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When there are multiple level 1 independent variables, the model can be expanded by substituting vectors and matrices in the equation.
When the relationship between the response <math> Y_{ij} </math> and predictor <math> X_{ij} </math> can not be described by the linear relationship, then one can find some non linear functional relationship between the response and predictor, and extend the model to [[nonlinear mixed-effects model]]. For example, when the response <math>Y_{ij} </math> is the cumulative infection trajectory of the <math>i</math>-th country, and <math> X_{ij} </math> represents the <math>j</math>-th time points, then the ordered pair <math>(X_{ij},Y_{ij})</math> for each country may show a shape similar to [[logistic function]].<ref>{{Cite journal |last1=Lee|first1=Se Yoon |first2=Bowen |last2=Lei|first3=Bani|last3=Mallick| title = Estimation of COVID-19 spread curves integrating global data and borrowing information|journal=PLOS ONE|year=2020|volume=15 |issue=7 |pages=e0236860 |doi=10.1371/journal.pone.0236860 |arxiv=2005.00662|pmid=32726361 |pmc=7390340 |doi-access=free}}</ref><ref name="ReferenceA">{{Cite journal |last1=Lee|first1=Se Yoon |first2=Bani|last2=Mallick| title = Bayesian Hierarchical Modeling: Application Towards Production Results in the Eagle Ford Shale of South Texas|journal=Sankhya B|year=2021|doi=10.1007/s13571-020-00245-8|doi-access=free}}</ref>
==Level 2 regression equation==
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