Evaluation of path analysis through computer simulation: effect of incorrectly assuming independent distribution of familial correlations.
Path analysis of family data has been widely applied to resolve genetic and environmental patterns of familial resemblance. A prevalent statistical approach in path analysis has been, first, to estimate the familial correlations and, second, by assuming these estimates to be independently distributed, define a likelihood function from which maximum likelihood estimates of model parameters can be obtained and likelihood ratio tests of hypotheses performed. Although it is generally known that the independence assumption does not hold when multiple familial correlations are estimated from the same family data, this statistical method has still been used in these situations owing, in part, to the lack of any viable alternatives and, in part, to the lack of any knowledge about the specific quantitative effects of not meeting the assumption of independence. Here, using computer-simulation methods, we evaluate the robustness of this statistical method to deviations from the assumption of independence. In general, we found that the failure to meet the assumption of independence leads to a conservative test of the goodness-of-fit of the path model, although likelihood ratio tests of specific null hypotheses were at times liberal, at times conservative, and at times nearly exact. Although the test statistics were found to be distorted, the parameter estimates using this method were nearly unbiased.