# Negative estimates (such as A) - what to do if this corresponds to lowest AIC

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Joined: 11/19/2018 - 19:32
Negative estimates (such as A) - what to do if this corresponds to lowest AIC

Hi,

I was wondering what one should do if the estimates of the model have a negative component for the variances of a given component. I am familiar that in the direct variance approach paper it mentions there can be negative A estimates, and this can make biological sense. Similarly, at least for the ACE/ADE base model, there is a negative/positive parameter estimate relationship in which interpretability should win out (so whichever one is positive here, since the AIC will be the same in any case for ACE/ADE). However, if the A estimate is negative, or any of the submodels have a negative estimate, and this corresponds to the lowest AIC, is there a potential explanation to this, other than that the model is not well-suited (given the paper itself mentions there can be negative A estimates and biologically this may be feasible)?

I appreciate it! Offline
Joined: 03/01/2013 - 14:09
One thing you might want to

One thing you might want to do is to examine the significance of the negative estimate. If, in reality, the variance component is zero, then half the time its estimate will be below zero. Even if the variance component in the true world is small, it may result in a negative estimate. So if you fix it to zero and examine the likelihood ratio test of fixing that parameter to zero, you can get an idea of whether it is "significantly" negative. If not, the data are compatible with fixing the component to zero. If it is significantly negative, you may want to consider alternative models for the data. In the case of C in an ACE model, it is reasonable to note that C is merely an aggregate of C, Assortative mating and age effects (if not corrected), non-additive genetic effects including dominance and epistasis. Significantly negative C implies that variance due to non-additivity has overwhelmed any C that was there.
HTH! Offline
Joined: 03/01/2020 - 08:52
Model selection

I would like to ask a similar question. Namely, I ran an ACE and ADE model on my data and got the following estimates:
ACE: A) 15.33 [12.11, 18.16] C) <0.001 [-9.87, 9.87] E) 16·89 [14.89, 19.21]
ADE: A) -7.56 [-17.65, 17.65] D) 14·07 [-18.62, 18.62] E) 16.27 [14.23, 18.77]
I then tested the significance of the paths by comparing the submodes to the according full model and neither A, nor D were significant in the ADE model, but A was significant in the ACE model. I assume, in this case I should select the ACE model over the ADE model (even if the AIC is higher) and report the AE sub-model?
Leslie Offline
Joined: 03/01/2013 - 14:09
Estimate ACE variance component model instead?

Hi

One thing you might try is to fit a model where the variance components are not constrained to be positive. See Verhulst & Neale. Also, it is useful to note the MZ and DZ correlations. In the long run, I don't think the approach to examine constrained-positive estimates in ACE vs ADE models is very sound statistically. If you fit the can-go-negative model, you may find that you get a negative estimate of C, which would indicate that the balance of C and D (including dominance AxA and higher order epistatic interactions) was such that the non-additivity outweighs the common environmental effects. Offline
Joined: 03/01/2013 - 14:09
ACE and ADE have same -2lnL

If not restricted to be positive (by estimating a path that is always squared in the expected covariance matrix or explicitly adding a lower bound) then ADE and ACE models fit the same. C and D are confounded so in either case you get a blend of non-additivity (dominance, gxe, epistasis) with shared environment plus genetic effects of assortative mating. We have to live with these indeterminacies until we include other types of relative.