Female dogs and cats do not technically menstruate. Intact female pets often experience mild vaginal bleeding when they are in heat, but the bleeding is different from menstruation. The bleeding in pets occurs during ovulation, when the pet is most likely to become pregnant. In people, the opposite generally is true–menstruation usually occurs midway between ovulation cycles.
Nonetheless, although Basset Hounds don’t actually menstruate, they do experience cyclical hormone surges during heat cycles. The surges can lead to behavior changes. The surges are especially strong prior to and during heats. The effects of hormone surges on personality can resemble premenstrual syndrome.
Spayed pets do not experience hormone surges and do not have heat cycles. Preventing canine or feline PMS is not by itself a good reason to spay a pet. However, spaying has many other documented health benefits. The elimination of hormone-induced personality changes is simply a fringe benefit.