topic Re: mixed modelling, help with correct model writing in Statistical Procedures

mixed modelling, help with correct model writing

Ruhi — Wed, 20 Jul 2016 16:50:47 GMT

Hi All

I am writting a model to estimate the varaince components, and I am not sure of the correct model to estimate the components I need. Please help me.

So I have 60 patients, who each got scanned on 6 days, and 6 times everyday. Each scan contains 20 images. I want to estimate intraday, interday and intrascan variance. With my model my residual variance is higher than the intraday varaince, which is causing doubts. 20 images within a scan should be very close and should have least variability. scans within a day should than have less varaibility than variability between days. Please help me with correct model writing.

proc mixed data=p2.req;
class pt_nbr day_nbr scan_nbr image_nbr ;
model Y= ;
random day_nbr pt_nbr day_nbr*pt_nbr scan_nbr(day_nbr) ;
run;

SAS Output

Covariance Parameter Estimates
Cov Parm	Estimate
day_nbr	0
pt_nbr	1078.39
pt_nbr*day_nbr	12.7373
scan_nbr(day_nbr)	2.1783
Residual	13.0825

Re: mixed modelling, help with correct model writing

SteveDenham — Wed, 20 Jul 2016 17:55:08 GMT

You may wish to fit a fully factorial random model. I have a hunch that the missing terms are falling to the residual error, and consequently inflating it. What happens if you try:

proc mixed data=p2.req;
class pt_nbr day_nbr scan_nbr image_nbr ;
model Y= ;
random pt_nbr|day_nbr|scan_nbr ;
run;

I used the pipe notation to get all main effects, the three first order interactions and the second order interaction. You could also delete image_nbr from the class statement.

The problem I see here is that these repeated measurements mean that the actual experimental unit is the scan_nbr, and the residual error is pseudo-replication. With that in mind, what happens with:

proc mixed data=p2.req;
class pt_nbr day_nbr scan_nbr image_nbr ;
model Y= ;
random pt_nbr|day_nbr|scan_nbr@2 ;
repeated image_nbr/subject=pt_nbr*day_nbr*scan_nbr;
run;

Have to admit I am spitballing at this.

Steve Denham

Re: mixed modelling, help with correct model writing

Ruhi — Thu, 21 Jul 2016 15:16:09 GMT

Hello Steve

Thanks for your quick reply. I tried your both models. I personally think first one is better, I think because I understand it better :).FYI, I don't have missing data.

Fit statistics are also better with the first model. From the sas output that follows , I think the highlighted portions of the data will give me the required estimates I need. Please let me know if you think I am thinking correct?

SAS Output

Covariance Parameter Estimates
Cov Parm	Estimate
pt_nbr	1042.21
day_nbr	0.1685
pt_nbr*day_nbr	13.0275 (interday)
scan_nbr	0.2490
pt_nbr*scan_nbr	0.3753
day_nbr*scan_nbr	0
pt_nbrday_nbscan_n	9.9088(Intraday)
Residual	4.3063(intrascan)

SAS output form the second model you suggested.

SAS Output

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
pt_nbr		1041.89
day_nbr		0.1569
pt_nbr*day_nbr		14.5853
scan_nbr		0.2367
pt_nbr*scan_nbr		2.2446
day_nbr*scan_nbr		0.07033
image_nbr	pt_nbrday_nbscan_n	11.0527

Re: mixed modelling, help with correct model writing

SteveDenham — Thu, 21 Jul 2016 18:05:05 GMT

I agree--the first model is more easily interpreted (and since it was my first thought, that says something as well). Sometimes, overthinking a model will lead to trouble. I did see a zero estimate, so you probably saw something about the G matrix not being positive definite. In this case, that is not a problem--the REML estimates of variance components are better estimators.

Steve Denham