Crime/violence, gender, sexual orientation, cognitive ability
In a recent paper, Beaver et al looked at the relationships between crime, gender and sexual orientation:
This study examined the association between sexual orientation and nonviolent and violent delinquency across the life course. We analyzed self-reported nonviolent and violent delinquency in a sample of heterosexual males (N=5220–7023) and females (N=5984–7875), bisexuals (N=34–73),gay males (N=145–189), and lesbians (N=115–150) from the National Longitudinal Study of Adolescent to Adult Health (Add Health). The analyses revealed, in general, that bisexuals were the most delinquent of the sexual orientation categories for both males and females. Additional analyses revealed that heterosexual males reported significantly higher levels of both violent and nonviolent delinquency than gay males, whereas lesbians reported more involvement in nonviolent delinquency and, to a lesser extent, violent delinquency relative to heterosexual females. Analyses also revealed that lesbians reported significantly more delinquent behavior, particularly for nonviolent delinquency, than gay males. Future research should explore the mechanisms that account for these observed patterns and how they can be used to more fully understand the etiology of delinquency.
I decided to see if this pattern held in the OKCupid dataset. I could find three questions about related matters, all of which are yes/no:
Have you ever been arrested, even if just for a small crime or misdemeanor?
Have you ever hit a significant other in anger?
Excluding childhood fights, have you ever punched someone in the face?
Coding these so that "yes" = 1 and "no" = 0, we can use logistic regression. The second outcome variable had too few datapoints to give useful results, so I skipped it.
The raw associations are:

I include only persons who self-identified as man or woman (>99% of the sample). I include age and cognitive ability as covariates.
Results:
> fit = glm(formula = "arrested ~ CA + gender_orientation + age", family = "binomial", data = d_main, subset = v_3bigorien & v_menwomen)
> MOD_summary(fit)
$coefs
Beta SE CI.lower CI.upper
CA -0.29 0.02 -0.33 -0.24
gender_orientation: Hetero_female 0.00 NA NA NA
gender_orientation: Bisexual_female 0.65 0.12 0.41 0.88
gender_orientation: Gay_female 0.32 0.23 -0.13 0.78
gender_orientation: Gay_male 0.70 0.12 0.47 0.93
gender_orientation: Bisexual_male 1.13 0.15 0.83 1.43
gender_orientation: Hetero_male 1.04 0.06 0.92 1.17
age 0.19 0.02 0.15 0.23
$meta
N pseudo-R2 deviance AIC
11895.00 0.05 12237.69 12253.69
> #punched in face
> fit = glm(formula = "punched_face ~ CA + gender_orientation + age", family = "binomial", data = d_main, subset = v_3bigorien & v_menwomen)
> MOD_summary(fit)
$coefs
Beta SE CI.lower CI.upper
CA -0.29 0.02 -0.32 -0.26
gender_orientation: Hetero_female 0.00 NA NA NA
gender_orientation: Bisexual_female 0.58 0.08 0.42 0.74
gender_orientation: Gay_female 0.35 0.15 0.07 0.64
gender_orientation: Gay_male -0.13 0.10 -0.32 0.06
gender_orientation: Bisexual_male 0.70 0.12 0.46 0.93
gender_orientation: Hetero_male 1.03 0.04 0.95 1.12
age -0.11 0.02 -0.14 -0.07
$meta
N pseudo-R2 deviance AIC
17188.00 0.04 20926.46 20942.46
Observations:
Cognitive ability was consistently negatively related to crime/violence, standardized beta = -.29.
Female bisex. and homosex. were more criminal than heterosex.
Male homosex. were less violent/criminal, and male bisex. had inconsistent relationships in the controlled analyses, but lower levels in the raw analyses.
Project files: https://osf.io/zp8fx/