**Appendix A**


**Table A1.** Identification results for *n* = 60, *p* = 30 with an actual dimension of 124.

Mean (sd) based on 100 replicates. A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.

**Table A2.** Estimation accuracy results for *n* = 60, *p* = 30 with an actual dimension of 124.


Mean (sd) based on 100 replicates. A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.


**Table A3.** Data simulated based on the underlying main effect only model. Identification results for *n* = 250, *p* = 75, *ρ* = 0.8 with an actual dimension of 304.

Mean (sd) based on 100 replicates. A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.

**Table A4.** Null models.


Mean (sd) based on 100 replicates. A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.

**Table A5.** Stability selection percentages for all 17 true effects in the simulated data when *n* = 250, *p* = 75, *ρ* = 0.8 with an actual dimension of 304.


A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.


**Table A6.** Validation methods. Identification results for *n* = 250, *p* = 75 with an actual dimension of 304.

Mean (sd) based on 100 replicates. A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.

**Table A7.** Validation methods. Estimation accuracy results for *n* = 250, *p* = 75 with an actual dimension of 304.


Mean (sd) based on 100 replicates. A1–A3: methods accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively. A4–A6: methods not accommodating the lipid–environment interactions with exchangeable, AR(1), and independence working correlations, respectively.
