How do I go about compositing a matte shadow? which render elements do I need to include and how do I stack them up in photoshop?
I have an object on a pure white floor that only shows shadows.
In photoshop I currently have:
Diffuse x GI + Diffuse x Light + Reflection + specular. what else is needed to catch the shadows on the ground plane?
I would just set the white ground plain as a matte object in its vray properties. Then your shadow will show up in your alpha channel and you can put any pic in the background. Then in this instance you dont need any render elements - just a straight render and its alpha. Remember to set your max environment to black, and set VRay environment override to with whatever you like (recommend a VRayHDRI)
does the alpha contribution need to be 1 or -1?
I tried your method and the alpha channel doesn’t have any shadow information in it. 
it would do if I used a matte shadow material in a material wrapper, But how do I composite that pass in photoshop along with the other passes to complete the full RGB image?
Think you need to make sure “affect shadow” is on for your matte object. It should show up in the alpha I think.
alpha should be -1
and like Brett says, make sure “affect shadow” is also ticked