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PreprintCC BY 4.0arXiv

Selective Inference in Growth Curve Models

  • Haochen Lei
  • Qian Zhang
  • Hongyuan Cao
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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 na\"ıve post-selection inference can be biased. An application to the Longitudinal Study of American Youth illustrates the proposed framework.

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Cite

BibTeXRIS
BibTeX
@misc{lei2026selective,
  title = {{Selective Inference in Growth Curve Models}},
  author = {Haochen Lei and Qian Zhang and Hongyuan Cao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19573},
  eprint = {2609.19573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19573},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Selective Inference in Growth Curve Models
AU  - Haochen Lei
AU  - Qian Zhang
AU  - Hongyuan Cao
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19573
UR  - https://arxiv.org/abs/2609.19573
AB  - 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 na\"ıve post-selection inference can be biased. An application to the Longitudinal Study of American Youth illustrates the proposed framework.
ER  -