Section 5: Statements for SAS and SPSS MIXED Models


A. Commands with SAS PROC MIXED

The examples which follow in subsequent sections demonstrate how the most 
commonly applied statements from PROC MIXED resemble and how they are 
different from statements from PROC GLM.

In THE PROC MIXED list of keywords, notice that the frequently invoked 
statements (defined by the initial keywords in capital letters) have 
several of the same keywords found with PROC GLM; however, there are 
subtle to major differences to be aware of.

PROC MIXED <options>;
WHERE ( <variable> eq <condition>);
BY <variables>;
CLASS <classification variables> <subject id> ;
MODEL dep_var = <fixed effects and their interactions>
                <continuous covariates and interactions> / <options>;
REPEATED <var> / < options >;
RANDOM <random effects> / < options >;
LSMEANS <fixed effects listed on MODEL statement> / <options>;
ESTIMATE 'description' <fixed effects> | <random est> / <options>;
CONTRAST 'description' <difference among 1 or more fixed effects>;
RUN;

Very brief descriptions of important points to note for a few of these 
statements are listed below. More details for their functions will be 
presented in subsequent sections.

PROC MIXED <options>

Invokes the procedure and allows entry of several data processing options.

CLASS <classification factors > 

Print classification factors and subject id variable names.


MODEL dep_var = cls1 cls2 x1 x2 / solution ddfm=bw ;

The variables cls1 and cls2 must appear in the CLASS statement; x1 x2 
represent numerical covariates

solution : prints a solution to the output
    ddfm : selects one of several degree of freedom calculation options.


REPEATED time / SUBJECT=id TYPE=cs rcorr;

The ID variable should always appear on the CLASS statement. If it does 
not, then you can get peculiar results.  Here is what the SAS 
documentation states:

  "Continuous variables are permitted as arguments to the SUBJECT=option.
   PROC MIXED does not sort by the values of the continuous variable; 
rather,
   it considers the data to be from a new subject or group whenever the 
value
   of the continuous variable changes from the previous observation. Using 
a
   continuous variable decreases execution time for models with a large 
number
   of subjects or groups and also prevents the production of a large 
'Class
   Levels Information' table."

Different results may be obtained for different sort orders. To get 
correct results, sort by the subject ID and repeated variable (time) 
first. Note that the repeated variable factor time is not required on the 
REPEATED statement if the data are sorted; however, it is a good idea to 
enter it to remind yourself of its function.

The rcorr option prints the within-subject correlation matrix of the type 
specified with TYPE= to the output.


Some of these statements perform the same or very similar functions as 
statements with the same keywords in PROC GLM; however, very important 
differences are observed with the REPEATED and RANDOM statements. Another 
advantage of the MIXED model over GLM is the functionality of the LSMEANS 
(or EMMEANS in SPSS) statements, especially when computing differences 
between means. The difference can be the most appreciated when combined 
with the flexibility of the Output Delivery System (see Section 11).


B. Placement of Fixed and Random Effects

Details showing how to enter fixed and random effects appear in later 
sections. However, a brief introduction is given here since the MODEL (for 
fixed effects) and the RANDOM (for random effects) statements are 
structured quite differently than found with GLM.

A very simple example describes how to structure statements to analyze a 
fixed and/or random effects ANOVA. A two-way design with factors A and B 
is presented under two scenarios:   

1) Factors A, B, and their interaction A*B are all both fixed 

PROC MIXED METHOD=type3;
CLASS a b;
MODEL y = a b a*b;
RUN;

2) Factor A is fixed; Factors B and A*B are random

PROC MIXED method=type3;
CLASS a b;
MODEL y = a;
RANDOM b a*b; * this form of the RANDOM statement is identical to PROC 
GLM;
RUN;

In both scenarios the ANOVA results will be the same as produced by GLM.  
Both factors A and B, whether fixed or random, must appear in the CLASS 
statement; however, unlike PROC GLM, the random effects in PROC MIXED are 
placed only in the RANDOM statement.

Note that in most situations a model with one factor treated as fixed (A) 
and the other factor treated as random (B) should also have their 
interaction defined as random (A*B).





C. Basic command lines for Mixed Models with SPSS include:

MIXED
  y BY <fixed_effects> WITH <covariates>
  / FIXED = <main effects and interactions>  | SSTYPE(3)
  / METHOD = REML
  / PRINT = R SOLUTION
  / REPEATED = time | SUBJECT(id) COVTYPE(cs)
  / EMMEANS = TABLES(<effect>) COMPARE ADJ(LSD)  .


The structure of these statements and how they work together appear in 
subsequent sections of this extended article.