The script simulates academic performance data ('grade') for students ('student') grouped by class ('class') within schools ('school'). A program effect ('program') is also simulated. The GLIMMIX procedure is then used to fit a generalized mixed model with a binomial distribution and a logit link function, incorporating random effects for school and class nested within school. The script presents two similar runs, the second one fitting the model with a slight variation in data generation and the addition of the `fastquad` option.
Data Analysis
Type : INTERNAL_CREATION
The 'test' data is entirely created within the script using DATA steps, simulating a hierarchical structure (students in classes in schools) and random effects.
1 Code Block
DATA STEP Data
Explanation : This DATA step block generates a dataset named 'test'. It simulates a hierarchical structure with 10 schools, 5 classes per school, and 10 students per class. Random effects 'schef' (school) and 'clsef' (class) are added. A binary 'program' variable is generated. The 'grade' variable is simulated according to a binomial distribution, depending on a probability 'p' calculated from a linear combination of fixed and random effects.
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data test;
do school = 1 to 10;
schef = rannor(1234)*4;
do class = 1 to 5;
clsef = rannor(2345)*2;
program = ranbin(12345,1,.5);
do student = 1 to 10;
eta = 3 + program + schef + clsef ;
p = 1/(1+exp(-eta));
grade = ranbin(23456,1,p);
output;
end;
end;
end;
run;
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DATA test;
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DO school = 1 to 10;
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schef = rannor(1234)*4;
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DO class = 1 to 5;
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clsef = rannor(2345)*2;
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program = ranbin(12345,1,.5);
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DO student = 1 to 10;
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eta = 3 + program + schef + clsef ;
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p = 1/(1+exp(-eta));
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grade = ranbin(23456,1,p);
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OUTPUT;
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END;
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END;
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END;
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RUN;
2 Code Block
PROC GLIMMIX
Explanation : This GLIMMIX procedure fits a generalized mixed model to the 'test' data. The quadrature method (quad(qpoints=3)) is used. The variables 'school', 'class', and 'program' are declared as classification variables. The model specifies 'grade' as the dependent variable, 'program' as a fixed effect, with a binomial distribution and a logit link. Random effects ('random int') are included for 'school' and 'class' nested within 'school'.
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proc glimmix data=test method = quad(qpoints=3);
class school class program;
model grade = program/s dist=binomial link=logit solution;
random int /subject = school;
random int /subject = class(school);
run;
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PROC GLIMMIXDATA=test method = quad(qpoints=3);
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class school class program;
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model grade = program/s dist=binomial link=logit solution;
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random int /subject = school;
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random int /subject = class(school);
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RUN;
3 Code Block
DATA STEP Data
Explanation : This second DATA step block is similar to the first but generates data with 10 classes per school (instead of 5). It again simulates a hierarchical structure with random effects and the 'grade' variable following the same principles as the first block.
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data test;
do school = 1 to 10;
schef = rannor(1234)*4;
do class = 1 to 10;
clsef = rannor(2345)*2;
program = ranbin(12345,1,.5);
do student = 1 to 10;
eta = 3 + program + schef + clsef ;
p = 1/(1+exp(-eta));
grade = ranbin(23456,1,p);
output;
end;
end;
end;
run;
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DATA test;
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DO school = 1 to 10;
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schef = rannor(1234)*4;
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DO class = 1 to 10;
5
clsef = rannor(2345)*2;
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program = ranbin(12345,1,.5);
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DO student = 1 to 10;
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eta = 3 + program + schef + clsef ;
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p = 1/(1+exp(-eta));
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grade = ranbin(23456,1,p);
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OUTPUT;
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END;
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END;
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END;
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RUN;
4 Code Block
PROC GLIMMIX
Explanation : This second GLIMMIX procedure fits a model identical to the first, but on the newly generated 'test' data. The 'fastquad' option is added to the quadrature method, which can potentially speed up calculation by using a different approximation for the integrals.
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proc glimmix data=test method = quad(qpoints=3 fastquad);
class school class program;
model grade = program/s dist=binomial link=logit solution;
random int /subject = school;
random int /subject = class(school);
run;
model grade = program/s dist=binomial link=logit solution;
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random int /subject = school;
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random int /subject = class(school);
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RUN;
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