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I am looking to model physical activity (in minutes) as my dependent variable. I have several independent variables of the environment around the school (intersections, traffic, etc).

What type of model would make sense? I was thinking multiple linear regression but some of the variables do not really have a linear relationship.

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    $\begingroup$ Could you tell us something about the evidence you have of nonlinear relationships? In many cases a little bit of nonlinearity won't matter. $\endgroup$
    – whuber
    Aug 22, 2012 at 19:08

2 Answers 2

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Linear regression can accommodate non-straight-line relationships between IVs and the DV through various transformations of variables, addition of polynomial terms and so on.

That is a model like

$y = b_0 + b_1x_1^2 + b_2x_1 + b_3x_3^5$

is a linear model. But a model such as

$y = b_0 + 2^{b_1x_1}$

is not.

If the data are really nonlinear, then the choice of model depends partly on what you know about the relationships. If you don't know much, a spline regression may work well.

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  • $\begingroup$ I have tried to create log's for the IV but there is still no linear relationship, is there another way to transform the variables. Findings to date on the relationships between these variables is quite mixed. I will look into a spline regression. Thanks $\endgroup$
    – user10720
    Aug 22, 2012 at 18:29
  • $\begingroup$ Have you looked into Box-Cox? It's been discussed here a lot, and there are also lots of resources on the web. $\endgroup$
    – Peter Flom
    Aug 22, 2012 at 18:36
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I don't know if this suggestion might be too advanced, but if you want to model duration (i.e., time until cessation), the appropriate approach is survival analysis. Most likely, the Cox proportional hazards model is best.

With regard to non-linear relationships, @PeterFlom is giving you good advice that transformations (such as squared terms) and splines can help.

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  • $\begingroup$ Is physical activity recorded over time as well as measured in duration of activity? If so then a time series model might be more appropriate. $\endgroup$ Aug 22, 2012 at 19:01
  • $\begingroup$ That's a good point, @MichaelChernick, I'm not sure. I'm interpreting "I am looking to model physical activity (in minutes)" as meaning that how many minutes physical activity lasted is the DV, but I could be wrong. $\endgroup$ Aug 22, 2012 at 19:03
  • $\begingroup$ No I interpret it that way too. But what is not said is whther or not duration of physical activity is continuously recorded over time or not. I think your assumption when you suggested survival analysis was that it is recorded once for each of a number of students. $\endgroup$ Aug 22, 2012 at 19:09
  • $\begingroup$ Yes I am trying to model minutes of PA as the DV. It is measured as the duration of PA over a 1 hour sample (0 minutes to 60 minutes). The sample is quite large and evenly distributed. It is the IV's where they are skewed and have a non-linear relationship. What is my best bet? Should I transform the IV's for multiple linear regression? Or use another form of regression? $\endgroup$
    – user10720
    Aug 22, 2012 at 19:09
  • $\begingroup$ Each student has a number of minutes when they are active (0-60). No intensity is being included $\endgroup$
    – user10720
    Aug 22, 2012 at 19:16

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