For many multivariate twin models, the numerical Type I error rates are lower than theoretically expected rates using a likelihood ratio test (LRT), which implies that the significance threshold for statistical hypothesis tests is more conservative than most twin researchers realize. This makes the numerical Type II error rates higher than theoretically expected. Furthermore, the discrepancy between the observed and expected error rates increases as more variables are included in the analysis and can have profound implications for hypothesis testing and statistical inference. In two simulation studies, we examine the Type I error rates for the Cholesky decomposition and Correlated Factors models. Both show markedly lower than nominal Type I error rates under the null hypothesis, a discrepancy that increases with the number of variables in the model. In addition, we observe slightly biased parameter estimates for the Cholesky decomposition and Correlated Factors models. By contrast, if the variance-covariance matrices for variance components are estimated directly (without constraints), the numerical Type I error rates are consistent with theoretical expectations and there is no bias in the parameter estimates regardless of the number of variables analyzed. We call this the direct symmetric approach. It appears that each model-implied boundary, whether explicit or implicit, increases the discrepancy between the numerical and theoretical Type I error rates by truncating the sampling distributions of the variance components and inducing bias in the parameters. The direct symmetric approach has several advantages over other multivariate twin models as it corrects the Type I error rate and parameter bias issues, is easy to implement in current software, and has fewer optimization problems. Implications for past and future research, and potential limitations associated with direct estimation of genetic and environmental covariance matrices are discussed.

中文翻译：

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多元行为遗传模型中的 I 型错误率和参数偏差。

对于许多多元双胞胎模型，数值类型 I 错误率低于使用似然比检验 (LRT) 的理论预期错误率，这意味着统计假设检验的显着性阈值比大多数双胞胎研究人员意识到的更为保守。这使得 II 类错误率数值高于理论预期。此外，随着分析中包含更多变量，观察到的错误率与预期错误率之间的差异也会增加，并且可能对假设检验和统计推断产生深远的影响。在两项模拟研究中，我们检查了 Cholesky 分解和相关因素模型的 I 类错误率。两者都显示出明显低于原假设下名义 I 类错误率，这种差异随着模型中变量数量的增加而增加。此外，我们观察到 Cholesky 分解和相关因素模型的参数估计略有偏差。相比之下，如果直接估计方差分量的方差-协方差矩阵（无约束），则数值类型 I 错误率与理论预期一致，并且无论分析的变量数量如何，参数估计都不会出现偏差。我们称之为直接对称方法。似乎每个模型隐含的边界，无论是显式的还是隐式的，都会通过截断方差分量的采样分布并在参数中引入偏差来增加数值和理论 I 类错误率之间的差异。直接对称方法比其他多元孪生模型有几个优点，因为它纠正了 I 类错误率和参数偏差问题，易于在当前软件中实现，并且优化问题较少。讨论了对过去和未来研究的影响，以及与直接估计遗传和环境协方差矩阵相关的潜在局限性。