lmer error: number of observations <= number of random effects

TT FF

Mon, May 6, 2024 9:59 AM

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 at 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 at r-project.org <mailto:r-sig-mixed-models-bounces at r-project.org>> on behalf of Srinidhi Jayakumar via R-sig-mixed-models <r-sig-mixed-models at r-project.org <mailto:r-sig-mixed-models at r-project.org>>
Reply-To: Srinidhi Jayakumar <srinidhi.jayakumar at stonybrook.edu <mailto:srinidhi.jayakumar at stonybrook.edu>>
Date: Monday, May 6, 2024 at 9:54 AM
To: TT FF <trashfaket at gmail.com <mailto:trashfaket at gmail.com>>
Cc: <r-help at r-project.org <mailto:r-help at r-project.org>>, <r-sig-mixed-models at r-project.org <mailto:r-sig-mixed-models at r-project.org>>, <r-devel at r-project.org <mailto:r-devel at 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 at gmail.com <mailto:trashfaket at 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 at r-project.org <mailto:r-sig-mixed-models at 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 at inbo.be <mailto:thierry.onkelinx at inbo.be>
Havenlaan 88 bus 73, 1000 Brussel
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Op ma 6 mei 2024 om 01:59 schreef Srinidhi Jayakumar via R-sig-mixed-models
<r-sig-mixed-models at r-project.org <mailto:r-sig-mixed-models at 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&gt;>

lmer error: number of observations <= number of random effects

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