Interpreting the effect of a continuous time-varying predictor

[Nicholas-33]

Dear all,

I would like to ask a beginner's question. In a longitudinal study using
SPSS mixed (i.e., time nested within individuals) if I add a continuous
grand-mean centered time-varying predictor , would its slope represent
a)      Its average effect on the DV over time? or
b)      Its effect on the DV at baseline (assuming that time has been
centered at baseline)?



Any explanations would be greatly appreciated.


Thanks

Nicholas

[russell-19]

> it should simply reflect the relationship between the response and the
predictor variable at the mean value of the predictor. Its average
effect is a fixed effect or "intercept." This is what SPSS or any
statistical software would print. if you suspect that this average
relationship differs across time and this average value (fixed value)
differs across persons, then you can of course add a random component to
your model. For the first requirement (differs across time) you should
then form an interaction of this predictor with time and for the latter
(differs across persons), you should add a random component to the
model.

HTH,
Russell


Dear all,

>
> I would like to ask a beginner's question. In a longitudinal study using
> SPSS mixed (i.e., time nested within individuals) if I add a continuous
> grand-mean centered time-varying predictor , would its slope represent
> a)      Its average effect on the DV over time? or
> b)      Its effect on the DV at baseline (assuming that time has been
> centered at baseline)?
>
>
>
> Any explanations would be greatly appreciated.
>
>
> Thanks
>
> Nicholas
>

[westholme11]

Russell,

many thanks for your response. Time is included as a covariate in the regression equation. I've read a paper by Aber et al. (2003) in Developmental Psychology (I'll attach it in a separate e-mail) which on p. 330 states that time ("age" ) was centered at the beginning of the study (i.e., age=8.8 years). In that paper, a series of conditional models estimated the effects of demographic characteristics and two time-varying predictors on the intercept and rate of growth for each examined outcome.  The authors  state  on p. 330 that "any differences reported in intercepts should be interpreted in the subsequent figures as differences when the children were 8.8 years old". Based on this statement, I thought that the effect of my time-varying predictor should represent its effects on the DV at baseline (I have also centered time at the beginning of the study).

Any additional comments/clarifications from you or anyone else in the list would be gratefully received.

Nicholas


-----Original Message-----
From: [hidden email]
To: [hidden email]
Cc: [hidden email]
Sent: Mon, 14 May 2007 9:40 AM
Subject: Re: Interpreting the effect of a continuous time-varying predictor


> it should simply reflect the relationship between the response and the
predictor variable at the mean value of the predictor. Its average
effect is a fixed effect or "intercept." This is what SPSS or any
statistical software would print. if you suspect that this average
relationship differs across time and this average value (fixed value)
differs across persons, then you can of course add a random component to
your model. For the first requirement (differs across time) you should
then form an interaction of this predictor with time and for the latter
(differs across persons), you should add a random component to the
model.

HTH,
Russell


Dear all,

>
> I would like to ask a beginner's question. In a longitudinal study using
> SPSS mixed (i.e., time nested within individuals) if I add a continuous
> grand-mean centered time-varying predictor , would its slope represent
> a)      Its average effect on the DV over time? or
> b)      Its effect on the DV at baseline (assuming that time has been
> centered at baseline)?
>
>
>
> Any explanations would be greatly appreciated.
>
>
> Thanks
>
> Nicholas
>

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[russell-19]

>>Hi there Nicholas,
>
> Forgive me if I do not understand your problem 100% but I am going to try
> and pen a response anyway.
>
> 1) it is not the usual practice to say that time has been included as a
> covariate in a longitudinal design because time IS the fundamental
> predictor. There is no longtitudinal design without "time" however we may
> choose to express it.
>
> 2) This does not prevent researchers from including both time varying and
> time invariant predictors/covariates. The difference being that the former
> change values over the defined time metric in the study, while the latter
> stay the same over various waves.
>
> 3) If time has been centered at its mean sample value or some other
> meaningful point (in this case age), then the intercept (or the initial
> value) represents the average attainment for someone who is 8.8 years old
> etc/or the true value of Y at that particular age to paraphrase Singer and
> Willet.
>
> 4) the rate of change (or slope if you have posited a linear change model)
> represents the relationship between the outcome and time when time/age is
> 8.8 years. Of course, in the actual data file, this would reflect a  value
> for time of 0 because of the centering.
>
> 5) When you add time-varying or time invariant predictors, you would have
> to interpret their effects in each of the level 2 sub-models that you
> formulate. Let's assume that you have chosen a time-varying predictor and
> used it in both the intercept and rate of change (slope) sub-models.  It
> represents the impact of a one unit increase in the predictor on the
> intercept AND the impact of a one unit increase in the predictor on the
> rate of change/slope.
>
> 6)  if you have centered your covariate on the sample mean of that
> predictor, then the "intercepts" (the average value of Y for someone who
> is 8.8 years old and the slope) represent someone with average values on
> the covariate. So that the initial value represents someone who is 8.8
> years old and who has an average score on the covariate. Or the
> relationship between the outcome and time when time/age is 8.8 years for
> someone who has an average score on the covariate.
>
> Hope this helps,
> Russell
>
>      Russell,
>>
>> many thanks for your response. Time is included as a covariate in the
>> regression equation. I've read a paper by Aber et al. (2003) in
>> Developmental Psychology (I'll attach it in a separate e-mail) which on
>> p.
>> 330 states that time ("age" ) was centered at the beginning of the study
>> (i.e., age=8.8 years). In that paper, a series of conditional models
>> estimated the effects of demographic characteristics and two
>> time-varying
>> predictors on the intercept and rate of growth for each examined
>> outcome.
>> The authors  state  on p. 330 that "any differences reported in
>> intercepts
>> should be interpreted in the subsequent figures as differences when the
>> children were 8.8 years old". Based on this statement, I thought that
>> the
>> effect of my time-varying predictor should represent its effects on the
>> DV
>> at baseline (I have also centered time at the beginning of the study).
>>
>> Any additional comments/clarifications from you or anyone else in the
>> list
>> would be gratefully received.
>>
>> Nicholas
>>
>>
>> -----Original Message-----
>> From: [hidden email]
>> To: [hidden email]
>> Cc: [hidden email]
>> Sent: Mon, 14 May 2007 9:40 AM
>> Subject: Re: Interpreting the effect of a continuous time-varying
>> predictor
>>
>>
>>> it should simply reflect the relationship between the response and the
>> predictor variable at the mean value of the predictor. Its average
>> effect is a fixed effect or "intercept." This is what SPSS or any
>> statistical software would print. if you suspect that this average
>> relationship differs across time and this average value (fixed value)
>> differs across persons, then you can of course add a random component to
>> your model. For the first requirement (differs across time) you should
>> then form an interaction of this predictor with time and for the latter
>> (differs across persons), you should add a random component to the
>> model.
>>
>> HTH,
>> Russell
>>
>>
>> Dear all,
>>>
>>> I would like to ask a beginner's question. In a longitudinal study
>>> using
>>> SPSS mixed (i.e., time nested within individuals) if I add a continuous
>>> grand-mean centered time-varying predictor , would its slope represent
>>> a)      Its average effect on the DV over time? or
>>> b)      Its effect on the DV at baseline (assuming that time has been
>>> centered at baseline)?
>>>
>>>
>>>
>>> Any explanations would be greatly appreciated.
>>>
>>>
>>> Thanks
>>>
>>> Nicholas
>>>
>> ________________________________________________________________________
>> Check Out the new free AIM(R) Mail -- 2 GB of storage and
>> industry-leading
>> spam and email virus protection.
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>
>