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

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
*Postadres:* Koning Albert II-laan 15 bus 186, 1210 Brussel
*Poststukken die naar dit adres worden gestuurd, worden ingescand en
digitaal aan de geadresseerde bezorgd. Zo kan de Vlaamse overheid haar
dossiers volledig digitaal behandelen. Poststukken met de vermelding
?vertrouwelijk? worden niet ingescand, maar ongeopend aan de geadresseerde
bezorgd.*
www.inbo.be


///////////////////////////////////////////////////////////////////////////////////////////
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
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be> <https://www.inbo.be&gt;>


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;>