Linear mixed models are widely used to analyze non-independent data, but inference for fixed effects can be unreliable under misspecification of the random-effects distribution, inaccurate Fisher information estimation, or convergence failures, leading to a lack of control over false positives. These difficulties are amplified in multivariate settings, where within-cluster and between-response dependence must be modeled jointly. We propose a testing procedure for fixed effects in multivariate linear mixed models that avoids Fisher information estimation and does not require correct specification of the random-effects distribution by combining score statistics with clusterwise sign-flipping transformations. Our method accommodates both forms of dependence and yields asymptotically valid inference under weak distributional assumptions on the data-generating process.

翻译：线性混合模型广泛应用于非独立数据分析，但当随机效应分布设定错误、Fisher信息估计不准确或收敛失败时，对固定效应的推断可能不可靠，导致对假阳性控制不足。这些问题在需联合建模簇内依赖与响应间依赖的多元场景中更为突出。本文提出一种适用于多元线性混合模型的固定效应检验程序，通过结合得分统计量与簇内符号翻转变换，既避免了Fisher信息估计，也无需正确指定随机效应分布。该方法能同时处理两种依赖形式，并在关于数据生成过程的弱分布假设下，实现渐近有效的推断。