PROC NLIN changing initial conditions

[linlin87]

Hi SAS community

I have data over time for ~200 participants. For each participant, I want to fit the same model, but I have a different set of initial conditions for the PROC NLIN routine (derived by looking at data for each paritcipant). How do I get this to work (code below)? Any help really appreciate. I keep get error like this:

NOTE: DER.a not initialized or missing. It will be computed automatically.
NOTE: DER.b not initialized or missing. It will be computed automatically.
NOTE: DER.c not initialized or missing. It will be computed automatically.
NOTE: DER.d not initialized or missing. It will be computed automatically.
WARNING: Zero observations could be evaluated.
NOTE: The data set WORK.PARAMS_OUT_4 has 0 observations and 9 variables.

data initial_params;
set in.initial_params;
nf+1;
call symputx("last_nf",nf);
run;

data participant_data;
set in.participant_data;
run;

%macro fit;
%do j=1 %to &last_nf.;

data _null_; 
 	set initial_params;
 	where nf=&j;
 	call symputx("beta10",beta10);
	call symputx("beta20",beta20);
	call symputx("beta30",beta30);
    call symputx("beta40".beta40);
	call symputx("participant",subject); 
run;
proc nlin data = participant_data g4 plots = fit maxiter = 50 outest = params_out_&j.;
where subject="&participant";
parameters a = &beta10. &beta20. = -3 c = &beta30. d = &beta40.;
model response = a*exp(time/b) + c*time + d;
run;

%end;

%mend;

%fit;

suggesting what I do wrong would be very helpful to me!

[FreelanceReinh · Accepted solution]

Hi @linlin87,

First of all, I see two syntax errors in your code which would prevent the PROC NLIN step from even producing the messages you show:

1. The period between "beta40" and beta40 in the fourth CALL SYMPUTX of the DATA _NULL_ step must be a comma.
2. Instead of &beta20. = -3 in the PARAMETERS statement I would rather expect something like b = &beta20. (or does macro variable BETA20 contain a variable name such as b?).

One situation in which the warning "Zero observations could be evaluated" would occur is that the WHERE condition subject="&participant" is not met for any observation of dataset PARTICIPANT_DATA. So, make sure that those character values match exactly.

But most importantly, I think you could both simplify your program and make it more robust if you used a single PROC NLIN step with a BY statement (by subject) instead of the macro, macro variables and the WHERE condition. Then you could name the dataset containing the subject-specific initial parameter values in the PDATA= option of the PARAMETERS statement. See the syntax and section "Assigning Starting Values from a SAS Data Set" in the PROC NLIN documentation.

Edit: Below is an example of what your PROC NLIN step could look like. Note the structure of the PDATA= dataset (which I named init_params).

/* Create test data for demonstration */

data temp;
input subject a b c d;
cards;
1  8 2 0.2  1
2  7 1 0.3 -1
;

proc transpose data=temp out=init_params(rename=(col1=estimate)) name=parameter;
by subject;
run;

data participant_data(drop=a--d);
set temp;
do time=1 to 5;
  response=a*exp(time/b) + c*time + d + rannor(1);
  output;
end;
run;

/* Use BY-group processing and the PDATA= option in PROC NLIN */

proc nlin data = participant_data g4 plots = fit maxiter = 50 outest = params_out;
by subject;
parameters / pdata=init_params;
model response = a*exp(time/b) + c*time + d;
run;

[linlin87]

Thank you @FreelanceReinh !!

One more questions for you. Now I have this

proc nlin data = participant_data g4 plots = fit maxiter = 50 outest = params_out;
by subject;
parameters / pdata=init_params;
model response = a*exp(time/b) + c*time + d;
run;

but actually I need that a+d = value. So:

proc nlin data = participant_data g4 plots = fit maxiter = 50 outest = params_out;
by subject;
parameters / pdata=init_params;
bounds d+a = value;
model response = a*exp(time/b) + c*time + d;
run;

Note that value is different for each SUBJECT. How do I do?

[FreelanceReinh]

You're welcome.

I think the BOUNDS statement is more suitable for constraints in the form of inequalities about the parameters. Given that all these numbers are non-integers, an exact equality such as d+a=value would be a risky requirement anyway. (Note that, e.g., 0.1+0.2 ne 0.3 in Windows SAS due to rounding errors in the binary system.) Also, the BOUNDS statement, unlike the PARAMETERS statement, does not allow for varying values coming from a dataset. There is a different procedure, PROC HPNLMOD, which offers a RESTRICT statement where you could specify your linear constraint. But I have never used PROC HPNLMOD before today, so let's stay with PROC NLIN.

In PROC NLIN it's probably better to implement the constraint d+a=value in the model equation. You have two options for that: Either replace d with value-a, or replace a with value-d. Let's follow the first approach, i.e., eliminate parameter d in the model equation and introduce value as a new variable (not parameter) in the input dataset participant_data.

Here is the example from my earlier post, with the new constraint implemented. Changes are highlighted in blue.

/* Create test data for demonstration */

data temp;
input subject a b c value; /* parameter d has been eliminated by the constraint d+a=value */
cards;
1  8 2 0.2 9
2  7 1 0.3 6
;

proc transpose data=temp(drop=value) out=init_params(rename=(col1=estimate)) name=parameter;
by subject;
run;

data participant_data(drop=a--c);
set temp;
do time=1 to 5;
  response=a*exp(time/b) + c*time + value - a + rannor(1);
  output;
end;
run;

/* Use BY-group processing and the PDATA= option in PROC NLIN */

proc nlin data = participant_data g4 plots = fit maxiter = 50 outest = params_out;
by subject;
parameters / pdata=init_params;
model response = a*exp(time/b) + c*time + value - a;
run;

As you can see in dataset participant_data, variable value is a subject-dependent constant over time. Parameters a, b, c are estimated, starting with (unchanged) subject-specific initial values from dataset init_params, as before. For each subject, you could use the estimate for parameter a computed by PROC NLIN and the known value of variable value to compute d = value - a, if needed:

data est(drop=_:);
set params_out;
where _type_='FINAL';
run;

data values;
set participant_data(keep=subject value);
by subject;
if first.subject;
run;

data want;
merge values est;
by subject;
d=value-a;
run;

Obviously, the estimates will satisfy the constraint a+d = value, possibly up to tiny rounding differences like 1E-16 as in this example:

138   data _null_;
139   d=0.9-0.3;
140   if 0.3+d ne 0.9 then put 'Surprised?';
141   delta=0.3+d-0.9;
142   put delta=;
143   run;

Surprised?
delta=1.110223E-16