It's True.
The Roman Family, which usually called the famillias, was structured around elders and obidience within the household.
Usually there was a clear hierarchy of dominance in every roman household, which usually placedd the elders at very top and the youngest on the rock bottom of the hierarchy.
And as written on Plutarch, Life of Cato the Elders, a piety for Gods within the household is a must.
I hope this helps