Dear colleagues,
I am asking your kind comments or recommendation on analyzing hierarchical- and multiple responses (outcomes). I use hierarchical and multiple responses to express my outcome variable which is because my outcome is Quality of life (by Rand-36 or SF-36). However, by calculating the 36-items questions, I would have a continuous mean score for the total quality of life. But, as you may know, under SF-36, we also could calculate 8 domain scores (separately PF, RP, BP, GH, and MH, RE, VT, SF), and 2 dimensions (summary) scores (the PCS and MSC). Therefore, in a way, my outcomes are multiple responses and also are hierarchical.
level 1: total mean score of quality of life
level 2: --- Physical component summary
level 3: ------ PF: physical functioning
level 3: ------ RF: role limitation due to physical problems
level 3: ------ BP: body pain
level 3: ------ GH: general health
level 2: --- Mental component summary
level 3: ------ MH: mental health
level 3: ------ RE: role limitation due to emotional problems
level 3: ------ VT: vitality (fatigue or energy)
level 3: ------ SF: social functioning
My purpose of study (cross-sectional design) is to understand associated factors to hemodialysis patients' quality of life. Therefore, I have a series of explanatory variables (Xs) to estimate the Ys. My original analysis was using "multiple regression" to each of the quality of life scores (Three hierarchical levels of scores: the total QoL mean score, each of the 8 domain scores, and each of the 2 dimension scores).
But, this brings me to the problem of "multiple comparisons" and also I treated each type of scores (no matter the total QoL mean score, or the domain score, or the summary score) as "independent to each other" which actually are correlated. However, from the QoL measurement instrument, there is inherent hierarchical and also correlations among the three levels of scores in the designed conceptual framework: SF-36.
Therefore, Ii would like to kindly ask for your comments or recommendation:
1). how can I analyze my (Y (outcomes) when they are multiple-responses and hierarchical?
2). will multilevel analysis (hierarchical linear regression) work for my Ys?
3). other analysis methods could try?
4), could you please suggest to me some literature to explore this issue I am countering?
Teshita Uke Chikako Thank you so much for your paper recommendation. I will read through carefully.
Michael Wei-Chih Liu Path analysis allows you to examine multiple dependent (and multiple independent) variables in a single statistical model. You can allow the residuals of the DVs to be correlated to account for the fact that these are closely related above and beyond what can be predicted from the IVs. Path analysis does not address the hierarchical nature of the constructs, that is, you would only use the "first-order" facets/constructs as DV, not the overall summary score.
Hierarchical and/or bifactor confirmatory factor models are sometimes used to examine hierarchically structured constructs through "general" and "specific" factors. For this, you would need a measurement model (multiple indicators such as items) for each facet.
Christian Geiser Thank you so much for your suggestion. I will try path analysis.
The thing about your scores on individual dimensions is that they have to add up to the total score. This causes an interesting problem (read "headache"). Because when you fix all but one of the subscales, the final subscale is also fixed.
This is a Dirichlet distribution, and it is much studied in areas like breakdown of household expenditure. There's an introduction here : https://epub.wu.ac.at/4077/
Essentially, not only can your total scores vary but the relative importance of each subscale can vary within that. When modelling the joint distribution of the subscales, it makes sense (to me, at least!) to use the total score as a predictor in whatever model you build. This is because the relative scores on subscales may be a function of the total score. Such an effect could confound relationships with other predictors.
In addition, you have to be careful with SF-36 scores. While they are apparently scaled between 1 and 100, subscales can have relatively few possible scores and, in my experience, can have horrible clusters at one end.
It's the sort of interesting problem that I'm kinda glad isn't mine!
Ronán Michael Conroy thank you so much for your kind advice. I will read through the Dirichlet distribution.
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