Category: Statistical methods

As I mentioned in the post yesterday, I think the debates about group-based trajectory modeling have some unresolved issues. For this reason, I submitted a commentary to Journal of Research in Crime and Delinquency. I had two reasons for doing so. First, I think Nagin mischaracterized his critics, and I believe his essay was a willful attempt to avoid serious criticism by ignoring serious arguments. (Maybe I could have been less outspoken about that). But after all, he has not addressed the actual argument I (and others) have put forward. I can only interpret this as an attempt to avoid discussing the substantive matter by keeping silent, and now subtly dismissing the whole thing. If Nagin find it worthwhile saying his critics have misunderstood, he should also bother to point out how. So far, he has done no such thing.

Second, I actually think there is a need to clarify whether GBTM can test for the presence of groups or not. If the advocates of GBTM had been clear about this, it would obviously not have been needed. There is no doubt that Nagin and others have been clear that GBTM can – or maybe even should – be interpreted as an approximation to a continuous distribution. There is no disagreement on that point. But they have also given the impression that one can identify meaningful real groups in the data by way of GBTM. They have not been clear on what this really means or under what conditions this can be done. A clarification is in order, since it is clear in the literature that findings from GBTM analyses have been interpreted as giving very strong evidence to a certain typological theory (see e.g. here). I have claimed this empirical evidence is weak and largely based on overinterpretation of empirical studies using GBTM (see, here and here). It would be helpful if Nagin could clarify the strength of this evidence.

So I wrote a commentary and submitted it to The Journal of Research in Crime and Delinquency. (See the full commentary here). According to the letter from the editor, it was rejected because:

Language at the top of page 2 in your comment underscores a fundamental misunderstanding and misreading of Nagin’s work.
(See the full rejection letter here).

Well, maybe I should have put things more politely, but I still believe my arguments are right. I can understand that there might be good editorial reason for why not having another debate about GBTM in the journal, but I am not impressed with the reason given. My fundamental misunderstanding is revealed (on the top of page 2) where I point out that Nagin himself is responsible for some of the confusion regarding the interpretation of the groups. I do so with clear references, so you can decide for yourself whether these are misreadings or not.

Even in his recent essay, Nagin presents one of the main motivations for using GBTM by first arguing that other methods are not capable of testing for the presence of groups, and then suggesting that GBTM can indeed solve this problem:

To test such taxonomical theories, researchers had commonly resorted to using assignment rules based on subjective categorization criteria to construct categories of developmental trajectories. While such assignment rules are generally reasonable, there are limitations and pitfalls attendant to their use. One is that the existence of distinct developmental trajectories must be assumed a priori. Thus, the analysis cannot test for their presence, a fundamental shortcoming. (…) The trajectories reported in Figure 2 provide an example of how GBTM models have been applied to empirically test predictions stemming from Moffitt’s (1993) taxonomic theory of antisocial behavior.
(My emphasis).

It might not say straight out whether the groups from GBTM are interpretable as real or not in this setting, nor what can be concluded from such “tests”. But given the previous debates and misconceptions, this is hardly a clarification.

My point is simply this: it has been claimed that GBTM can be used to test for the presence of distinct groups, and generally to test typological theories. (I have discussed this in more detail here and here). However, it is hard to see how such typological theories can be tested using GBTM. That is indeed very vaguely explained by the advocates of the methodology. I think (but I am not entirely sure), that in this context “testing a theory” only means findings that are consistent with a given theory. I think this is a generous use of the term “test”. I prefer to reserve the word “test” for situations where something is ruled out – or when using methods that at least in principle would be able to rule something out. In other words: If the findings are consistent with a theory but also consistent with one or several competing (or non-competing) theories, this is at best weak evidence for either theory. (This holds regardless of methods used). It is good that a theory is consistent with the empirical findings, but that is far from enough. I know of no published criminological study using GBTM that provides a test of typological theories in the stricter sense of the term. So far, it seems to me that the advocates of GBTM have not been clear on this issue. Some clarification would be in order.