Your question deals more with hybridization. First we have to note that $\ce{NH3}$ has a lot more hybridization than the other molecules with hydrogen of the group e.g. $\ce{PH3}$. This means for example that $\ce{PH3}$ and $\ce{AsH3}$ have bonding angles near 90°. Because the tetraedric angle needs a $sp^3$ hybridization.
The transition state of the inversion can be stabilized by a $sp^2$ hybridization which again practically happens only for the ammoniak.