What were the factors that have stopped insects from growing to an equivalent size as dinosaurs & mammals?

Insects grow through a process of moulting.  At certain times they shed their exoskeletons, their bodies quickly expand somewhat, and then they grow a new hard exterior.  Above a certain size on land a body without a skeleton would not be able to support itself, and it would be crushed by its own weight.  This size is larger than insects are today: insects are limited today by a lack of lungs, so that larger insects would suffer from lack of oxygen (insects breathe through a series of tubes called spiracles).  In the past there has been a higher proportion of oxygen in the atmosphere and insects have grown considerably larger.

During the Carboniferous and Permian periods, there was a lot more oxygen in the atmosphere. Prehistoric insects breathed air that was about 35% oxygen, as compared to just around 20% in the air today. Atmospheric oxygen limits insect size for reasons already explained in previous answers, so then there were much bigger insects than today. Even then, however, the largest insects weren't that large and their size and ability to fit into niches within their ecosystem may have also been due to the relatively primitive lizards and amphibians that they were competing with.

Insects don't have lungs like we do; they breath through ity bitty holes in their body (awesone right!) and if they got too big all the oxygen would be absorbed before it could get to the end of the hole. This is why a long long long long time ago (like Dino age) insects were much much bigger - there was a higher percentage of oxygen in the air so they could have deeper ity bitty holes while keeping oxygen flowing through the entire thing.