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

Mon May 6 18:59:03 CEST 2024

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 <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>> 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>>
> Reply-To: Srinidhi Jayakumar <srinidhi.jayakumar using stonybrook.edu <mailto: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>>
> Cc: <r-help using r-project.org <mailto:r-help using r-project.org>>, <r-sig-mixed-models using r-project.org <mailto:r-sig-mixed-models using r-project.org>>, <r-devel using r-project.org <mailto: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>> 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>> 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
>> thierry.onkelinx using inbo.be <mailto:thierry.onkelinx using inbo.be>
>> Havenlaan 88 bus 73, 1000 Brussel
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>> 
>> 
>> ///////////////////////////////////////////////////////////////////////////////////////////
>> To call in the statistician after the experiment is done may be no more
>> than asking him to perform a post-mortem examination: he may be able to say
>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner
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>> ensure that a reasonable answer can be extracted from a given body of data.
>> ~ John Tukey
>> 
>> ///////////////////////////////////////////////////////////////////////////////////////////
>> 
>> <https://www.inbo.be> <https://www.inbo.be>>
>> 
>> 
>> 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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