Existing Approaches Sample Clauses

Existing Approaches. ‌ Currently there exist two commonly used approaches to estimating heritability, one based on method of moments, and another based on maximum likelihood. The so- called “Xxxxxxxx’x formula” (Xxxxxxxx and Xxxxxx, 1996) is a simple point estimate for heritability using twin data based on moment matching. The best-practice and commonly used likelihood-based method constructs a variance component model using a variance decomposition, which parameterizes the varying degree of covari- ance expected with varying relatedness between subjects; the variance parameters are estimated by maximizing the likelihood or restricted likelihood function with respect to those parameters. Hypothesis tests are generally made with likelihood ratio test, and the asymptotic standard error of the maximum likelihood estimator can be computed with the Xxxxxx information matrix. These methods for heritabil- ity inference will be discussed in Section 3.2. While the first neuroimaging studies measuring heritability used Xxxxxxxx’x method, e.g., Xxxxxx et al. (2002), likelihood-based approaches are becoming more prevalent, with the use of variance components or structural equation modeling methods. But such methods cannot exploit the spatial nature of the imaging data to improve the statistical sensitivity, nor provide inferences corrected for searching the brain for heritability; in particular, neuroimaging researchers wish to control the rate of family-wise errors (FWE), the chance of making one or more false positives among all hypotheses in the whole brain. Although a simple Bonferroni correction is a p-value adjustment approach offering the control of FWE, it is typically quite conservative for smooth images, and thus is often not useful with brain imaging data. When feasible, permutation inference offers an exact control of false positive risk and allows the use of specialized spatial statistics while implicitly accounting for the spatial dependence. However, the maximum-likelihood-based approaches mentioned above are mostly iterative and can be too time-consuming and unreliable (i.e., can fail to converge) to allow permutations. Another, quite practical concern, is that current tools are not designed for brain imaging data, cannot compute basic spatial statistics, and can neither read nor write brain image file formats.