[Rd] lmer error: number of observations <= number of random effects

[Srinidhi Jayakumar]

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>

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