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## A question about 'Example 56.2 Repeated Measures' using proc mixed

Example 56.2 uses proc mixed to examine growth measurements for girls and boys at ages 8, 10, 12 and 14. The proposed syntax is:

```data pr;
input Person Gender \$ y1 y2 y3 y4;
y=y1; Age=8;  output;
y=y2; Age=10; output;
y=y3; Age=12; output;
y=y4; Age=14; output;
drop y1-y4;
datalines;
1   F   21.0    20.0    21.5    23.0
2   F   21.0    21.5    24.0    25.5
3   F   20.5    24.0    24.5    26.0
4   F   23.5    24.5    25.0    26.5
5   F   21.5    23.0    22.5    23.5
6   F   20.0    21.0    21.0    22.5
7   F   21.5    22.5    23.0    25.0
8   F   23.0    23.0    23.5    24.0
9   F   20.0    21.0    22.0    21.5
10   F   16.5    19.0    19.0    19.5
11   F   24.5    25.0    28.0    28.0
12   M   26.0    25.0    29.0    31.0
13   M   21.5    22.5    23.0    26.5
14   M   23.0    22.5    24.0    27.5
15   M   25.5    27.5    26.5    27.0
16   M   20.0    23.5    22.5    26.0
17   M   24.5    25.5    27.0    28.5
18   M   22.0    22.0    24.5    26.5
19   M   24.0    21.5    24.5    25.5
20   M   23.0    20.5    31.0    26.0
21   M   27.5    28.0    31.0    31.5
22   M   23.0    23.0    23.5    25.0
23   M   21.5    23.5    24.0    28.0
24   M   17.0    24.5    26.0    29.5
25   M   22.5    25.5    25.5    26.0
26   M   23.0    24.5    26.0    30.0
27   M   22.0    21.5    23.5    25.0
;```

```   proc mixed data=pr method=ml covtest;
class Person Gender;
model y = Gender Age Gender*Age / s;
repeated / type=un subject=Person r;
run;```

With regards to the 'Solution for Fixed Effects' (see below), the authors conclude that "The girls' starting point is larger than that for the boys, but their growth rate is about half of the boys".

Output 56.2.8 Repeated Measures Analysis (continued)
Solution for Fixed Effects Effect Gender Estimate Standard Error DF t Value Pr > |t| Intercept   Gender F Gender M Age   Age*Gender F Age*Gender M
 15.8423 0.9356 25 16.93 <.0001 1.5831 1.4658 25 1.08 0.2904 0 . . . . 0.8268 0.07911 25 10.45 <.0001 -0.3504 0.1239 25 -2.83 0.0091 0 . . . .

So my question is why age was not included in the class statement?

A proc means analysis for age=8 shows that the value for boys is larger than that for girls. Also below is the solution for fixed effects when age(ref=first) is added to the class statement. Wouldn't this better reflect the data?

Analysis Variable : y Gender N Obs N Mean Std Dev Minimum Maximum F 11 M 16
 11 21.1818 2.12453 16.5 24.5 16 22.875 2.45289 17 27.5

Solution for Fixed Effects Effect Gender Age Estimate Standard
Error DF t Value Pr > |t| Intercept     Gender F   Gender M   Age   10 Age   12 Age   14 Age   8 Gender*Age F 10 Gender*Age F 12 Gender*Age F 14 Gender*Age F 8 Gender*Age M 10 Gender*Age M 12 Gender*Age M 14 Gender*Age M 8
 22.875 0.5598 25 40.86 <.0001 -1.6932 0.8771 25 -1.93 0.0650 0 . . . . 0.9375 0.4910 25 1.91 0.0678 2.8438 0.4842 25 5.87 <.0001 4.5938 0.5369 25 8.56 <.0001 0 . . . . 0.108 0.7693 25 0.14 0.8895 -0.9347 0.7585 25 -1.23 0.2293 -1.6847 0.8411 25 -2.00 0.0561 0 . . . . 0 . . . . 0 . . . . 0 . . . . 0 . . . .
2 REPLIES 2
SAS Super FREQ

## Re: A question about 'Example 56.2 Repeated Measures' using proc mixed

Age is a continuous variable, so the model treated it as such. The authors want one parameter to indicate the dependence on age.

If the subjects were classifed as "Children", "Teenagers", and "Adults", then the variable would be treated as a classification effect. There would be three parameters (two independent parameters) in that model.

## Re: A question about 'Example 56.2 Repeated Measures' using proc mixed

If you want to account for possible nonlinearity of response due to age, you could change the code slightly (including age as a class effect) to get:

``````proc mixed data=pr method=ml covtest;
class Person Gender Age;
model y = Gender Age Gender*Age / s;
repeated  Age/ type=un subject=Person r;
run;``````

Note that this will "use up" some degrees of freedom, so that standard errors may be larger and tests somewhat different.  There are many ways to proceed at this point, especially if you wished to make comparisons of expected values at various ages.

Steve Denham

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