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Thread: Generate model from known independent & dependent variables. Does this make sense?

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    Question Generate model from known independent & dependent variables. Does this make sense?




    I am on a new job as a statistician, after studying stats some years ago. So please bear with me as I seek a solution to my problem.

    I'm trying to generate a model that relates known physical characteristics (height of palms of hands with outstretched arms overhead, inclinometry measurements at the hip and waist, joint integrity, stretch ability of hamstrings…) to known reach curves.

    Presently, we measure a person's reach by having them start at a standing position with arms outstretched overhead then bend forward and downward while drawing a curve on a white board. This reach test is done at varying barrier heights that may restrict ones reach. We also collect their physical characteristics as mentioned above.

    Each curve appeared to be arcs of circles, so upon further examination and the use of photo/video physics software, I plotted points and fitted them to curves. The best fit was indeed obtained with a circle. So now I have known equations of circles varying by the radii differing by barrier height and ones physical characteristics and known physical characteristics.

    With both pieces of information in hand (curves drawn and physical characteristics), I am hopeful that I will be able to find a model with physical characteristics as independent variables that will give the person’s reach as the outcome (arcs of circle). We want the ability to use physical characteristics data to determine future reaches. We’d also like to go backward and determine the reaches of individuals who didn’t do the reach test, yet we did collect physical characteristics data for them.

    Does this make sense? Is it statistically possible? If so, how? Please offer suggestions.

    Thank you kindly,
    Bnew

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    Re: Generate model from known independent & dependent variables. Does this make sense

    It is difficult to answer your question given the complexity of the subject matter [of which I understood precisely nothing}. That said if independent variables can theoretically predict some phenomenon it makes sense to test it through regression. It is not clear to me how you measure your dependent variable - it seems that reach might comprise more than one dimension and or be difficult to quantify in any useful way. To me it seems that some of you independent variables might be multicolinear but you can test for this with something like a VIF test. And of course they might not be, because I know nothing of the phenomenon you are describing.

    You can always predict reaches and see how good the model does in practice. Understanding that just because it works with your test population does not mean it will work with others [the issue of generalizability].

    Sounds like interesting analysis.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Generate model from known independent & dependent variables. Does this make sense

    Hi,
    I would split the problem in several parts and see later if the parts fit together. If I understand you correctly you are modelling the reach as a collection of circles. So could you predict using a regression for instance the parameters (center, radius) of the first arc, using measured data? If yes, you could move to the second circle and so on..

    I hope this makes sense.
    regards

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    Re: Generate model from known independent & dependent variables. Does this make sense

    Quote Originally Posted by rogojel View Post
    Hi,
    I would split the problem in several parts and see later if the parts fit together. If I understand you correctly you are modelling the reach as a collection of circles. So could you predict using a regression for instance the parameters (center, radius) of the first arc, using measured data? If yes, you could move to the second circle and so on..

    I hope this makes sense.
    regards
    Yes, part of the problem is to use the radius to predict the entire reach depicted by an arc of a circle. 2/3 of the points fit nicely to the arc of a circle using the radius measured at the center of the arc, yet the portion of the arc near the starting point (highest point with arms outstretched overhead with person standing upright) seem to have a larger radius.

    The other part of the problem is to use known physical characteristics like height of arms outstretched overhead, lumbar flexibility, arm length to name a few as predictors to give the outcome reach over the entire area that the person can reach (arc of a circle) from highest to lowest point. I'd like to find a model that does this.

    Either an equation similar to a circle would be the outcome or the radius would be the outcome.

    Thank you

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    Re: Generate model from known independent & dependent variables. Does this make sense


    Thank you. I am reviewing multicollinearity and the VIF test now.

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