What factors give rise to stem elongation?

Higher PAR levels

When plants are starved of light, they will also elongate towards the direction of available light. Generally the higher the light levels in the tank, the shorter the internodes. Some stem plants will start to grow sideways or creep on the substrate at higher light levels. Plants in open areas of the aquarium will receive significantly more light than areas adjacent to hardscaping or tall plants that may partially shade the surrounding area. This is the most well known reason that causes stem elongation.

Running tanks at 100 to 200 umols of PAR will make stem plant bushes much denser. 

Access to CO2/O2

In nature, most aquatic plants are marginal/marsh plants. Gas exchange under water is 10000 times slower than in air - it's much easier for these marginal plants to grow if they have the aerial advantage, giving them free access to CO2/O2 in the air.

How does the plant know if it's underwater or not?

When a plant's access to CO2/O2 is cut off sharply by submergence, this sends signals to the plant that it is drowning. This leads to rapid accumulation of the hormone ethylene in the plant meristem, which induces rapid stem elongation in an attempt to break back up the water surface to access air. When CO2/O2 levels are low, plants will put all available energy into stem elongation, even sacrificing the maintenance of older leaves, in order to access surface air and survive. This is why bare lower parts on stem plants are quite common in setups without CO2 injection.

Rotala macrandra mini type 4 from our 2hr Aquarist gallery tank. A combination of high light, good CO2 availability and cool temperatures produces compact plants.

Does blue spectrum light suppress inter-nodal distance?

How far can we extrapolate what we know about terrestrial plants to our freshwater aquatic plants?

In terrestrial plants, blue light suppresses the hormone auxin, resulting in a shorter distance between leaf nodes on the stem. This is illustrated by experiments such as the one below:

However, most aquatic plants do not respond so directly to blue light as stem elongation is more influenced by the flooding response mentioned in the first section 'Access to CO2/O2'. Depending on the species, this may have a marginal effect on the compactness of the growth. The other factors, such as total PAR and growth rate, have a greater effect on internode distance.

Temperature

One of the most important factors in determining internodal distance is actually growth rate. Plants in a faster growth mode tend to have longer internodes than plants in a slower growth mode. Temperature is an important factor in determining the rate of plant metabolism - cooler tanks with lower temperatures will reduce plant metabolism and result in more compact plants.

Warm tanks generally have longer stem elongation and less branching, making it harder for stem plants to attain a bushy look. The Bacopa salzmannii grown in 31C (left) vs 24C (right). The left plant has longer internodes and smaller leaves compared to the exact same species grown in a cooler aquarium environment.

Lower nutrient levels/CO2 levels

Slower growth parameters / slower growth rates (including lower CO2 and nutrient levels) result in more compact stem plants. Ironically, CO2 deprivation can cause stem plants to elongate in an attempt to break through the water surface, but high CO2 levels often also significantly accelerate growth rates, also resulting in less compact plants.

The combination of high light, lower temperatures, lower nutrient levels and the availability of some CO2 (say 10ppm) but not high levels will generally produce the most compact plants.