sTeamTraen wrote: ↑Fri Nov 20, 2020 3:01 pm

To my surprise the PDF wasn't even available on Sci-Hub, so I've put it

here.

Thanks!

sTeamTraen wrote: ↑Fri Nov 20, 2020 3:01 pm

However, you are probably right in suggesting that whether men or women do better or worse in each type of community ought to be the outcome of interest. In the PNAS article, the authors presented the first type of comparison only narratively (with no chi-square test statistics), and they didn't mention the second.

I interpreted the following from the abstract

We tested the hypothesis that female-biased gender norms ameliorate gender disparities in health by comparing gender differences in inflammation and hypertension among the matrilineal and patrilineal Mosuo of China. Widely reported gender disparities in health were reversed among matrilineal Mosuo compared with patrilineal Mosuo, due to substantial improvements in women’s health, with no concomitant detrimental effects on men.

as meaning that they had compared the frequency of each condition between the sexes in both kinds of society, and done that comparison. Now I can see the paper, it seems that indeed they have:

Using Bayesian logistic regression, we modeled an interaction between gender and kinship to test whether men and women experience differences in chronic inflammation and hypertension in matrilineal and patrilineal communities, controlling forage (Table 1). Fig. 1 shows the predicted probabilities of elevated CRP and hypertension resulting from this model. We find reversed gender disparities in both inflammation and hypertension under matriliny, driven primarily by reduced probabilities of both chronic inflammation (0.02) and hypertension (0.17) for women in matriliny compared with patriliny (inflammation: 0.05,∆= 0.03; hypertension: 0.32,∆= 0.15). These effects were robust to controls for both age and body mass index (SI Appendix,Table S1).

So they're use a logistic regression rather than a series of chi-square tests, which seems like a better use of the data to me, maximising the information from relatively rare observations. Chi-squared is a particularly low-powered test so it's not necessarily surprising that it doesn't find effects that regression can, especially breaking it down by sex and community instead of doing an omnibus analysis.

sTeamTraen wrote: ↑Fri Nov 20, 2020 3:01 pm

Normally the correct way to test this kind of thing is with an interaction (gender x community type x outcome).

That's pretty much what their analysis is: a logistic regression for each health condition, with gender x community type as predictors.

sTeamTraen wrote: ↑Fri Nov 20, 2020 3:01 pm

The PNAS authors have built something using a Bayesian modelling package which they claim shows an effect; this may be as good a way as any other. I need to write to them anyway, because the numbers that they reported in each condition for hypertension don't match what my code calculated, so I will ask them about their reasoning and keep this thread informed. I will also ask one of my Bayesian friends what they think of the analyses (Bayesians *love* to explain other people's Bayesian models).

It's just a standard formulation of a logistic regression:

To model the effect of matriliny on elevated inflammation and hyper-tension, we estimated the logit function using a binomial prior. Predictor variables were given weakly regularizing priors (μ= 0,σ= 10), which make the model more skeptical of nonzero parameter estimates than the flat priors assumed by a frequentist approach. Patrilineal women were used as the reference category for all models. Age was included as a control in all models because the data show a monotonically increasing prevalence of elevated inflammation and hypertension with age for all groups. The models were specified as follows:

Pr(outcome)∼Binomial(1,p)

Logit(p)∼α+β1×age+β2×men+β3×matriliny+β4×men×matriliny

β1∼Normal(0, 10)

β2∼Normal(0, 10)

β3∼Normal(0, 10)

β4∼Normal(0, 10).

The 'regularising priors' thing just means that the estimation procedure starts off by assuming the effect of sex or matriliny is 0, that it's equally likely to be positive or negative, and that the procedure will need a lot of evidence to change its estimate from 0 (the second parameter of the normal distribution given is Bayesian analyses is generally the precision, which is the reciprocal of the variance you might be expecting - in other words ~N(0,10) is a big spike at 0).

The package they used is the one from Richard McElreath's

Statistical Rethinking book, which I've seen highly recommended but not used myself. (It uses Stan for the Bayesian programming bits, whereas most of the work on the obscure classes of hierarchical models I use has been done in BUGS or now JAGS).

I'd expect you ought to be able to get pretty similar results using a frequentist logistic regression, though, especially as the posterior probability distributions look relatively symmetrical.