[R-sig-ME] lmer to estimate batch variability

John Fox j|ox @end|ng |rom mcm@@ter@c@
Sat Mar 5 03:00:27 CET 2022

Dear John,

On 2022-03-04 8:08 p.m., array chip via R-sig-mixed-models wrote:
> Dear all, I have this simple dataset to measure the yeild of a crop collected in 2 batches (https://drive.google.com/file/d/1lgVZVLHeecp9a_sFxEPeg6353O-qXZhM/view). when I ran a simple inear mixed model using lmer to estimate within-batch and between-batch variability, the between-batch variability is 0. The run showed that data is singular. Does anyone know why the data is singular and what's the reason for 0 variability? is it because the dataset only has 2 batches?

I'd say yes and no.

Yes, in that you have effectively approximately only 1 degree of freedom 
for between-group variability, very little data in each group, and small 
variability between groups relative to within-group 
variability--apparently sufficiently small that the REML criterion is 
maximized at the boundary of the parameter space:

 > # not quite right because group n's differ:
 > sd(with(daty, tapply(yield, batch, mean)))
[1] 0.3032702

 > with(daty, tapply(yield, batch, sd))
        D        K
2.952165 2.779894

Perhaps someone else can provide a more precise explanation.

No, in that it's not hard to construct data for which a proper solution 
can be obtained; e.g.,

 > set.seed(123)

 > Data <- data.frame(yield=c(rnorm(100, -5, 1), rnorm(100, 5, 1)),
+                    batch=rep(c("D", "K"), each=100))

 > lmer(yield ~ 1 + (1|batch), Data)
Linear mixed model fit by REML ['lmerMod']
Formula: yield ~ 1 + (1 | batch)
    Data: Data
REML criterion at convergence: 554.1332
Random effects:
  Groups   Name        Std.Dev.
  batch    (Intercept) 6.9305
  Residual             0.9403
Number of obs: 200, groups:  batch, 2
Fixed Effects:

 > sd(with(Data, tapply(yield, batch, mean))) # estimates 5
[1] 6.931094

 > with(Data, tapply(yield, batch, sd)) # estimate 1
         D         K
0.9128159 0.9669866

BTW, your data *were* included with the original message that you sent 
to r-help, because .txt-file attachments are permitted, but, as you can 
see, your input and output are garbled here because your email wasn't 

>> daty<-read.table("datx.txt",sep='\t',header=T,row.names=NULL)
>> library(lme4)> lmer(yield~1+(1|batch),daty)boundary (singular) fit: see ?isSingularLinear mixed model fit by REML ['lmerMod']Formula: yield ~ 1 + (1 | batch)   Data: datyREML criterion at convergence: 115.6358Random effects: Groups   Name        Std.Dev. batch    (Intercept) 0.000    Residual             2.789   Number of obs: 24, groups:  batch, 2Fixed Effects:(Intercept)        5.788
> Thanks!John

I hope this helps,

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John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://socialsciences.mcmaster.ca/jfox/

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