Here's some sample data and proc mixed code that describes the model and a provisional ESTIMATE statement.
/* read in raw data for 9 batches */
data a0 ;
input Month B01 B02 B05 B06 B08 B09 B10 B12 B20 ;
datalines ;
0 103.7 103.7 103.7 100.8 101.2 100.1 99.9 102.7 101.5
3 99.4 103.1 100.9 100.8 98.1 101.3 101.6 101.7 104.7
6 102.4 102.4 102.4 93.4 99.9 100.1 95.1 99.4 100.8
9 101.0 98.9 99.7 101.2 98.2 98.4 99.5 98.7 99.9
12 100.0 101.2 99.3 96.5 92.7 92.3 98.1 98.7 97.8
18 99.2 91.7 98.7 94.3 95.7 96.1 95.9 100.1 95.1
24 95.5 96.2 94.3 93.4 94.4 92.8 96.1 94.8 95.9
;
run;
proc print data=a0 ;
title1 "Raw Data 9 Batches Page 8/22" ;
run ;
/* Create vector of responses by batch */
data a1 ; set a0 ;
array batx (9) B01 B02 B05 B06 B08 B09 B10 B12 B20 ;
array baty (9) $3 ('B01' 'B02' 'B05' 'B06' 'B08' 'B09' 'B10' 'B12' 'B20') ;
do i = 1 to 9 ;
y = batx(i) ;
batch =baty(i) ;
output;
end ;
keep batch month y;
run ;
proc print data=a1 ;
title1 "Data for analysis" ;
run;
proc mixed data=a1 nobound covtest ranks mmeq mmeqsol ;
class batch ;
model y = month / solution covb outpm = out1 alphap=0.10 solution ddfm=kr ;
random intercept / subject=batch;
estimate "A2 - Process Model 12 months Including batch component"
intercept 1 month 12 | Intercept 1
/ cl alpha=0.10 e ;
ods output mmeqsol=invmmeq coef=e;
title1 "Mixed regression model with random batch intercept only";
title2 "Batch mean and Product calculations for 0.50 OOS, 95% Coverage" ;
run;
the point estimate is correct in the estimate card. But what I want is
sqrt[Var(InterceptF + 12*Month) + Var(InterceptR)]
where Var=Variance, InterceptF is the fixed intercept estimate, Month is the fixed time covariate and InterceptR is the estimate of the random component on intercept due to Batch.
This is not really a standard error as such, it's the standard deviation of the population of batches at time 12 months. The challenge here is to get the Satterthwaite adjusted degrees of freedom for this sum of variances. Actually this is the simple case. If we add the random component due to batch on the time covariate, Month, and assume an unstructured covariance matrix, then we have the sum of 3 variances where 2 are correlated. In addition, note that Var(InterceptF + 12*Month) is not a chi-square.
