linear mixed commands for growth curve

[William Dudley WNDUDLEY]

I need some help in setting up a linear mixed model to estimate individual growth curves
 in a doubly nested model in which subjects are observed across
five  TRIALS and  within each TRIAL they are observed at several TIME points. 

Thus if I estimate quadratic model, each individual will have
5 INTERCEPTS, 5 SLOPES and 5 QUADRATIC parameters.

Second I need to export these parameters for further analyses.
Thus I need  new SPSS file with five variables,
 ID, TRIAL, INTERCEPT, SLOPE, QUAD.
 I wonder if anyone has code for this type of analysis that they would be willing to share ?


Thanks in advance.


--
William N. Dudley, PhD
Associate Dean for Research
The School of Health and Human Performance Office of Research
The University of North Carolina at Greensboro
126 HHP Building, PO Box 26170
Greensboro, NC 27402-6170
VOICE 336.2562475
FAX [phone]

[Ryan]

William,

While I'm not entirely sure I understand what you are asking, I might
be able to help get you started.

I assume that your data set is structured as follows:

ID     Trial     Time     Y
1         1          1      23
1         1          2      13
1         1          3      10
.
.
1         2          1      12
1         2          2      10
1         2          3        4
.
.
2         1          1        8
2         1          2      12
2         1          3      10
.
.
2         2          1        7
2         2          2        8
2         2          3      10
.
.
3         1          1      22
3         1          2      15
3         1          3        9
.
.
3         2          1      21
3         2          2      10
3.        2          3       6
.
.

The design I have presented above may not be entirely accurate, but
this is my best guess for the moment. Anyway, if you were to treat
"Trial" and "Time" as categorical variables, this might be one
acceptable parameterization employing the MIXED procedure.

MIXED Y BY Trial Time
  /FIXED=Trial Time Trial*Time | SSTYPE(3)
  /METHOD=REML
  /PRINT=SOLUTION
  /RANDOM= INT | SUBJECT(ID*Trial) TYPE=VC
  /REPEATED=Time | SUBJECT(ID*Trial) COVTYPE(AR1).

The RANDOM statement allows for different within-subject correlations
between trials. The REPEATED statement assumes residuals obtained from
within-subject observations close in time for trial x are more highly
correlated than residuals obtained from within-subject observations
distant in time for trial x.

Now, suppose we want to test if there is a difference in linear trends
over time between trials. If we assume there are five time points,
then we could write the following TEST statement:

  /TEST = 'Linear Trend Contrast' Trial*Time -2 -1 0 1 2 2 1 0 -1 -2

Let's say we wanted to test if the mean change from time 1 to time 2
was significantly different between trials, then the TEST statement
would be:

  /TEST = 'Difference in Mean Change Contrast' Trial*Time -1 1 0 0 0 1 -1 0 0 0

Now, you did mention that you were interested in setting up a
"Quadratic" model. You should be able to take what I've presented and
build more complex models, if that is what you desire. For instance,
if you wanted to add a quadratic effect of time on Y, then you would
treat time as a continuous variable and incorporate time^2 into the
model.

It's important to note that I have not encountered this type of model
in my own work. Also, I have not tried to test a linear trend contrast
using the TEST statement. I assume what I've written should work. Take
what I've stated with a grain of salt, and of course, please do write
back if you think I've made an error somewhere along the way.

Best,

Ryan

On Wed, Jun 30, 2010 at 2:56 PM, William Dudley <[hidden email]> wrote:

>
>
> I need some help in setting up a linear mixed model to estimate individual
> growth curves
>  in a doubly nested model in which subjects are observed across
> five  TRIALS and  within each TRIAL they are observed at several TIME
> points.
>
> Thus if I estimate quadratic model, each individual will have
> 5 INTERCEPTS, 5 SLOPES and 5 QUADRATIC parameters.
>
> Second I need to export these parameters for further analyses.
> Thus I need  new SPSS file with five variables,
>  ID, TRIAL, INTERCEPT, SLOPE, QUAD.
>  I wonder if anyone has code for this type of analysis that they would be
> willing to share ?
>
>
> Thanks in advance.
>
>
> --
> William N. Dudley, PhD
> Associate Dean for Research
> The School of Health and Human Performance Office of Research
> The University of North Carolina at Greensboro
> 126 HHP Building, PO Box 26170
> Greensboro, NC 27402-6170
> VOICE 336.2562475
> FAX [phone]
>

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