Deficit Model
A kind of parent involvement model often used in compensatory programs (programs created to compensate or make up for things children are missing).  This model implies that early childhood educators are knowledgable, and that families lack knowledge and skills needed to be effective parents.
A model of early childhood created for disadvantaged children, designed to intervene in development in order to improve outcomes for children.  Head Start is an intervention program.

A model for family involvement that sees parents as knowledgeable and competent, and that encourages families to be active participants in the educational process.
A law or requirement. Some early childhood programs mandate parent involvement.  Head Start is one example; NC PreK is another.
Family Centered
A model that integrates early childhood education with adult education.

 Title I programs such as Even Start are family centered literacy programs.