Ok, I have managed to run a couple more tests on the effect of uprgrading infrastructrure. Playing Spain, which has 43 home provinces and 12 other provinces, I put in a single industry in a total of 34 provinces. When I simultaneoulsy upgraded 33 provinces to experimental railroad, I raised the IR from 49 to 58. I didn't upgrade Madrid in this test, because I wanted to avoid having these results mixed with any additional effect by capitalists. I had taxed the other Spanish capitalists out of existence, but failed to completely eliminate those in Madrid. Persistent little guys!
So: I upgraded 33 out of 55 provinces (12 colonial) to experimental railroad and obtained an IR increase of 18%.
I then built up the Spanish economy so that nearly every home province had 2 fully staffed factories. Together with others posting in this thread, I have found that whether those people actually make anything appears not to figure into IR, so all I wanted was to get those factories staffed.
In this second test, I upgraded 37 provinces with two factories (again, not Madrid) to experimental railroad and obtained an IR increase from 79 to 91, a 17% increase.
Based on these two tests, therefore, it really does appear that the number of factories does not affect where you should upgrade infrastructure, at least as far as increasing the IR rating is concerned.
Two other observations: Although I cannot be sure, it seems to me that certain techs, such as mechanical production and interchangeable parts, bestow 1 IR point upon completion of the research. I cannot be sure of this, because IR rises by 1 point for undeterminable reasons along the way (!). But I did notice that the IR went up immediately after these two techs were discovered.
The other observation is in response to Duke Ringo's claim above that the price of a factory's goods affects IR. I haven't found this to be the case, but I haven't tested it systematically. Perhaps I'll find the time to do it & resurrect this thread. But if you simply look at France's starting factory situation and take all the workers out of the luxury clothing factory in Ile de France and put all those workers in the cement factory, your IR increases from 50 to 54. Nor is this some effect of the WM settling. I ran this over a couple of weeks in various configurations and found the same thing. This happened even though the listed price of luxury clothing was well above that of cement.
Well, that's all for the present. I'm off to download the latest release of the CORE mod in HOI! I'll keep an eye out here for comments, though.