First, it could be good to look in to the definition of R1 and R2 universities.
See Carnegie Classification Methodology PDF for 2022 and the website. They basically do PCA on the cumulative doctorates awarded and per capita research expenditures at each institution with >20 PhDs/year and >$5 million in external funding.
Their data sources are available and the summary statistics can be found here. They do consider and weigh science and engineering vs non-science and engineering separately, but are combined via the PCA for analysis. For the sake of comparison, let's look at the science and engineering analysis. The two factors with the highest loading are:
- Median full-time research staff per faculty (explains 71% of the variance of the per-capita differences)
- Median total STEM PhDs per institution per year (explains 70% of the variance of the to total institutional differences)
So the major difference between R1 and R2 is the environment (what resources are available at the institution beyond your PhD advisor) and the number of PhDs produced. This is just segmenting in to two groups, not putting value on the quality, just describing differences between the groups. From their own description of the analysis:
While this approach is suitable for classification purposes, we do not believe the institution-level results should be used for institution-by-institution comparison and ranking.
Another interesting comparison (second highest coefficient for the per-capita productivity score):
- Median research expenditures per faculty
Now with that context, I think we get some insight to the answer to the questions.
... I didn't know about the stigma [PhDs from] regional institutions carry in the United States.
Why is this the case? Why is it that regional institutions are frowned upon in academic circles?
I wouldn't call it a stigma as much as PhDs from R2s were in a far less resourced environment, and their productivity quantity and quality could be lower than one from an R1. There are far fewer PhDs from R2s, and the groups they came from had 5x less funding and significantly less institutional support than their R1 counterparts. I'd go even further and say that there's a similar drop off from the "top 10" R1 institutions where most faculty are hired from and the rest of the R1s.
So there isn't so much a "stigma" against R2s as there is a "bias" towards "top 10" institutions. On one hand, the top graduates from there were the top-of-the-top and succeeded at the highest level in the best resource environment, so it's not unlikely that they would continue that trajectory. However, this leads to a situation where 80% of US faculty come from only 20% of the institutions, and 1/8 faculty came from one of 5 institutions. (EDIT: the original paper appeared in Nature, at this link.)
To me, a key benefit of regional institutions is more individualized attention due to smaller class sizes. This was the major reason I attended my regional college since I graduated from high school with a class of 8 people and it would've been too much of a culture shock to go to a school with 50k undergrad
These are two different issues.
- Class size (and classes) are irrelevant to a PhD. Classes themselves are largely irrelevant except in how they prepare you to produce scholarly work.
- Class size (and classes) are extremely relevant for an undergrad degree and is an advantage you gain at a regional school at the expense of the lack of opportunities (due to lack of funding and institutional support) for the "R1 research experience." But you can still get the "R1 experience" doing a summer REU. R2 undergrads can go on to be successful in an R1 PhD program.
I've heard reasons for regional colleges' bad reputation all across the board from high acceptance rates to suboptimal graduation rates, or to not being known to most graduate schools in the United States. Are all of those reasons true? Or, is there more to the story?
I think this is also conflating grad vs. undergrad. For undergrad, the top regional college graduates are usually pretty good in R1 PhD programs (especially if they did some summer program at an R1 school). The median student, however, can be unprepared for an R1 PhD for the reasons you cite. I have been on R1 PhD admissions committees and have had an outstanding student from a regional school in my R1 research group. An additional significant advantage regional students have are that they are often US citizens, which matters for some funding and fellowships.
For grad school, it's not that the schools have a bad reputation, but when you compare two graduating PhDs on paper (and hide the school name), there is very often a significant difference in quantity and quality of publications between an R1 and R2 graduate. There's an argument that they should be evaluated based on what they could achieve based upon the resources available to them, but institutions are typically risk-adverse. An open line is very important (and expensive, on the order of several million dollars), it's hard for departments to justify hiring a PhD from an R2 institution that did well with limited resources when another candidate from an R1 institution is ready to go now.
However, post-docs can help a lot. Doing a post-doc at an R1 after an R2 will give you that institutional experience.