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In the following excerpt, the author noted an association with the dependent variable based solely on the p-value and not the magnitude of the coefficient. Here is a link to the study.

GLM Coefficients

I thought that the coefficients would tell us the magnitude of change in the dependent variable with a change in the feature; like a gradient. Why are Followers and Followees strong predictors if they have such small coefficients?

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    $\begingroup$ Please give a reference to this study in usual academic form or alternatively a stable and accessible URL. $\endgroup$ – Nick Cox Jan 7 '16 at 0:53
  • $\begingroup$ If I changed a variable from being measured in mm to being measured in km (or from dollars to millions of dollars), the coefficient would change by six orders of magnitude, but the p-value would remain unchanged. $\endgroup$ – Glen_b Jan 7 '16 at 1:46
  • $\begingroup$ @NickCox I have added the URL. $\endgroup$ – Duck Jan 7 '16 at 13:54
  • $\begingroup$ Thanks. The .pdf there carries no standard bibliographic details but here they are: Bongwon Suh, Lichan Hong, Peter Pirolli, and Ed H. Chi. 2010. Want to be Retweeted? Large Scale Analytics on Factors Impacting Retweet in Twitter Network. In Proceedings of the 2010 IEEE Second International Conference on Social Computing (SOCIALCOM '10). IEEE Computer Society, Washington, DC, USA, 177-184. DOI=dx.doi.org/10.1109/SocialCom.2010.33 $\endgroup$ – Nick Cox Jan 7 '16 at 14:29
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Understanding the magnitude of the effect as expressed through the regression coefficient depends entirely on the scale on which the X variables are measured. Remember, the coefficient in a GLM model represents the change in Y for a one unit change in X. In this example, a number of the predictors are binary variables (those with the 'orNot' suffixes). Thus, for these variables, a one unit change represents moving from the minimum value (0) to the maximum value (1). Variables such as Followers and Followees are continuous variables, and thus a one unit change in these X variables means something very different as they range from a minimum of zero to a maximum of (possibly) several thousand.

Accordingly, it is not possible to directly compare the estimated coefficients for different variables in a GLM model without taking into account the scale on which those variables are measured.

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    $\begingroup$ Agreed. I think it's consistent with that to point out that some rescaling of predictors would have been a very good idea in the study cited. The coefficients of four predictors are given to just 1 sig. fig. as a side-effect of working with values $>> 1$. While it's perhaps unlikely that any one would want to use this particular equation for comparison, in other fields of science using other studies' results for prediction is important. Indeed it's a criterion of scientific or practical worth if a fitted model is of wider interest. $\endgroup$ – Nick Cox Jan 7 '16 at 0:51
  • $\begingroup$ Indeed - I suppose it is possible that they did some rescaling in other tables in the paper, though without a reference it is impossible to tell! $\endgroup$ – user2728808 Jan 7 '16 at 11:20

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