We are working on two skewed dependent variables. In this particular case, the few people at the end of one or both scales are of clinical importance. Thus, we opted that we focus the analysis of them against all the others.
We split scores on both scales at the 0.8 quantile. Then we construct four groups: those who exhibit high scores in either scale (2 groups: Beh1 and Beh2), those who exhibit high scores in both scales (1 group: Beh12), and those that exhibit none (1 group: Beh0).
We need to examine Beh1 , Beh2 , and Beh12 in terms of their scores in three continuous variables X1, X2 , X3, and one categorical variable G with two levels. Since the three continuous variables are correlated, we performed MANOVA (The categorical variable G is independent of being in omitted Beh0 or any of the groups included in the analysis) The MANOVA is significant.
Then we used LDA to find out whether we can also predict the group one is in from their score pattern in (X1 , X2 , X3). Due to LDA not taking a categorical variable as a predictor, we did this for each level of G separately. The LDA prediction has accuracy 63%, different from chance level, for G1, while only 58% for G2, not different from chance.
These findings are corroborated by descriptive statistics showing that for all Gi x Behj combinations, except for G1:Beh12 , X1, X2, X3 lie in roughly the same level within each combination. Only G1:Beh12 exhibits a rather low X1 outside the CI's of X2 and X3 .
We interpret this as follows: X1 is important in predicting Beh12 membership, but only for G1. This is corroborated by a moderation analysis on the same data.
Would you accept this interpretation, based on the methods used above? I would appreciate any feedback on this workflow. Thanks in advance!
Dear Nikolaos,
If I understand properly, you have two scales X1 X2 which you classified high or low. Since by construction B1, B2, B12 are built out of differences in X1 X2 there is no surprise that the MANOVA is significant. is variable B1 exclusive of B12 or overlapping? I will presume the latter given your LDA result.
So now you ask the question: given that membership in high scores on X1 and X2 can overlap we construct a discriminant function that separates them; and ideally relate this to G as well.
My understanding of your result is that x1 discriminates between b12 groups for group G1 but not G2.
So, first of all, I think that not all of this workflow was necessary, but there is nothing critically misleading in this. However, 1) G can be recoded 0, 1 and used inside a LDA much the same way that B1, B2, B12 have been done. 2) The difference in fit between the LDA at 63% and that at 58% is almost certainly NOT significant. Concluding that the impact of G is important in this situation is likely to be a large mistake. Obviously if your sample size is large enough then I am incorrect in this!
Personally, I would generate variables B1, B2 but not B12 or B0. The variables B1, B2 are sufficient to describe the 4 groups and there are complexities in including B12 as a variable. If I was curious about the role of G in the prediction of which group I was in I would code G as 0, 1 and then run a logistic regression (or others) predicting G using B1 and B2.
I realize that I may be misunderstanding the question you are ultimately trying to answer, but I don't understand the use of B1, B2 in the same LDA as X1, X2 on which they are based! If you explain what you are ultimately trying to find out I may be able to better help.
Thank you for your feedback. It is very helpful.
The variables X1, X2, X3 are not the same variables used in defining the Behavior groups, say Y1, Y2 . The sample size for the LDA (after excluding Beh0) is 122. The Beh1 and Beh2 groups are not overlapping with Beh12. The two figures are accuracies, thus proportions. We did not compare them directly as such, rather each figure is compared with the chance level, apparently 33% for three outcomes.
We will certainly try Logistic Regression, it sounds more convenient. We went for MANOVA in order to examine the three X variables simultaneously, and then needed to follow it up, thus the LDA.
We are interested in different patterns in the three X variables across the clinically important behavioral groups. The variables are correlated.
Hope this clarifies the points you mention. Thanks again for taking some time to think about this!
So if beh1, 2, 12 are not based on the DVs x1,2,3 I understand why you were interested in the MANOVA. However, I am still potentially unclear on the variables beh1, 2, 12. If I am understanding this you have defined B1 as being high on some variable Y1 while not being high on some Y2, and B2 as being high on Y2 but not Y1, and B12 as being high on both. The question is then, how similar or different are the groups created in this way? And how meaningful is it to define B1 as excluding members of B12.
The question you wish ultimately to pose is whether or not there are differences in pattern over X1-3 that relate to groups Beh1, Beh2, Beh12. In this context I would create variables B1, B2 and try an LDA over X1,X2,X3 only if I though that "pattern" meant different mean scores. Although there are plenty of statistical (especially exploratory) techniques that can help you navigate this sort of question, the best would be to define what sort of patterns are of interest. You could then generate definitions of those patterns, score people, and run something nice and simple!
Consider as well some ordination techniques to properly incorporate the potential interactions between G and B1, B2.
Anyway, best of luck.
Thanks, this was also useful. I will focus on B1 and B2 , as a starting point. Thanks again for reviewing this!
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