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I am doing a research and want to analyze factors that are associated with dental erosion using binary regression analysis. Dental erosion (dependent variable) was graded using a scale criteria with 5 points (0= No erosion, 1=mild erosion, 2=moderate erosion, 3=severe erosion, 4=very severe erosion). No one in the sample had grade zero. Therefore, because severe and very severe erosion are the most important clinically I am interested to see which factors are associated with occurrence of severe and very severe erosion (grades 3 and 4). The data were collected for 3 age groups (5, 13 and 18 years old children). I have 3 questions: 1- I dichotomized the dependent variable into two groups: group with grades (0,1) and other group with grades (3,4) and excluded grade 2 to create good contrasting groups. This resulted in massive drop in sample size but resulted in high odds ratios. Is that correct to do or should I include grade 2 with the first group as (0,1,2)?

2- Its known that older children have more erosion, therefore I guess I should control for age by including age as a dependent variable. This means that the final model will be made for the whole three samples rather than for each age group separately. Is that correct or should I do analysis for each age group separately?

3- If I want to include 11 independent variables, what is the best analysis method that should I use ( Enter method or forward stepwise)?

Thank you in Advance

Imad Saga
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  • Sorry, age as independent variable (typo) – Imad Saga Dec 03 '15 at 19:50
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    Stepwise selection is not the best -- it's possibly the worst you can do, see: http://stats.stackexchange.com/questions/20836/algorithms-for-automatic-model-selection/20856#20856 – Tim Dec 03 '15 at 19:52
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    (1) What @Tim says. (2) [Categorizing variables is a bad idea.](http://biostat.mc.vanderbilt.edu/wiki/Main/CatContinuous) (Although in your case, your variables are already only ordinal, not continuous, so it's less bad in this case.) (3) "Controlling" for a variable that is inherently confounded with another variable makes no sense. See Miller & Chapman (2001), *Misunderstanding Analysis of Covariance*, for a discussion. – Stephan Kolassa Dec 03 '15 at 19:56
  • Should I exclude grade 2 or not? – Imad Saga Dec 03 '15 at 21:21
  • @StephanKolassa What about this situation makes you say "inherently confounded"? I just see age as correlated with (but not part and parcel of) erosion and therefore an intuitive choice for a control variable. – rolando2 Dec 04 '15 at 04:22
  • @rolando2: age appears to be inherently strongly correlated with erosion, similar to an example discussed by Miller & Chapman. They consider modeling basketball ability in grade school children, with height as the predictor, and "controlling for" grade. This does not make sense, because 4th graders are inherently bigger than 1st graders. Including both variables essentially asks "how well would a 1st grader play if he were as large as a 4th grader?" But there *are* no 1st graders that are as tall as 4th graders (or if they are, they are strongly abnormal in ways that go beyond height... – Stephan Kolassa Dec 04 '15 at 07:22
  • ... they may have repeated a grade, or have hormonal issues, or whatever). I frequently have the same problem where the DV is PTSD, and reviewers want us to "control for" depression - but depression is highly comorbid with PTSD, so "controlling for" depression would simulate a highly unusual *non-depressed* PTSD patient. Bottom line: some effects are ontologically given and cannot be meaningfully disentangled using only statistics. – Stephan Kolassa Dec 04 '15 at 07:24
  • Could anyone please advice whether to exclude grade 2 cases or is it better to include them!! – Imad Saga Dec 04 '15 at 09:45
  • @StephenKolassa I appreciate your response. To me the problem there would be that grade not only is correlated with height, but cannot be meaningfully disentangled from height. It is part and parcel of it. Virtually all children grow as they age. It's hardly meaningful to say, "suppose a 1st-grader never grew through 4th grade." (Similar to your point: Elazar Pedhazur points out the absurdity of asking, "how tall would this bean plant be if it were a corn plant?") But I don't see a parallel situation with age and dental erosion. – rolando2 Dec 04 '15 at 12:17
  • I'm seeing that Miller and Chapman's example is even more extreme: not grade with height but grade with age. – rolando2 Dec 04 '15 at 15:23
  • @rolando2: I should really re-read that article every year ;-) Thanks! Re your earlier comment: the original post sounded to me exactly similar - I'd expect pretty much any child's teeth to be progressively eroded as the child ages. After all, the teeth are used for chewing, and are brushed. So I'd say that the Miller & Chapman argument holds here. – Stephan Kolassa Dec 04 '15 at 16:20
  • I see what you mean. "Your argument is defensible if not compelling." :-) Cheers. – rolando2 Dec 04 '15 at 20:21

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