studying different rates of deceleration

[Zdaniuk, Bozena-3]

What would be the best way to study different rates of deceleration? For example, group A has means for five repeated measurements: 20, 12, 8, 6, 5
And group B has means: 24, 20, 18, 17, 16
Both groups show a decelerated curve but group A decelerates at greater rate than group B.
Would computing Area Under Curve capture this difference?
Thanks so much for any suggestions.
Bozena

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[Maguin, Eugene]

How about fitting a regression with a quadractic term plus a group*quadractic term along with the usual group and linear trend terms?
Gene Maguin

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Zdaniuk, Bozena
Sent: Wednesday, January 22, 2014 5:58 PM
To: [hidden email]
Subject: studying different rates of deceleration

What would be the best way to study different rates of deceleration? For example, group A has means for five repeated measurements: 20, 12, 8, 6, 5 And group B has means: 24, 20, 18, 17, 16 Both groups show a decelerated curve but group A decelerates at greater rate than group B.
Would computing Area Under Curve capture this difference?
Thanks so much for any suggestions.
Bozena

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[Richard Ristow]

At 05:58 PM 1/22/2014, Zdaniuk, Bozena wrote:

>What would be the best way to study different rates of deceleration?
>For example, group A has means for five repeated measurements: 20, 12, 8, 6, 5
>And group B has means: 24, 20, 18, 17, 16
>Both groups show a decelerated curve but group A decelerates at
>greater rate than group B.

At 09:09 AM 1/23/2014, Maguin, Eugene wrote:

>How about fitting a regression with a quadratic term plus a
>group*quadratic term along with the usual group and linear trend terms?

An excellent approach: summarize each time series as three values:
. Mean
. Linear rate of change
. Quadratic rate of change.

For this, you need an independent variable, time, across the repeated
measurements. I'm guessing the measurements are equally spaced in
time, so it's natural to use 1, 2, 3, 4 and 5 as the time values for
the five points.

I'd recommend, instead, centering the time variable; that is using
values -2, -1, 0, 1 and 2. That will dramatically reduce the
covariance of the linear and quadratic trend terms, and give you
cleaner estimates.

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[Rich Ulrich]

You do get your best test when you use an
appropriate model, so including a quadratic
term is certainly appropriate if these numbers
are locations.

Taking the use of a model just one step further:
If you *know* that you are measuring deceleration,
it could be proper to omit the linear term and
use a contrast with a declining quadratic for time,
like (16, 8, 4, 2, 1).  You would include Group
as a nuisance parameter and test Group*QuadTime .l

--
Rich Ulrich

----------------------------------------

> Date: Sat, 25 Jan 2014 11:52:34 -0500
> From: [hidden email]
> Subject: Re: studying different rates of deceleration
> To: [hidden email]
>
> At 05:58 PM 1/22/2014, Zdaniuk, Bozena wrote:
>
>>What would be the best way to study different rates of deceleration?
>>For example, group A has means for five repeated measurements: 20, 12, 8, 6, 5
>>And group B has means: 24, 20, 18, 17, 16
>>Both groups show a decelerated curve but group A decelerates at
>>greater rate than group B.
>
> At 09:09 AM 1/23/2014, Maguin, Eugene wrote:
>
>>How about fitting a regression with a quadratic term plus a
>>group*quadratic term along with the usual group and linear trend terms?
>
> An excellent approach: summarize each time series as three values:
> . Mean
> . Linear rate of change
> . Quadratic rate of change.
>
> For this, you need an independent variable, time, across the repeated
> measurements. I'm guessing the measurements are equally spaced in
> time, so it's natural to use 1, 2, 3, 4 and 5 as the time values for
> the five points.
>
> I'd recommend, instead, centering the time variable; that is using
> values -2, -1, 0, 1 and 2. That will dramatically reduce the
> covariance of the linear and quadratic trend terms, and give you
> cleaner estimates.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

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[Ryan]

Assuming you have repeated measurements on each subject, you ought to take residual correlation into account within your model. 

Ryan

On Wed, Jan 22, 2014 at 5:58 PM, Zdaniuk, Bozena <[hidden email]> wrote:

What would be the best way to study different rates of deceleration? For example, group A has means for five repeated measurements: 20, 12, 8, 6, 5
And group B has means: 24, 20, 18, 17, 16
Both groups show a decelerated curve but group A decelerates at greater rate than group B.
Would computing Area Under Curve capture this difference?
Thanks so much for any suggestions.
Bozena

=====================
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