topic Re: Testing difference in genmod in Statistical Procedures

Testing difference in genmod

Miracle — Fri, 24 Jul 2015 04:32:00 GMT

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

Re: Testing difference in genmod

SteveDenham — Fri, 24 Jul 2015 12:07:04 GMT

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

Re: Testing difference in genmod

Miracle — Mon, 27 Jul 2015 02:45:05 GMT

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.

Re: Testing difference in genmod

SteveDenham — Mon, 27 Jul 2015 12:14:49 GMT

Hi KC,

Some answers:

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:

lsmeans time var1/diff cl ilink;

to get the marginal means and differences.

Steve Denham