[R-sig-ME] lme varFix under ML fit does not match coefficients standard error

[Ben Bolker]

   Note that the initial example provided gave a singular or 
close-to-singular fit, so we would expect very similar answers from REML 
and ML.

On 2024-02-20 3:40 p.m., Dimitris Rizopoulos wrote:
> In principle, the standard errors should be different with REML and ML. When I try different datasets, I see differences. For example,
> 
> fm_reml <- lme(distance ~ age, data = Orthodont, random = ~ age | Subject)
> fm_ml <- lme(distance ~ age, data = Orthodont, random = ~ age | Subject,
>               method = "ML")
> 
> coef(summary(fm_reml))
> coef(summary(fm_ml))
> 
> Best,
> Dimitris
> 
> 
> -----Original Message-----
> From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> On Behalf Of Vaida, Florin via R-sig-mixed-models
> Sent: Tuesday, February 20, 2024 9:25 PM
> To: Ben Bolker <bbolker using gmail.com>; r-sig-mixed-models using r-project.org
> Subject: Re: [R-sig-ME] lme varFix under ML fit does not match coefficients standard error
> 
> 
> 
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> 
> 
> Thanks Ben, interesting!
> Any particular reason for this default choice?
> It sounds like separating parameter estimation (ML) from SE of the parameters (REML), but presumably when someone chooses ML for estimation they assume this goes to how the SE's are computed too.
> 
> Florin
> 
> On 2/18/24, 11:52 AM, "R-sig-mixed-models on behalf of Ben Bolker" <r-sig-mixed-models-bounces using r-project.org on behalf of bbolker using gmail.com> wrote:
> 
>         From ?summary.lme:
> 
>      adjustSigma: an optional logical value.  If ‘TRUE’ and the estimation
>                 method used to obtain ‘object’ was maximum likelihood, the
>                 residual standard error is multiplied by sqrt(nobs/(nobs -
>                 npar)), converting it to a REML-like estimate.  This argument
>                 is only used when a single fitted object is passed to the
>                 function.  Default is ‘TRUE’.
> 
> 
> 
> 
>      On 2024-02-18 2:34 p.m., Vaida, Florin via R-sig-mixed-models wrote:
>      > Hello all,
>      >
>      > This is probably known, but it’s news to me: the standard errors printed for the lme model fit run under method=”ML” are in fact those computed under method=”REML”.
>      > Is this the expected behavior?  And if so, are there any reasons for this choice?
>      > Reproducible example below.
>      >
>      > Thanks,
>      > Florin
>      >
>      > library(nlme)
>      > fit.reml =  lme(log(conc) ~ Time, random=~1|Subject, data=Glucose, na.action=na.omit, method="REML")
>      > (se.reml = summary(fit.reml)$tTable[,2])
>      > ## (Intercept)        Time
>      > ## 0.019457141 0.005829144
>      > (se.reml = sqrt(diag(summary(fit.reml)$varFix)))
>      > ## (Intercept)        Time
>      > ## 0.019457141 0.005829144
>      > fit.ml =  lme(log(conc) ~ Time, random=~1|Subject, data=Glucose, na.action=na.omit, method="ML")
>      > (se.ml = summary(fit.ml)$tTable[,2]) # they match the REML SE’s
>      > ## (Intercept)        Time
>      > ## 0.019457141 0.005829144
>      > (se.ml = sqrt(diag(summary(fit.ml)$varFix))) # they do not match the tTable SE’s
>      > ## (Intercept)        Time
>      > ## 0.019405324 0.005813621
>      >
>      >   [[alternative HTML version deleted]]
>      >
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