In　this　paper,　we　propose　a　nested　modified　Cholesky　decomposition　for　modeling　the　covariance　structure　in　multivariate　longitudinal　data　analysis.　The　entries　of　this　decomposition　have　simple　structures　and　can　be　interpreted　as　the　generalized　moving　average　coefficient　matrices　and　innovation　covariance　matrices.　We　model　the　elements　of　these　matrices　by　a　class　of　unconstrained　linear　models,　and　develop　a　Fisher　scoring　algorithm　to　compute　the　maximum　likelihood　estimator　of　the　regression　parameters.　The　consistency　and　asymptotic　normality　of　the　estimators　are　established.　Furthermore,　we　employ　the　smoothly　clipped　absolute　deviation　(SCAD)　penalty　to　select　the　relevant　variables　in　the　models.　The　resulting　SCAD　estimators　are　shown　to　be　asymptotically　normal　and　have　the　oracle　property.　Some　simulations　are　conducted　to　examine　the　finite　sample　performance　of　the　proposed　method.　A　real　dataset　is　analyzed　for　illustration.　(C)　2016　Elsevier　B.V.　All　rights　reserved.