[R-sig-ME] lmer error: number of observations <= number of random effects

[Srinidhi Jayakumar]

Hi,

Thank you very much for your response. Index1 is the time point variable.
So, we collected social anhedonia, and LSI at time points of age 12, 15,
and 18. So for every participant the time point variable (Index1) was coded
as 0 (for the 1st time point, i.e., age 12), 1  (for the 2nd time point,
i.e., age 15), and 2 (for the 3rd time point, i.e., age 18). So Index1 in
the fixed  effects would mean the average trajectory of SA, and Index1 as a
random effect would mean the variation in trajectories of SA. So it would
be a within subjects factor. I am looking into whether trajectory of social
anhedonia over these time points would differ depending on the LSI values
at the time points. I am assuming that LSI at each time point would affect
SA at each time point differently (e.g, 1 unit increase in LSI at time
point 0 would be associated with a 1 unit increase in SA at time point 0
but a 0.5 unit increase in SA at time point 1, if that makes sense).
I believe in this case, you are suggesting that I try
mdl<-lmer(SA ~ Index1*LSI+ (1 | ID)+(1 +LSI | ID:Index1),data = LSIDATA,
control = lmerControl(optimizer ="bobyqa"), REML=TRUE)].
Could you please let me know what would be the difference between the above
model vs when I nest the inviduals with time, i.e.,
mdl<-lmer(SA ~ Index1*LSI+ (1 | ID)+(1 +LSI | Index1/ID),data = LSIDATA,
control = lmerControl(optimizer ="bobyqa"), REML=TRUE)]. I am thinking in
this case, it would be that for each person, over time, we are examining
the variation in LSI and how that affects variation in SA. Whereas, in the
model you had suggested, it would be that between IDs, over time, we  are
examining the variation in LSI and how that affects variation in SA
correct? So the model you had suggested wouldn't tell me about variation in
LSI and its effects on variation in SA per person over time is that correct?
Thank you in advance for your sincere help!


Thank you,
Srinidhi


On Mon, May 6, 2024 at 12:59 PM TT FF <trashfaket using gmail.com> wrote:

> if I understood the design correctly.
>
> Index is a wihtin subject factor (the same participant tested at 3
> different ages), while LSI is instead a numerical predictor.
>
> If the above is correct,
> AND
> If you assume the LSI will affect similarly across ages, then I would try
> the following:
> mdl<-lmer(SA ~ Index1*LSI+ (1+LSI | ID)+(1 | ID:Index1),data = LSIDATA,
> control
> lmerControl(optimizer ="bobyqa"), REML=TRUE)].
> car::Anova(mdl, type 3, test F)
>
> If you assume the LSI will affect differently across ages, then I would
> try the following:
> mdl<-lmer(SA ~ Index1*LSI+ (1 | ID)+(1 +LSI | ID:Index1),data = LSIDATA,
> control
> lmerControl(optimizer ="bobyqa"), REML=TRUE)].
> car::Anova(mdl, type 3, test F)
>
>
> However,
> if Index1 is a between subjects factor (i.e, each ID has one age only).
> Then, I would keep Index1 as numerical predictor (given that is also
> equally spaced) and run
> mdl<-lmer(SA ~ Index1*LSI+ (1 +Index1:LSI | ID)),data = LSIDATA, control
> lmerControl(optimizer ="bobyqa"), REML=TRUE)].
> car::Anova(mdl, type 3, test F)
>
> The latter is based on (https://doi.org/10.3389/fpsyg.2013.00328) that
> suggests to keep the highest interaction.
>
> if you want to keep the age as between subjects factor (i.e, not a
> numerical predictor), then I would run
> mdl<-lmer(SA ~ Index1*LSI+ (1+LSI | ID)),data = LSIDATA, control
> lmerControl(optimizer ="bobyqa"), REML=TRUE)].
> car::Anova(mdl, type 3, test F)
>
> But I would not make model comparisions by altering the random effect
> strcuture to see if LSI and Index has a different contribution. I would
> achieve that goal with a single model and by keeping them always in the
> fixed part of the LMM.
>
>
> I hope this makes sense.
>
> Best
>
> On 6 May 2024, at 16:33, Marc Schwartz <marc_schwartz using me.com> wrote:
>
> Hi All,
>
> As an FYI, there is no need for this thread to be cross-posted to three
> different lists: R-help, R-sig-mixed-models and R-devel.
>
> I am removing R-Help and R-Devel from this reply and only replying to the
> authors and R-sig-mixed-models, which is the appropriate list for this
> thread.
>
> For any future e-mails to this thread, please only reply to the author(s)
> and to R-sig-mixed-models, removing the other two lists.
>
> Thank you,
>
> Marc Schwartz
> R-Devel Co-Admin
>
>
> -----Original Message-----
> From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org <
> mailto:r-sig-mixed-models-bounces using r-project.org
> <r-sig-mixed-models-bounces using r-project.org>>> on behalf of Srinidhi
> Jayakumar via R-sig-mixed-models <r-sig-mixed-models using r-project.org <
> mailto:r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>
> >>
> Reply-To: Srinidhi Jayakumar <srinidhi.jayakumar using stonybrook.edu <
> mailto:srinidhi.jayakumar using stonybrook.edu
> <srinidhi.jayakumar using stonybrook.edu>>>
> Date: Monday, May 6, 2024 at 9:54 AM
> To: TT FF <trashfaket using gmail.com <mailto:trashfaket using gmail.com
> <trashfaket using gmail.com>>>
> Cc: <r-help using r-project.org <mailto:r-help using r-project.org
> <r-help using r-project.org>>>, <r-sig-mixed-models using r-project.org <
> mailto:r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>>>,
> <r-devel using r-project.org <mailto:r-devel using r-project.org
> <r-devel using r-project.org>>>
> Subject: Re: [R-sig-ME] lmer error: number of observations <= number of
> random effects
>
>
> Thank you very much for your responses!
>
>
> What if I reduce the model to
> modelLSI3 <- lmer(SA ~ Index1* LSI+ (1+LSI |ID),data = LSIDATA, control =
> lmerControl(optimizer ="bobyqa"), REML=TRUE).
> This would allow me to see the random effects of LSI and I can drop the
> random effect of age (Index1) since I can see that in the unconditional
> model [model0 <- lmer(SA ~ Index1+ (1+Index1|ID),data = LSIDATA, control =
> lmerControl(optimizer ="bobyqa"), REML=TRUE)]. Would the modelLSI3 also
> have a type 1 error?
>
>
> Thank you,
> Srinidhi
>
>
>
>
>
>
>
>
> On Mon, 6 May 2024, 03:11 TT FF, <trashfaket using gmail.com <
> mailto:trashfaket using gmail.com <trashfaket using gmail.com>>> wrote:
>
>
> See if this paper may help If it helps reducing the model when you have
> few observations. the (1|ID) may increase the type 1 error.
> https://journals.sagepub.com/doi/10.1177/25152459231214454 <
> https://journals.sagepub.com/doi/10.1177/25152459231214454>
>
> Best
>
> On 6 May 2024, at 07:45, Thierry Onkelinx via R-sig-mixed-models <
> r-sig-mixed-models using r-project.org <mailto:r-sig-mixed-models using r-project.org
> <r-sig-mixed-models using r-project.org>>> wrote:
>
> Dear Srinidhi,
>
> You are trying to fit 1 random intercept and 2 random slopes per
> individual, while you have at most 3 observations per individual. You
> simply don't have enough data to fit the random slopes. Reduce the random
> part to (1|ID).
>
> Best regards,
>
> Thierry
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
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> <thierry.onkelinx using inbo.be>>
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> ///////////////////////////////////////////////////////////////////////////////////////////
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>
> Op ma 6 mei 2024 om 01:59 schreef Srinidhi Jayakumar via R-sig-mixed-models
> <r-sig-mixed-models using r-project.org <mailto:r-sig-mixed-models using r-project.org
> >>:
>
> I am running a multilevel growth curve model to examine predictors of
> social anhedonia (SA) trajectory through ages 12, 15 and 18. SA is a
> continuous numeric variable. The age variable (Index1) has been coded as 0
> for age 12, 1 for age 15 and 2 for age 18. I am currently using a time
> varying predictor, stress (LSI), which was measured at ages 12, 15 and 18,
> to examine whether trajectory/variation in LSI predicts difference in SA
> trajectory. LSI is a continuous numeric variable and was grand-mean
> centered before using in the models. The data has been converted to long
> format with SA in 1 column, LSI in the other, ID in another, and age in
> another column. I used the code below to run my model using lmer. However,
> I get the following error. Please let me know how I can solve this error.
> Please note that I have 50% missing data in SA at age 12.
> modelLSI_maineff_RE <- lmer(SA ~ Index1* LSI+ (1 + Index1+LSI |ID), data =
> LSIDATA, control = lmerControl(optimizer ="bobyqa"), REML=TRUE)
> summary(modelLSI_maineff_RE)
> Error: number of observations (=1080) <= number of random effects (=1479)
> for term (1 + Index1 + LSI | ID); the random-effects parameters and the
> residual variance (or scale parameter) are probably unidentifiable
>
> I did test the within-person variance for the LSI variable and the
> within-person variance is significant from the Greenhouse-Geisser,
> Hyunh-Feidt tests.
>
> I also tried control = lmerControl(check.nobs.vs.nRE = "ignore") which gave
> me the following output. modelLSI_maineff_RE <- lmer(SA ~ Index1* LSI+ (1 +
> Index1+LSI |ID), data = LSIDATA, control = lmerControl(check.nobs.vs.nRE =
> "ignore", optimizer ="bobyqa", check.conv.singular = .makeCC(action =
> "ignore", tol = 1e-4)), REML=TRUE)
>
> summary(modelLSI_maineff_RE)
> Linear mixed model fit by REML. t-tests use Satterthwaite's method
> ['lmerModLmerTest']
> Formula: SA ~ Index1 * LSI + (1 + Index1 + LSI | ID)
> Data: LSIDATA
> Control: lmerControl(check.nobs.vs.nRE = "ignore", optimizer = "bobyqa",
> check.conv.singular = .makeCC(action = "ignore", tol = 1e-04))
>
> REML criterion at convergence: 7299.6
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -2.7289 -0.4832 -0.1449 0.3604 4.5715
>
> Random effects:
> Groups Name Variance Std.Dev. Corr
> ID (Intercept) 30.2919 5.5038
> Index1 2.4765 1.5737 -0.15
> LSI 0.1669 0.4085 -0.23 0.70
> Residual 24.1793 4.9172
> Number of obs: 1080, groups: ID, 493
>
> Fixed effects:
> Estimate Std. Error df t value Pr(>|t|)
> (Intercept) 24.68016 0.39722 313.43436 62.133 < 2e-16 ***
> Index1 0.98495 0.23626 362.75018 4.169 3.83e-05 ***
> LSI -0.05197 0.06226 273.85575 -0.835 0.4046
> Index1:LSI 0.09797 0.04506 426.01185 2.174 0.0302 *
> Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
> (Intr) Index1 LSI
> Index1 -0.645
> LSI -0.032 0.057
> Index1:LSI 0.015 0.037 -0.695
>
> I am a little vary of the output still as the error states that I have
> equal observations as the number of random effects (i.e., 3 observations
> per ID and 3 random effects). Hence, I am wondering whether I can simplify
> the model as either of the below models and choose the one with the
> best-fit statistics:
>
> modelLSI2 <- lmer(SA ~ Index1* LSI+ (1 |ID)+ (Index1+LSI -1|ID),data =
> LSIDATA, control = lmerControl(optimizer ="bobyqa"), REML=TRUE) *OR*
>
> modelLSI3 <- lmer(SA ~ Index1* LSI+ (1+LSI |ID),data = LSIDATA, control =
> lmerControl(optimizer ="bobyqa"), REML=TRUE) [image: example of dataset]
> <https://i.sstatic.net/JcRKS2C9.png> <
> https://i.sstatic.net/JcRKS2C9.png>>
>
>
>
>
>
>

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