If you look at the Advanced Search page you'll see a checkbox for whether you want the results returned as Thread or Posts:
HTML Code:
<fieldset class="fieldset">
<legend>Show Results as</legend>
<div style="padding:3px">
<label for="rb_showposts_0"><input type="radio" name="showposts" value="0" id="rb_showposts_0" checked="checked" />Threads</label>
<label for="rb_showposts_1"><input type="radio" name="showposts" value="1" id="rb_showposts_1" />Posts</label>
</div>
</fieldset>
So, it looks like the variable you want is "showposts" and you want to set it to "0"