Interpretation of interaction with time-varying predictor (Growth model)

[Oliver]

 
Hi everyone,

I have a question regarding the interpretation of an interaction effect
involving time-varying (i.e., Level 1) variables in a growth model. In this
study, participants (n = 1000) provided ratings of pain (Outcome: 0-10) and
depressive symptoms (Dep: 0-10) across 5 time points (i.e., baseline, 3m,
6m, 9m, 12m).  Results indicated a significant (linear) effect of time (B =
-.49, p = .000), indicating that pain decreased linearly over time. There
was also a significant main effect of depression on pain (B = .23) as well
as a significant (Time * Dep) interaction (*B = .05,* p = .000). The syntax
is copied below.

I am a bit uncertain about the interpretation of the interaction effect. The
variables are not centered (uncentered). By examining the beta coefficient
of the interaction, would results suggest that the effect of time on the
outcome (i.e., linear decrease in pain over time) is more pronounced among
those who have higher depressive (Dep) symptoms ?

MIXED Pain WITH Time Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time Dep Time*Dep | SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1).

Thanks in advance for your assistance.
O.



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[Rich Ulrich]

I have problems with the statistical design, particularly because

I've been involved with studies of Depression.  And it seems that

your Pain may have this same feature:  It is HIGH at start, and

decreases rapidly to Time 2, after which it stays the same or

decreases a bit more.

For my analyses, I looked at Time 1 vs. 2, then 2-5, in order to

separate the huge changes from the lesser ones.  If you have that

sort of time profile, I recommend doing the same.  It reduces the

complications of interpretation.

I don't know how your Depression is measured, but I know that

many Dep scales do have a somatic component -- like, severe pain

will interfere with ability to sleep, and bad sleep can count towards

Depression.  (Somatic "depression" items were horrible, but not

the "sadness" ones, on a tuberculosis ward in the 1960s.)

--

Rich Ulrich

---

From: SPSSX(r) Discussion <[hidden email]> on behalf of Oliver <[hidden email]>
Sent: Monday, March 15, 2021 2:40 PM
To: [hidden email] <[hidden email]>
Subject: Interpretation of interaction with time-varying predictor (Growth model)

 

Hi everyone,

I have a question regarding the interpretation of an interaction effect
involving time-varying (i.e., Level 1) variables in a growth model. In this
study, participants (n = 1000) provided ratings of pain (Outcome: 0-10) and
depressive symptoms (Dep: 0-10) across 5 time points (i.e., baseline, 3m,
6m, 9m, 12m).  Results indicated a significant (linear) effect of time (B =
-.49, p = .000), indicating that pain decreased linearly over time. There
was also a significant main effect of depression on pain (B = .23) as well
as a significant (Time * Dep) interaction (*B = .05,* p = .000). The syntax
is copied below.

I am a bit uncertain about the interpretation of the interaction effect. The
variables are not centered (uncentered). By examining the beta coefficient
of the interaction, would results suggest that the effect of time on the
outcome (i.e., linear decrease in pain over time) is more pronounced among
those who have higher depressive (Dep) symptoms ?

MIXED Pain WITH Time Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time Dep Time*Dep | SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1).

Thanks in advance for your assistance.
O.



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[Bruce Weaver]

The original model...

MIXED Pain WITH Time Dep (etc.)

... treated Time as a quantitative variable and included the linear term
only.  In other words, the fitted values are forced to fall on a straight
line.  What Rich has suggested below is that a straight line probably
doesn't provide the best fit.  Given the large sample size, and the
relatively small number of time points, I think you can afford to treat Time
as categorical (BY Time rather than (WITH Time) and include contrasts of
interest.  IIRC, MIXED has no /CONTRAST sub-command, so you'll likely have
to use /TEST to and generate the codes for the contrasts you want.  Helmert
contrasts (each level vs the mean of all subsequent levels) might make
sense, given Rich's expectation, and would have the virtue of being
orthogonal.  Repeated (aka., adjacent) contrasts (1v2, 2v3, 3v4, 4v5) would
be another option, but they are not orthogonal.  

HTH.





Rich Ulrich wrote

> I have problems with the statistical design, particularly because
> I've been involved with studies of Depression.  And it seems that
> your Pain may have this same feature:  It is HIGH at start, and
> decreases rapidly to Time 2, after which it stays the same or
> decreases a bit more.
>
> For my analyses, I looked at Time 1 vs. 2, then 2-5, in order to
> separate the huge changes from the lesser ones.  If you have that
> sort of time profile, I recommend doing the same.  It reduces the
> complications of interpretation.
>
> I don't know how your Depression is measured, but I know that
> many Dep scales do have a somatic component -- like, severe pain
> will interfere with ability to sleep, and bad sleep can count towards
> Depression.  (Somatic "depression" items were horrible, but not
> the "sadness" ones, on a tuberculosis ward in the 1960s.)
>
> --
> Rich Ulrich
> ________________________________
> From: SPSSX(r) Discussion &lt;

> SPSSX-L@.UGA

> &gt; on behalf of Oliver &lt;

> momartel.bwh.harvard@

> &gt;
> Sent: Monday, March 15, 2021 2:40 PM
> To:

> SPSSX-L@.UGA

>  &lt;

> SPSSX-L@.UGA

> &gt;
> Subject: Interpretation of interaction with time-varying predictor (Growth
> model)
>
>
> Hi everyone,
>
> I have a question regarding the interpretation of an interaction effect
> involving time-varying (i.e., Level 1) variables in a growth model. In
> this
> study, participants (n = 1000) provided ratings of pain (Outcome: 0-10)
> and
> depressive symptoms (Dep: 0-10) across 5 time points (i.e., baseline, 3m,
> 6m, 9m, 12m).  Results indicated a significant (linear) effect of time (B
> =
> -.49, p = .000), indicating that pain decreased linearly over time. There
> was also a significant main effect of depression on pain (B = .23) as well
> as a significant (Time * Dep) interaction (*B = .05,* p = .000). The
> syntax
> is copied below.
>
> I am a bit uncertain about the interpretation of the interaction effect.
> The
> variables are not centered (uncentered). By examining the beta coefficient
> of the interaction, would results suggest that the effect of time on the
> outcome (i.e., linear decrease in pain over time) is more pronounced among
> those who have higher depressive (Dep) symptoms ?
>
> MIXED Pain WITH Time Dep
> /METHOD = REML
> /PRINT = SOLUTION TESTCOV
> /FIXED = Time Dep Time*Dep | SSTYP(3)
> /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
> /REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1).
>
> Thanks in advance for your assistance.
> O.
>
>
>
> --
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>
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-----
--
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[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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[Oliver]

Rich & Bruce,

Thanks for your very useful input. This is much appreciated !

As suggested, I've coded "Time" as a categorical variable using "BY", and
results revealed a significant main effect of Time (p = .000). I've then
used the /TEST subcommand to perform planned contrasts to help data
interpretation of the "Time" effect on pain. Assuming that I did it
correclty, I conducted the Helmert contrast, as suggested by Bruce (i.e.,
comparing pain at each time point versus the mean of all other subsequent
time points.

MIXED Pain BY Time
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED =
Time
| SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)
/EMMEANS = TABLES(Time)
/TEST = "Planned contrasts of TimeBaseline versus subsequent" time  1 -1/4
-1/4 -1/4 -1/4
/TEST = "Planned contrasts of 3m versus subsequent" time  0 1 -1/3 -1/3 -1/3
/TEST = "Planned contrasts of 6m versus subsequent" time  0 0 1 -1/2 -1/2
/TEST = "Planned contrasts of 9m versus subsequent" time  0 0 0 1 -1


*At this point what I'm wondering is how to interpret the Time * Depression
(Dep) interaction effect. When coding "Time" as categorical, the
interaction effect (i.e., Time * Dep) is significant. But I don't know how
to use planned contrasts to probe the interaction effect. For instance, it
is possible that depression scores (continuous: 0-10) influenced pain
(continous: 0-10) but only between the baseline and the 3 month follow-up
time point. I read on the UCLA website that "*interaction contrasts*" could
be used
(https://stats.idre.ucla.edu/spss/faq/how-can-i-test-contrasts-and-interaction-contrasts-in-a-mixed-model/),
but for some reason I can't figure out how to apply the coding to my Time *
Dep interaction.

MIXED Pain BY Time WITH Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time Dep Time * Dep
| SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)

By any chance, does someone here know how to perform the "interaction
contrasts" ? Any assistance would be tremendously appreciated, as usual.
O.






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[Zdaniuk, Bozena-3]

Hi Oliver,
When you use time as categorical var, you should get the estimates of the interaction between depression and each time point compared to the reference time point. So, if you have four points, you should get three estimates of interaction. Those estimates tell you the nature and significance of the interaction (which time point interacts significantly with depression comparing to the ref time point). So if the estimate of T2 x Depr is significant you know that the difference between t2 and t1 depends on the values of depression (assuming t1 is your ref point) and that coefficient tells you about the direction of that interaction and its magnitude - all you need to know to interpret the interaction.
Cheers,
Bozena

-----Original Message-----
From: SPSSX(r) Discussion <[hidden email]> On Behalf Of Oliver
Sent: March 16, 2021 11:28 AM
To: [hidden email]
Subject: Re: Interpretation of interaction with time-varying predictor (Growth model)

[CAUTION: Non-UBC Email]

Rich & Bruce,

Thanks for your very useful input. This is much appreciated !

As suggested, I've coded "Time" as a categorical variable using "BY", and results revealed a significant main effect of Time (p = .000). I've then used the /TEST subcommand to perform planned contrasts to help data interpretation of the "Time" effect on pain. Assuming that I did it correclty, I conducted the Helmert contrast, as suggested by Bruce (i.e., comparing pain at each time point versus the mean of all other subsequent time points.

MIXED Pain BY Time
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED =
Time
| SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) /REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1) /EMMEANS = TABLES(Time) /TEST = "Planned contrasts of TimeBaseline versus subsequent" time  1 -1/4
-1/4 -1/4 -1/4
/TEST = "Planned contrasts of 3m versus subsequent" time  0 1 -1/3 -1/3 -1/3 /TEST = "Planned contrasts of 6m versus subsequent" time  0 0 1 -1/2 -1/2 /TEST = "Planned contrasts of 9m versus subsequent" time  0 0 0 1 -1


*At this point what I'm wondering is how to interpret the Time * Depression
(Dep) interaction effect. When coding "Time" as categorical, the
interaction effect (i.e., Time * Dep) is significant. But I don't know how
to use planned contrasts to probe the interaction effect. For instance, it
is possible that depression scores (continuous: 0-10) influenced pain
(continous: 0-10) but only between the baseline and the 3 month follow-up
time point. I read on the UCLA website that "*interaction contrasts*" could
be used
(https://stats.idre.ucla.edu/spss/faq/how-can-i-test-contrasts-and-interaction-contrasts-in-a-mixed-model/),
but for some reason I can't figure out how to apply the coding to my Time *
Dep interaction.

MIXED Pain BY Time WITH Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time Dep Time * Dep
| SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)

By any chance, does someone here know how to perform the "interaction
contrasts" ? Any assistance would be tremendously appreciated, as usual.
O.






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[Oliver]

Bozena,

Thanks for your input. I agree with you that the "estimates of fixed
effects" box from the SPSS output file will generate interaction terms with
p-values across all levels, but the problem is the "Reference category" that
SPSS uses by default. My understanding is that SPSS uses the highest
category as the reference, which may not be enough and relevant. In my
output, I see that the interaction is significant when comparing Time1
versus Time4, but I'm particularly interesting in examining what happens
with the interaction when Time0 (baseline) is used as the reference
category.

Is there any way to change the reference category ? This way, it would solve
the problem and perhaps avoid the need to rely on planned interaction
contrasts.

Thanks again everyone.
O.

<http://spssx-discussion.1045642.n5.nabble.com/file/t340718/Interaction%3B_output.jpg>



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[Zdaniuk, Bozena-3]

Hi Oliver,
You can just recode your time points so that time 0 has the highest numerical value, e.g., time 0 has a value of 4, time 1 =3, time 2=2 , time 3=1 and time 4=0.
You just have to remember to take the intercept from the first model before recoding the time if you report it.
Cheers
b

-----Original Message-----
From: SPSSX(r) Discussion <[hidden email]> On Behalf Of Oliver
Sent: March 16, 2021 1:11 PM
To: [hidden email]
Subject: Re: Interpretation of interaction with time-varying predictor (Growth model)

[CAUTION: Non-UBC Email]

Bozena,

Thanks for your input. I agree with you that the "estimates of fixed effects" box from the SPSS output file will generate interaction terms with p-values across all levels, but the problem is the "Reference category" that SPSS uses by default. My understanding is that SPSS uses the highest category as the reference, which may not be enough and relevant. In my output, I see that the interaction is significant when comparing Time1 versus Time4, but I'm particularly interesting in examining what happens with the interaction when Time0 (baseline) is used as the reference category.

Is there any way to change the reference category ? This way, it would solve the problem and perhaps avoid the need to rely on planned interaction contrasts.

Thanks again everyone.
O.

<http://spssx-discussion.1045642.n5.nabble.com/file/t340718/Interaction%3B_output.jpg>



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[Bruce Weaver]

This example is from the MIXED - EMMEANS documentation:

MIXED Y BY A B WITH X
  /FIXED A B X
  /EMMEANS TABLES(A*B) WITH(X=0.23) COMPARE(A) ADJ(SIDAK)
  /EMMEANS TABLES(A*B) WITH(X=MEAN) COMPARE(A) REFCAT(LAST) ADJ(LSD).

Notice the use of WITH(X=Value) to examine the A*B interaction with X set to
some desired value.  In your model, Time is the lone categorical variable,
so the EMMEANS sub-commands will look more like this:

  /EMMEANS TABLES(Time) WITH(Dep=a) COMPARE(Time) ADJ(SIDAK)
  /EMMEANS TABLES(Time) WITH(Dep=b) COMPARE(Time) ADJ(SIDAK)
  /EMMEANS TABLES(Time) WITH(Dep=c) COMPARE(Time) ADJ(SIDAK)

Replace a, b and c with low, medium and high values of Dep to inspect the
simple effects of Time at those values of Dep.  And if you want to look at
more than 3 values of Dep, go ahead.  

I'm not convinced that the COMPARE(TIME) part of those lines is needed,
given that you have Time as the only categorical variable.  You could try
with and without to see which one works, or whether they give the same
results if both work.  

HTH.  



Oliver wrote

> Rich & Bruce,
>
> Thanks for your very useful input. This is much appreciated !
>
> As suggested, I've coded "Time" as a categorical variable using "BY", and
> results revealed a significant main effect of Time (p = .000). I've then
> used the /TEST subcommand to perform planned contrasts to help data
> interpretation of the "Time" effect on pain. Assuming that I did it
> correclty, I conducted the Helmert contrast, as suggested by Bruce (i.e.,
> comparing pain at each time point versus the mean of all other subsequent
> time points.
>
> MIXED Pain BY Time
> /METHOD = REML
> /PRINT = SOLUTION TESTCOV
> /FIXED =
> Time
> | SSTYP(3)
> /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
> /REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)
> /EMMEANS = TABLES(Time)
> /TEST = "Planned contrasts of TimeBaseline versus subsequent" time  1 -1/4
> -1/4 -1/4 -1/4
> /TEST = "Planned contrasts of 3m versus subsequent" time  0 1 -1/3 -1/3
> -1/3
> /TEST = "Planned contrasts of 6m versus subsequent" time  0 0 1 -1/2 -1/2
> /TEST = "Planned contrasts of 9m versus subsequent" time  0 0 0 1 -1
>
>
> *At this point what I'm wondering is how to interpret the Time *
> Depression
> (Dep) interaction effect. When coding "Time" as categorical, the
> interaction effect (i.e., Time * Dep) is significant. But I don't know how
> to use planned contrasts to probe the interaction effect. For instance, it
> is possible that depression scores (continuous: 0-10) influenced pain
> (continous: 0-10) but only between the baseline and the 3 month follow-up
> time point. I read on the UCLA website that "*interaction contrasts*"
> could
> be used
> (https://stats.idre.ucla.edu/spss/faq/how-can-i-test-contrasts-and-interaction-contrasts-in-a-mixed-model/),
> but for some reason I can't figure out how to apply the coding to my Time
> *
> Dep interaction.
>
> MIXED Pain BY Time WITH Dep
> /METHOD = REML
> /PRINT = SOLUTION TESTCOV
> /FIXED = Time Dep Time * Dep
> | SSTYP(3)
> /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
> /REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)
>
> By any chance, does someone here know how to perform the "interaction
> contrasts" ? Any assistance would be tremendously appreciated, as usual.
> O.
>
>
>
>
>
>
> --
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>
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> LISTSERV@.UGA

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-----
--
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[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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[Oliver]

Bruce and Bozena,

Thanks to both of you for your great input. I've followed Bozena's
suggestion (i.e., to re-code the order to Waves as a way to have the right
reference category) and this works well. Thanks Bozena !

I've also followed Bruce's syntax suggestion to interpret the Level 1 (Time
* Dep) interaction effect on pain, and this works great as well. As
suggested, the effect of the Time (IV; categorical) on pain (outcome; 0-10)
was tested at different levels of the moderator (dep). Consistent with Aiken
& West, I chosen values corresponding to -1SD, Mean, and +1SD.  

MIXED Pain BY Time WITH Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time Dep Time * Dep | SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)
/EMMEANS TABLES(Time) WITH(Dep=0.15) COMPARE(Time) ADJ(SIDAK)
/EMMEANS TABLES(Time) WITH(Dep=2.85) COMPARE(Time) ADJ(SIDAK)
/EMMEANS TABLES(Time) WITH(Dep=5.55) COMPARE(Time) ADJ(SIDAK)

The syntax (and output) proposed by Bruce is extremely useful for the
interpretation of the Level 1 interaction effect. My question at this point
is this: The moderator values (-1SD, M, +1SD) were computed based on the
"Grand mean". For a specific question of interest in my study, I'd like to
know if the time (IV) effect on pain (outcome) varied as a function of
within-person changes in the moderator (dep) at each of the time points.
Would it be possible to change the specification  (/EMMEANS line) with
"cluster/within-person" centered scores ? For instance, perhaps the degree
of within-person changes in pain across time points varies as a function of
concurrent (within-person) changes in the moderator. This If so, would
someone know how to perform this ?

Thanks again everyone,
O.

 



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[Oliver]

Hi everyone,

I thought about something related to my previous question related to the
inclusion of a time-varying moderator (i.e., dep; 0-10) in a model that
examines the effect of time (IV; categorical) on the outcome (pain; 0-10).
The Level 1 (Time * dep) interaction is significant, but I want to interpret
this effect. Results suggest that the degree of within-person changes in
pain across time points varies as a function of concurrent/within-person
changes in the moderator across time points,

For data interpretation/data vizualization, perhaps it could be reasonable
to determine values that correspond to +/- 1SD based on the
cluster/within-person centered scores on the moderator ? These values (i.e.,
+/- 1SD) would be derived based on the grand-mean of centered scores (only
way, I guess), but perhaps this could still be a useful approach ? The
EMMEANS line could look like this:

MIXED Pain BY Time WITH c_Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time c_Dep Time * c_Dep | SSTYP(3)
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN)
/REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1)
/EMMEANS TABLES(TimeC) WITH(c_dep = -0.91) COMPARE(TimeC) ADJ(SIDAK)
/EMMEANS TABLES(TimeC) WITH(c_dep = 0) COMPARE(TimeC) ADJ(SIDAK)
/EMMEANS TABLES(TimeC) WITH(c_dep = 0.91) COMPARE(TimeC) ADJ(SIDAK).

Thanks in advance for your input!
O.




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[Zdaniuk, Bozena-3]

Hi Oliver,
I did longitudinal mediation analysis where I looked at changes in one variable mediating changes in the outcome (mediator and outcome were concurrent) in response to treatment. I used subject centered Level-1 scores as indicators of change for both the mediator and the outcome. Happy to send you a reference directly if you are interested.
Cheers,
Bozena

-----Original Message-----
From: SPSSX(r) Discussion <[hidden email]> On Behalf Of Oliver
Sent: March 24, 2021 6:49 AM
To: [hidden email]
Subject: Re: Interpretation of interaction with time-varying predictor (Growth model)

[CAUTION: Non-UBC Email]

Hi everyone,

I thought about something related to my previous question related to the inclusion of a time-varying moderator (i.e., dep; 0-10) in a model that examines the effect of time (IV; categorical) on the outcome (pain; 0-10).
The Level 1 (Time * dep) interaction is significant, but I want to interpret this effect. Results suggest that the degree of within-person changes in pain across time points varies as a function of concurrent/within-person changes in the moderator across time points,

For data interpretation/data vizualization, perhaps it could be reasonable to determine values that correspond to +/- 1SD based on the cluster/within-person centered scores on the moderator ? These values (i.e.,
+/- 1SD) would be derived based on the grand-mean of centered scores
+(only
way, I guess), but perhaps this could still be a useful approach ? The EMMEANS line could look like this:

MIXED Pain BY Time WITH c_Dep
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = Time c_Dep Time * c_Dep | SSTYP(3) /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) /REPEATED = Wave | SUBJECT(ID) COVTYPE(AR1) /EMMEANS TABLES(TimeC) WITH(c_dep = -0.91) COMPARE(TimeC) ADJ(SIDAK) /EMMEANS TABLES(TimeC) WITH(c_dep = 0) COMPARE(TimeC) ADJ(SIDAK) /EMMEANS TABLES(TimeC) WITH(c_dep = 0.91) COMPARE(TimeC) ADJ(SIDAK).

Thanks in advance for your input!
O.




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