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In many applications of hierarchical latent variable model, manifest variables could be missing due to various reasons. Improper missing data techniques or data imputation algorithms may lead to incredible data sets and inaccurate estimates. In our paper, we propose two types of imputation partial least square (PLS) algorithms to deal with missing data problems in hierarchical latent variable model. One is the imputation PLS algorithms based on linear regression (IPLSL), the other is the imputation PLS algorithms based on quantile regression (IPLSQ). In IPLSL, we apply the idea of complete case analysis (CC), inverse probability weighting (IPW) and fractional imputation (FI) to one kind of PLS algorithm which is different from the existing repeated indicators approach, two-step approach and hybrid approach. In IPLSQ, we also apply CC, IPW and FI to a modified PLS algorithm based on quantile regression. Compared with IPLSL, IPLSQ has the advantages in capturing overall view of structural relationships at different quantiles and highlighting the changing relations according to the explored quantile of interest. Together with mean and median imputation, we investigate the performances of our IPLSL and IPLSQ algorithms through simulation studies and then apply them to national science and technology innovation capability study based on part of World Bank database and Global Innovation Index report.

IPLSL and IPLSQ: Two types of imputation PLS algorithms for hierarchical latent variable model