Is barbarian invasion a political social economical or military reason?

The invasions of the western part of the Roman Empire by the Germanic peoples had mainly economic reasons. They were more than just military actions. They involved the migration of entire peoples due to population pressure on the land. There were part of the migration period.

There had been migrations from Scandinavia to Eastern Europe for about two centuries. Then there were migrations from northern Germany southwards. This created a population squeeze in central Europe just north of the frontiers of the Roman Empire. In the third century this led to many invasions into the empire from the neighbouring peoples. The Roman army managed to repel all of them, but the strain it caused resulted in this century being a century of military anarchy in the empire.

The invasion of Eastern Europe by the Huns in the late fourth century created a crisis in central Europe. It created a population squeeze in this area which led to peoples from this area to migrate into the western part of the Roman Empire in search of new land. These peoples were the Vandals, Sueves, Alans and Burgundians. The size of these migrations involved some 100,000 people for each of the invaders.

The Angles, Saxons, Jutes and Frisians migrated from northern Holland and northern Germany to Britain in waves and took it over.

The eastern part of the Roman Empire was not affected by these invasions and continued to exist for nearly 1,000 years.