Research published in July, missed by me a the time but now shared with me by a reader suggests a strong correlation between infection levels in care homes which were, for the elderly, large and in private ownership.

Carried out by staff at Glasgow and Edinburgh universities in association with researchers at 9 health boards in Scotland, it found:

Sixty-six (94.3%) outbreaks were in older people’s care-homes, where 60.6% had experienced an outbreak compared to six (5.0%) of all other care-home types (Table 2). Care home characteristics systematically varied by care-home type. Older people’s care-homes were much larger (median 48 beds vs eight for all other types combined), more likely to be in private ownership (67.9% vs 30.0%)

https://www.medrxiv.org/content/10.1101/2020.07.09.20149583v1.full.pdf