Late Roman Unit Sizes

[ValentinianVictrix]

Hypothetically, if I decided to define the units of the Lanciarii and Mattiarii as light armed infantry, could I get away with calling the heavy infantry scutati?

I think so, yes. That is the sense in which I read Vegetius' use of the term. I would be careful about categorising the Mattiarii as light infantry, although their association with the Lanciarii suggests as much. We don't know what the mattium was, as far as I am aware. Personally, I do not think that it is the same as the mattiobarbulis but others may disagree.

I do not run with your idea of the Lanciarii fighting at close-quarters like the old hastati. Depictions of lanciarii on tombstones show them holding a clutch of javelins, which suggests to me that their role was to stand back and put down a barrage of missiles over the heads of the line infantry. Scutati seems much more descriptive of troops fighting in the line.

Surely though Michael the Lanciarii and the Mattiarii were heavy infantry because both Ammianus and the Notitia lists them as Legiones? I have seen their units names translated by others as 'The Spear-bearers' and 'The Mattock wielders'. I think most people know believe that the unit titles actually have nothing at all to do with the weapons, armour, clothing or fighting-styles implied by the unit names. They are more a nick-name if anything.