This function (LKM) is used to perform Kernel Machine analysis (Yan et al., 2016) for quantitative traits in GWAS longitudinal data. # It considers random intercept and random time
LKM_Null_Model(phenotype, time, yid, covariates = NULL)
A vector of quantitative trait in the analysis (class: vector). The order should match the vector yid. No missing.
A vector of time points (class: vector). The order should match the vector yid. No missing.
A vector of id (class: vector). Although it doesn't have to be sorted, observations from the same subject have to be connected with each other. The repeated id numbers indicate multiple time points for one subject. Make sure it is not a factor. No missing.
A matrix of covariates (class: data.frame). The order of rows should match the vector yid. Default NULL. No missing.
output: object as input for LKM