Yes, the following parameters can be used to classify invasive plants: size, fecundity, competition, breadth of ecological niche, effect on total biomass, etc.
See:
Ecol Evol. 2015 May; 5(10): 1933–1943.
Published online 2015 Apr 17. doi: 10.1002/ece3.1432
Invasiveness of plants is predicted by size and fecundity in the native range
All of the above answers are essentially correct, but in my assessments I consider a species "invasive" when the introduced species in question out-competes or displaces at least one native species.
Une espèce invasive dans le domaine marin est le plus souvent une espèce non indigène dont la compétitivité est forte du fait de sa large tolérance à des conditions environnementales drastiques. Elle s'installe en conséquence de façon préférentielle dans les zones de forte déstabilisation des écosystèmes.
According to studies: "the invasion success of many species might depend more heavily on their ability to respond to natural selection than on broad physiological tolerance or plasticity (see attached paper)." Genetic factors can be important in invasion success. This include epistatic interactions and the action of a few genes which could facilitate invasion success.
Interesting invasive plant species is a species that invades land,water resources and other indigenous plant species aggressively. The seed of the plant species germinates fast. So invasive plant species like Prosopis juliflora which is introduced to Ethiopia, Afar regional state to protect dessert condition of the area now invaded area including the farmlands and grazing lands of the region out control of the national government.