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My data are proprietary. So, I am altering the data context a bit because I have signed an NDA agreement on the original dataset. This made up context, which mimicks my actual dataset, is about runners i.e., athletes. In my data situation, each athlete can either: (1) run indoors on a treadmill - I call this "DIST_INDOORS_1" (2) run indoors on track in the gym - I call this "DIST_INDOORS_2" (3) run outdoors on track in the ground - I call this "DIST_OUTDOORS".

The sum of "DIST_INDOORS_1, "DIST_INDOORS_2, and DIST_OUTDOORS is my dependent variable. I call this dependent variable, "TOTAL_DIST".

Data were collected over a single day, but over a large number of athletes. As indicated earlier, my dependent variable is TOTAL_DIST, but one of my important independent variables is DIST_OUTDOORS". However, I am NOT going to use DIST_INDOORS_1 are DIST_INDOORS_2 as independent variables. on and/or outdoors. Again, I will only be using DIST_OUTDOORS as the independent variable in the regression of TOT_DIST. I have several other independent variables, such as age, gender, height, number of years of prior training etc.

My question is as follows: Can I run a linear or a count model (such as Poisson or NegBin regression) of TOT_DIST using DIST_OUTDOORS as one of the independent variables? I will be including other independent variables, but will NOT be including DIST_INDOORS_1 and DIST_INDOORS_2 as independent variables. Or, will I need to execute some fancy regression? If so, which one? Advice/inputs will be greatly appreciated. Thanks in advance.

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  • $\begingroup$ What question are you trying to answer? As it's posed, you're asking "what variation in the sum of indoor and outdoor distance is explained by outdoor distance?". It's hard to imagine why you're interested in that question, so maybe you can explain what you're trying to get at. $\endgroup$ – Richard Border Mar 18 '18 at 1:18
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    $\begingroup$ Also, either way, a Poisson or negative binomial model is not likely to be what you want. Finally, you should post your follow-up questions and comments as comments, either to individual answers or here, not as answers. :) $\endgroup$ – Richard Border Mar 18 '18 at 1:20
  • $\begingroup$ Hearty thanks Richard. Sorry for the faux pas. I am new to posting here, and hence mistakenly did not follow the norms. Note that there are three types of exercise regimes namely, DIST_OUTDOORS, DIST_INDOORS_1, and DIST_INDOORS_2. What I am trying to understand is what proportion of one specific type of regime (namely, $\endgroup$ – sals Mar 18 '18 at 4:02
  • $\begingroup$ Hearty thanks Richard. Sorry for the faux pas. I am new to posting here, and hence mistakenly did not follow the norms. Note that there are three types of exercise regimes namely, DIST_OUTDOORS, DIST_INDOORS_1, and DIST_INDOORS_2. I think that I have failed to properly explain the motivation. What I am trying to understand is between men and women (i.e., gender), which gender has a stronger association between DIST_OUTDOORS and TOTAL_DIST. My apologies. I should have specified the motivation for my problem correctly earlier, and I failed to do that. $\endgroup$ – sals Mar 18 '18 at 4:10
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This is a bad idea. What I would do is to add only the two indoors measures and use that as my dependent variable.

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If DIST_OUTDOORS is your independent variable of interest then I would exclude that from your dependent variable. I don't think it makes sense to estimate the effect of your independent variable when it is your dependent variable. So, the coefficient of DIST_OUTDOORS would be the estimate on Total Dist (-DIST outdoors). I'd go with regression as opposed to Poisson model.

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