topic Re: How to specify AR(1) covariance structure in PROC NLMIXED in Statistical Procedures

How to specify AR(1) covariance structure in PROC NLMIXED

diametra — Thu, 26 Jan 2023 01:55:44 GMT

Hi all,

I would like to expand on a topic that was discussed in this thread.

Here is the mixed-effects repeated measures model that I'm working with:

proc mixed data = analysis;

class SubjectID Treatment Visit;

model AVAL = Treatment Visit Treatment*Visit / s;

repeated / subject = SubjectID type = AR(1);

run;

There are 2 treatment groups and 4 visits (Baseline, Month 1, Month 3, and Month 6). My goal is to estimate the Percentage Change between Month 6 and Baseline for each treatment group. In this thread, PROC NLMIXED was suggested as a method to estimate for the Percentage Change. I followed the example from the thread to build the following model:

proc nlmixed data = analysis;

parms b0=2 b1=0.5 b2=1.2 b3=1.2 b4=1.2 b5=1.2 b6=1.2 b7=1.2 sb=2 se=1;

mu = b0 + b1*(Treatment="Active") + b2*(Visit="Month 1") + b3*(Visit="Month 3") + b4*(Visit="Month 6")

+ b5*(Treatment="Active")*(Visit="Month 1") + b6*(Treatment="Active")*(Visit="Month 3") + b7*(Treatment="Active")*(Visit="Month 6") + u;

model AVAL ~ normal(mu, se);

random u ~ normal(0, sb) subject=SubjectID;

estimate 'Percentage Difference between Month 6 and Baseline for Active' ((b4 + b7)/(b0 + b1))*100;

run;

My question is: How would I specify the AR(1) covariance structure as I did in PROC MIXED using PROC NLMIXED?

Any help or suggestions would be greatly appreciated!

Best,

Diana

Re: How to specify AR(1) covariance structure in PROC NLMIXED

diametra — Thu, 26 Jan 2023 04:32:35 GMT

Additional info:

I've reviewed the example in this paper: https://www.lexjansen.com/wuss/2013/47_Paper.pdf

It described the setup for the First-Order Autoregressive covariance structure (page 3), but the example that they have is a lot more complicated than my model. I don't know how to translate this into my use case (which is a linear model). Additionally, the data in the example from the paper is in a wide (cases by variables) format, which further confuses me.

Re: How to specify AR(1) covariance structure in PROC NLMIXED

jiltao — Fri, 27 Jan 2023 00:27:47 GMT

1. AR(1) is often used in the REPEATED statement in PROC MIXED.

There is no REPEATED statement in PROC NLMIXED. The RANDOM statement in PROC NLMIXED is like fitting a random coefficients model, and AR(1) is almost never used to model the covariance between random intercept and slopes.

2. If for a reason beyond my understanding, you have to specify an AR(1) structure in PROC NLMIXED, then

you would need to have at least 3 random effects (u0, u1, and u2) in order for AR(1) to make sense. For example,

random u0 u1 u2 ~ normal([0, 0, 0],[s2, s2*rho, s2, s2*rho**2, s2*rho, s2]) subject=subject;

where s2 and rho are your model parameters.

Hope this helps,

Jill

Re: How to specify AR(1) covariance structure in PROC NLMIXED

lcw68 — Sat, 29 Jul 2023 03:17:11 GMT

Hi, if I have a correlated longitudinal model with one continuous outcome and one ordinal outcome (using probit normal to define category), say y1it = Xalphai + b1i + e_{1it}, y2it (latent normal) = Xbetai + b2i+e_{2it}, (b1i,b2i) are bivariate normal distribution, and (e_{1it},e_{2it})are random error that also have bivariate normal distribution (correlated). (the variance parameter is (sigcon, rhoe*sigcon*sigord, sigord)). How should I specify the "rhoe" here? I attach my SAS code here.

PROC NLMIXED data=auto2 qpoints=10 tech = NMSIMP corr ecorr;
PARMS beta0=6 beta1=-3 beta2=0 alpha0=25
alpha1=-10 alpha2=-1 sigcon = 2 sigor = 3 rhob=0.3 i1 = 2 i2=2 rhoe = 0.4;
bounds i1 > 0, i2 > 0;
if variable="continuous" then do;
pi=constant("pi");
m1=alpha0+alpha1*trt+alpha2*time+z1;
LL1=((-0.5)*log(2*pi*sigcon*sigcon)-((value1-m1)**2)/
(2*sigcon*sigcon));
END;
if variable="ordinal" then do;
eta = beta0+beta1*trt+beta2*time+z2;
if (value1=1) then p = probnorm(-eta/sigor);
else if (value1=2) then
p = probnorm((i1-eta)/sigor) - probnorm(-eta/sigor);
else if (value1=3) then
p = probnorm((i1+i2-eta)/sigor) - probnorm((i1-eta)/sigor);
else p = 1 - probnorm((i1+i2-eta)/sigor);
if (p > 1e-8) then LL2 = log(p);
else LL2 = -1e20;
END;
LL=LL1+LL2;
MODEL value1 ~ GENERAL(LL);
RANDOM z1 z2 ~ NORMAL([0,0],[1,rhob,1]) SUBJECT=id;
estimate "sigma2" sigor*sigor;
ods output ParameterEstimates=pars;
ods output FitStatistics=aic;
RUN;

My question is where should I specify rhoe here? I thought it should be similar like type = "un"...

Re: How to specify AR(1) covariance structure in PROC NLMIXED

sbxkoenk — Sun, 30 Jul 2023 13:17:12 GMT

Hello,

Previous reply by @lcw68 can be neglected.

@lcw68 has rightfully opened a new post (new topic) in this board with his / her question.

See:

How to incorporate correlation between random error (epsilon) in proc nlmixed joint MMRM model?
https://communities.sas.com/t5/Statistical-Procedures/How-to-incorporate-correlation-between-random-error-epsilon-in/m-p/886937#M43875

Koen