I'm trying to figure out the direction of my data from my GLM output analysis. For example, with linear regression, you can plot the x and y values on a scatter plot to determine the direction of the data with the fit line (up for a positive correlation; down for a negative correlation). How would you figure out the direction of a GLM with a dependent variable (response), two covariates (predictors), and the interaction between the two? Would the direction be found in the goodness of fit table (and which variable would it be), or something else?

  • $\begingroup$ Can you paste in some example output that illustrates the kind of situation you have trouble with? $\endgroup$ – gung - Reinstate Monica Dec 16 '19 at 18:11
  • $\begingroup$ @gung-ReinstateMonica how do you insert images I'm new to this platform sorry $\endgroup$ – Mae Dec 16 '19 at 19:04
  • $\begingroup$ When you click "edit", you get a text field with your question text in it. Above, you will see a series of icons, starting with a "B" on the far left for bold. A quarter of the way across, you see what looks like a picture of mountains with a sun. Click on that and either navigate to an image file on your computer, or enter a link to an image file on the internet. $\endgroup$ – gung - Reinstate Monica Dec 16 '19 at 19:32
  • $\begingroup$ awesome thank you @gung-ReinstateMonica I pasted the image $\endgroup$ – Mae Dec 16 '19 at 20:12
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    $\begingroup$ None of these are going to help you figure out the direction, unless I'm badly misunderstanding you. What is the nature of your dependent variable, is it binary or a count? Can you paste in the table of coefficients? $\endgroup$ – gung - Reinstate Monica Dec 16 '19 at 20:25

With multiple predictors, I'm not sure it make sense to talk about the "overall direction" of the model. One predictor might be associated with larger (more positive) responses, while another might go in the opposite direction. For example, suppose you were predicting a car's top speed. The power of its engine is probably positively associated with faster speeds, while heavier cars tend to go slower.

Instead, your model contains a set of coefficients, or $\beta$ values, one for each parameter (predictor or interaction term). The precise interpretation of those coefficients depends on your link function, but in general, their sign and magnitude would tell you how each predictor affects your response variable.

For a general linear model (no/identity) link function, positive $\beta$ values indicate that, holding everything else constant, an increase in the predictor is associated with an increase in the response. For a logistic regression, $\beta$ instead tells you how the log of the odds of a positive outcome changes. There's a nice worked example here.

The table you've posted seems to describe how well the overall model (pIC + AveKneeJ + pIC*AveKneeJ) predicts Gl+Gln_Cr_csf for two different cohorts of data, which is rather different.

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