I have a paper submitted to a journal and one of the reviewers suggested me to conduct a hierarchical logistic regression. I know how to conduct multilevel regression analysis by clustering the data at different levels. Like for example a sample of students can be clustered by classrooms, and then by schools etc. But, what the reviewer asked is clustering using the dependent variable. Is any one out there who could help by giving some clue or recommending any reading materials.
Is hierarchical regression appropriate for running a regression using multilevel dependent variable?
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$\begingroup$ Can you please give more details in general? The clustering is always done on the dependant variable using the independent variable information... In your example say you care about the students' grade, the clustering is based on the students classrooom, school, county, etc. Did you mean to say independent? I mean someone might want to add some arbitrary categories based on the dependent variable (say below, within or above a particular interval) but this seems rather ad-hoc (and very probably wrong). $\endgroup$– usεr11852Commented Jun 19, 2016 at 7:21
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$\begingroup$ To give a bit of detail. For example my dependent variable is students' total score ( composed of maths, English and aptitude results) and the independent variables are gender, income etc. my question is ...is that possible to run a hierarchical regression like first level regression for maths, then English and last stage for aptitude test scores? $\endgroup$– user120062Commented Jun 19, 2016 at 9:31
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$\begingroup$ Ah... :) OK... Isn't there a deterministic formula that corresponds to the final grade though? eg. $\text{Score}_\text{Total} = \alpha_1 \text{Score}_\text{Maths} + ... + \alpha_p \text{Score}_\text{English}$. I suspect they want to suggest that maybe some schools are better than other in certain subjects that carry more influence... You could break the model in different subject-specific sub-models and then combine them back but that feels rather odd... $\endgroup$– usεr11852Commented Jun 19, 2016 at 9:53
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$\begingroup$ Ah... :) OK... Isn't there a deterministic formula that corresponds to the final grade though? eg. $\text{Score}_\text{Total} = \alpha_1 \text{Score}_\text{Maths} + ... + \alpha_p \text{Score}_\text{English}$. I suspect they want to suggest that maybe some schools are better than other in certain subjects that carry more influence... You could break the model in different subject-specific sub-models and then combine them back but that feels rather odd... $\endgroup$– usεr11852Commented Jun 19, 2016 at 9:53
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2$\begingroup$ Why do you refer to logistic regression? That is not used when the outcome is a score measured on a fine-grained scale. $\endgroup$– rolando2Commented Jun 19, 2016 at 11:33
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1 Answer
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I don't see how you can have maths, English and aptitude outcomes at different levels of a hierarchical model.
If you want to separate the scores and have them as different outcomes in one model then you could use multivariate multiple regression or a structural equation model. Edit: I have just come across the ASReml package which allows for multiple response variables in a mixed/hierarchical model, so that could be a good option
I suspect the reviewer is asking for a hierarchical model with students at one level, clustered in (say) classrooms, or schools, at higher levels. However, why they suggest a logistic model makes no sense to me.
answered Jun 19, 2016 at 11:13
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$\begingroup$ I am not sure this is advice is very accurate. A hierarchical model at student level with the response variable being the composite test score would have a different random effects level per measurement. (I like your avatar by the way, personal hero of mine that guy...) $\endgroup$ Commented Jun 19, 2016 at 17:42
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$\begingroup$ One could "theoretically" reformulate the model so he aggregates the individual lesson scores into one response vector. Then he would be able to use
studentas a random effect but he would have to also use an indicator variable for each specificsubject-specific score to model the mean response. This could probably work but you would likely bleed out some serious degrees of freedom from the model. $\endgroup$ Commented Jun 19, 2016 at 17:52 -
$\begingroup$ @usεr11852 If the student is a random effect / cluster , then what is clustered within each student ? If the 3 scores per student are aggregated into one then there would be only 1 measurement per student in the model and hence no clustering. $\endgroup$ Commented Jun 19, 2016 at 18:37
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$\begingroup$ @usεr11852 glad you like it ! $\endgroup$ Commented Jun 19, 2016 at 18:47
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$\begingroup$ Yeah, that's what I am saying too. The idea of clustering within student seems implausible unless you change the response variable to be the aggregate vector of the subject-specific scores. The way the post is written doesn't really clear that up because you mention the word model for different models. $\endgroup$ Commented Jun 19, 2016 at 19:07