(Why) Do US studies of violence and mental illness tend to report no link but European studies seem to find one? Studying the link between mental illness and violence seems a sure way to

get attention from the mass media, and
contradict some other study, and not necessarily one published that long ago.

A pretty old review (and not in some high impact venue) by Stuart (2003) seems to me to still hold water 15 years later with respect to a few general observations:

Definitive statements are difficult to make and it is equally possible to find recent literature supporting the conclusions that the mentally ill are no more violent, they are as violent, or they are more violent than their nonmentally ill counterparts. [...]
Because of the significant methodological challenges faced by researchers in this field, the nature of this association remains unclear. For example, violence has been difficult to measure directly, so that researchers have often relied on official documentation or uncorroborated selfreports. The prevalence of violence has been demonstrated to differ dramatically depending on the source. [...]

And it goes on to talk about confounders as the perennial problem of epidemiological studies.
Stuart also highlights a (highly cited) US-sample study of the &quot;no-link&quot; variety (at least if substance-abuse is controlled for), Steadman et al. 1998 ... and I certainly found some newer ones myself, Elbogen &amp; Johnson (2009) or Anderson et al. 2012, just to mention some picked up by the press.
On the other hand, the Oxford group of Fazel has been publishing study after study on European samples including on Sweden (2015)
or UK, Finland and Netherlands (2017) that do find a link between depression and violence... and these have also been picked up the press. There are older studies in Scandinavian countries which concur; Hodgins et al. (1996) for instance.
So is this a trend? And (the really tough question) is there a meta-analysis of such studies that does moderator analysis (e.g. by meta-regression) to determine which study parameters matter most with respect to the finding? Is it the case that the Europeans are less violent overall so that the &quot;inherent&quot; violence of the mentally ill &quot;stands out&quot; in Europe but &quot;gets lost in the noise&quot; of the higher society violence in the US? (It certainly is the case the US is more violent than Sweden.) Or is it some other factor that is dominant, e.g. is depression more conductive to violence than other forms of severe mental illness (makes sense to ask since 2 of 3 US studies I've looked at aggregate severe mental illnesses — SMIs). To give you an example of the kind of meta-analysis I'm hoping to find, for ADHD prevalence it seemed that there might be geographical differences between US and Europe, but they turned out to be methodological.

I found a paper by Van Dorn et al. (2012) reanalyzing the same data as Elbogen &amp; Johnson, and coming to a European-style conclusion of a link between SMI and violence. The difference in methodology came down (in this case) to:

important is spatio-temporal contiguity (i.e., the causal factor must be
spatially near the effect).

So merely lifetime SMI prevalence wasn't a good predictor but recent symptoms (within 12 months) were. That and the fact that the control group of Elbogen &amp; Johnson apparently was not clean enough (of substance abusers) apparently tipped the scales.
But Eblogen didn't quote concede the field, and in a 2016 study on the exact same data (using 12 months window this time) but with more attention to confounders... found again in favor of their original findings:

Mediation analyses informed by the I3
model revealed
that the positive association between SMI and violence
was by and large indirect. Statistically controlling for
impellance and disinhibition completely wiped out any
positive relationship between SMI and violence.

This is somewhat similar result to what Anderson et al. (2012) obtained on different data after controlling for impulsivity and &quot;present orientation&quot; (using just two simple questions for these two factors!)
I have been away from here for a while as I have been concentrating on my University studies, however, I have just come back and boy have I come back at an opportune moment.  Your question showed a lot of research whilst being put together and this is an interesting topic of discussion as I have been discussing the subject of mental illness and violence myself with a couple of friends.

As you pointed out, Heather Stuart stated that


  Definitive statements are difficult to make and it is equally possible to find recent literature supporting the conclusions that the mentally ill are no more violent, they are as violent, or they are more violent than their nonmentally ill counterparts.


From what I have seen, I would agree with you that this still stands today as a response to your question.  The thing is, I have not seen an article which gives a definitive answer.

It is interesting to read the 2017 study on the FBC, RADAR and ALSPAC datasets you provided.  The thing to note with this study is that although


  In the additional sensitivity analyses, we also adjusted for other factors including parental criminality, conduct disorder, and maltreatment where data were available.


what about information regarding maltreatment etc. which was not available?  Those children who were subjected to undocumented external factors, which could affect their behaviours, would have been excluded from the adjustments and therefore, the statistics presented may be inaccurate.

Another point to make is that as the datasets seem to be based on self disclosures of violence, this, along with other issues raises all sorts of questions.

I would ask how the relevant studies defined violence when asking for the disclosures.  How were the questions put forward?  What was included in their definition of violence?  Was verbal and/or mental abuse considered to be violence or was the scope restricted to just physical violence?

This could be one reason why there is a discrepancy between US studies and European studies.  Another possibility is, were there cultural differences in play?

The differences in all the studies you pointed out using the Elbogen &amp; Johnson data highlights the complexity of such a study.  What mental illnesses were covered in the studies?  Were any of the mental illnesses a result of (or made worse by) substance abuse, and if so, what is the prevalence of this factor?

There could also be all sorts of problems with interpretation of the data.  @ArnonWeinberg shows an example of possible misinterpretation of data when referencing Sweden as the rape capital of the world.  (See here for what I am — and possibly also what Arnon is — referring to).

There are so many questions which seem hard to answer with what I have seen and these sort of questions may not be able to be answered in a full meta analysis involving all studies on the mentally ill as this may end in a great deal of speculation.  However, a full meta analysis of all studies in all age groups could point these flaws out and lead to a more thorough study which would iron out those wrinkles.  I personally would look forward to seeing one.