 or greater than 1.0) or none of the variance (zero or less than zero) is attributed to A, C or E. Regardless of statistical approach estimates are just that, i.e. estimates, so inference in such scenarios would be more conservatively interpreted as “most of the variance” or a “trivial amount of variance” rather than all or none.

Alternate approaches to correcting for standard errors include clustering standard errors on twin pairs using a GEE, random effects or a Huber–White approach. See Kohler and Rodgers (2001) for a more in-depth discussion of the degrees of freedom issues raised in DF models.

Purcell and Koenen (2005, p. 497) do suggest a reformulation of the DF Model that can test the effect of measured E variables independent of genetic effects, though this has yet to be widely employed.

It is important to re-emphasize that the essential issues here are not unique to DF models. Interpreting results for environmental variables as independent of any genetic influence is dependent more on the assumptions made by the analysis than the particular statistical approach.

The data employed in this project were collected with the financial support of the National Science Foundation in the form of SES-0721378, PI: John R. Hibbing; Co-PIs: John R. Alford, Lindon J. Eaves, Carolyn L. Funk, Peter K. Hatemi, and Kevin B. Smith, and with the cooperation of the Minnesota Twin Registry at the University of Minnesota, Robert Krueger and Matthew McGue, Directors.