Algorithm 1 The iterative imputation based on multivariate regression model

Input: $X_k^{\left(1\right)}\in {\mathbb{R}}^{mk\times n}$, $n_{long\_j}$

Output: The imputed data segment $X_k^{\left(2\right)}\in {\mathbb{R}}^{mk\times n}$

1. Begin

2.Calculate the variable missing proportion ${VMP}_j$ for each long-term missing variable, and sort these variables in ascending order by ${VMP}_j$, get $\left\{\left(x_{\_ ,1}\right),\left(x_{\_ ,2}\right),\dots ,\left(x_{{\_ ,n}_{long\_j}}\right)\right\}$;

3. Set $X_0=X_k^{\left(1\right)}$;

4. For $j=1$ to $n_{long\_j}$:

5.   Split $X_{j-1}$ into a training dataset $D_{train(j-1)}$ including only complete variables and a testing dataset $D_{test(j-1)}$ including only incomplete variables;

6.   Train the multivariate regression model ${model}_j$ by inputting $X_{train(j-1)}$ formed by $n-n_{long\_j}+(j-1)$ complete variables from $D_{train(j-1)}$;

7.   Input $X_{test(j-1)}$ formed by $n_{long\_j}-(j-1)$ incomplete variables from $D_{test(j-1)}$ into ${model}_j$, and get the predicted values $\left({\tilde{x}}_{\_ , j}\right)$ for variable $\left(x_{\_,j}\right)$;

8.    Impute $X_{j-1}$ using $\left({\tilde{x}}_{\_ , j}\right)$;

9.    Set $X_j=X_{j-1}$;

10. Return $X_k^{\left(2\right)}=X_{n_{long\_j}}$;

11. End