🤖 AI Summary
本文针对生长曲线模型中变量选择后的推断问题，提出了一种数据裂变框架，通过加减高斯噪声来分离选择和推断信息，提供有效推断。
📝 Abstract
Growth curve models are widely used in psychological research, and variable selection can help identify baseline characteristics associated with longitudinal heterogeneity. However, conventional inference after data-driven variable selection can be invalid because the same outcome data are used for both selection and inference. We develop a data-fission framework for post-selection inference in growth-curve models that separates the information used for selection and inference while retaining all participants in both stages through the addition and subtraction of Gaussian noise. The framework accommodates flexible variable-selection procedures and targets covariance-weighted linear projection parameters in the selected working model. It provides exact inference when the covariance structure is known, and we establish asymptotic validity under suitable regularity conditions when the covariance structure is estimated. Simulations show that the proposed method provides valid inference and improves efficiency over subject-level data splitting, whereas naïve post-selection inference can be biased. An application to the Longitudinal Study of American Youth illustrates the proposed framework.