Merging two object (NodeList) arrays in JavaScript

I am attempting to merge two arrays of objects to so I can validate a form. The usual concat method does not appear to work in this circumstance. Concat works with ordinary numerical and string arrays but doesn't with object arrays. The line var allTags = allInputs.concat(allSelects); does not work.

var allInputs = document.getElementsByTagName("input");
alert("Inputs: " + allInputs.length);

var allSelects = document.getElementsByTagName("select");
alert("Selects: " + allSelects.length);

var allTags = allInputs.concat(allSelects);
alert("allTags: " + allTags.length);