## Testing difference in genmod

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# Testing difference in genmod

Dear all, wish you all well.

Can anyone please enlighten me on my understanding of the partial genmod output below?

The result shows that there is a decreasing trend in y over the 2-year period and the decrease does not vary from responses to A1.

I tried to insert the interaction plot here to illustrate my question but it doesn't work and I don't know why given the small image size.

According to the interaction plot, all the lines joining the LSM mean values from 2010 and 2011 by A1 seem to be parallel and show a decreasing trend. However, 2=Disagree a little line intersects with 3=Neither agree nor disagree line. How do I find out/quantify which of the deceases from A1 responses is different given the output?

Your insight is greatly appreciated. Thank you very much.

proc genmod data=temp order=internal plots=all;

class id time var1;

MODEL y= var1 time var1*time / type3 dist=gamma link=log;

lsmeans time*var1 / om diff ilink cl plots=all;

slice time*var1 / sliceby=var1 ilink diff nof;

repeated subject=id / type=cs;

run;

 Score Statistics For Type 3 GEE Analysis Source DF Chi-Square Pr > ChiSq time 1 28.17 <.0001 p-value<0.05 indicates that there is a change in y over the 2-year period. A1 4 13.72 0.0082 p-value<0.05 indicates A1 responses do change in y. time*A1 4 3.56 0.4685 p-value>0.05 indicates that A1 responses do not change in y in different ways over the 2-year period.

 time*A1 Least Squares Means Year A1 Margins Estimate Standard Error z Value Pr > |z| Alpha Lower Upper Mean Standard Error of Mean Lower Mean Upper Mean 2010 1=Disagree a lot WORK.LONG 3.779 0.04276 88.38 <.0001 0.05 3.6952 3.8628 43.7739 1.8718 40.2548 47.6007 2010 2=Disagree a little WORK.LONG 3.8023 0.03689 103.06 <.0001 0.05 3.73 3.8746 44.8055 1.6531 41.6799 48.1654 2010 3=Neither agree nor disagree WORK.LONG 3.8649 0.06677 57.88 <.0001 0.05 3.734 3.9957 47.6962 3.1846 41.8457 54.3647 2010 4=Agree a little WORK.LONG 3.8583 0.05042 76.53 <.0001 0.05 3.7595 3.9571 47.383 2.3889 42.9249 52.3043 2010 5=Agree a lot WORK.LONG 4.1424 0.07728 53.6 <.0001 0.05 3.9909 4.2938 62.9528 4.8648 54.1049 73.2476 2011 1=Disagree a lot WORK.LONG 3.6229 0.03579 101.23 <.0001 0.05 3.5528 3.693 37.4459 1.3401 34.9094 40.1667 2011 2=Disagree a little WORK.LONG 3.7304 0.04632 80.53 <.0001 0.05 3.6397 3.8212 41.6977 1.9316 38.0786 45.6608 2011 3=Neither agree nor disagree WORK.LONG 3.6591 0.07028 52.07 <.0001 0.05 3.5213 3.7968 38.8256 2.7285 33.8298 44.5592 2011 4=Agree a little WORK.LONG 3.7249 0.0533 69.89 <.0001 0.05 3.6205 3.8294 41.4687 2.2103 37.3552 46.0353 2011 5=Agree a lot WORK.LONG 3.9732 0.08752 45.4 <.0001 0.05 3.8017 4.1447 53.1546 4.6522 44.7757 63.1015

 Simple Differences of time*A1 Least Squares Means Slice time _time Estimate Standard Error z Value Pr > |z| A1 1=Disagree a lot 2010 2011 0.1561 0.04432 3.52 0.0004 A1 2=Disagree a little 2010 2011 0.07188 0.04015 1.79 0.0734 A1 3=Neither agree nor disagree 2010 2011 0.2058 0.0817 2.52 0.0118 A1 4=Agree a little 2010 2011 0.1333 0.05185 2.57 0.0101 A1 5=Agree a lot 2010 2011 0.1692 0.06491 2.61 0.0092

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Solution
‎07-24-2015 08:07 AM
Posts: 2,655

## Re: Testing difference in genmod

The simple difference tests follow from the overall test--the two years differ, and it is roughly the same difference for all categories of A1.  The estimate values all indicate a change with a range of 0.07 to 0.21, where all changes have 'effect sizes' (Z scores) of at least 1.79.  (I'm weaseling around the p values here, because I don't know what your cutoff for significance is).  There really does not look like there is any strong evidence for an interaction.

Am I making sense, or did I miss the point of your question?

Steve Denham

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Solution
‎07-24-2015 08:07 AM
Posts: 2,655

## Re: Testing difference in genmod

The simple difference tests follow from the overall test--the two years differ, and it is roughly the same difference for all categories of A1.  The estimate values all indicate a change with a range of 0.07 to 0.21, where all changes have 'effect sizes' (Z scores) of at least 1.79.  (I'm weaseling around the p values here, because I don't know what your cutoff for significance is).  There really does not look like there is any strong evidence for an interaction.

Am I making sense, or did I miss the point of your question?

Steve Denham

Regular Contributor
Posts: 234

## Re: Testing difference in genmod

Hi Steve. I really appreciate you taking the time answering my question.

My analysis is based on 5% level of significance FYI.

If the p-value of the interaction term is > 0.05 indicates the change for all levels of var1 is no difference.

Does each of the significant simple difference tests by var1 reflect from the significant main time effect?

Also,  is it still sensible to quantify the simple differences and 95% C.I.  on the original scale as you previously posted here ()?

Thank you very much.

Posts: 2,655

## Re: Testing difference in genmod

Hi KC,

If the p-value of the interaction term is > 0.05 indicates the change for all levels of var1 is no difference.

A non-significant interaction, but significant main effects, implies that the differences between the levels of var1 is the same at all times, and that the differences between levels of time is the same for all levels of var1.  Therefore, the best estimates of effects are the marginal means (main effect means).

Does each of the significant simple difference tests by var1 reflect from the significant main time effect?

Yes, that is what is being shown.

Also,  is it still sensible to quantify the simple differences and 95% C.I.  on the original scale as you previously posted here

While you can report these, the marginal differences are probably more meaningful.  Try adding the following to your code:

to get the marginal means and differences.

Steve Denham

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