[R-sig-ME] lme and lmer degrees of freedom (and hence p values) from don't agree . . . Why?????????

[Ben Bolker]

Following up/amplifying: the heuristic inner-outer algorithm that lme
uses to guess the degrees of freedom can definitely fail for
random-slopes models (I should probably add this to the GLMM FAQ if I
haven't already). Logically, because slope varies across
random-effects groups, we have effectively 22 df (number of groups-1)
for estimating the significance of the slope fixed effect. The
Satterthwaite approximation that lmerTest uses gets it right here (as
would ddf="Kenward-Roger" in lmerTest anova()).

  Good to have this stated for the record.


  cheers
     Ben Bolker

On Tue, Jul 7, 2015 at 12:34 PM, Jake Westfall <jake987722 at hotmail.com> wrote:
> Hi John,
>
> lmer does not use or report degrees of freedom on its own. It appears that you are getting degrees of freedom from the lmerTest package. Just for future reference.
>
> The degrees of freedom from lme are based on an inner-outer rule that is described here: https://books.google.com/books?id=3TVDAAAAQBAJ&lpg=PR1&dq=pinheiro%20bates&pg=PA91#v=onepage&q&f=false
>
> The degrees of freedom from lmerTest are based on Satterthwaite's approximation, described here: https://en.wikipedia.org/wiki/Welch%E2%80%93Satterthwaite_equation
>
> It looks like the "Amp" predictor is being treated by the models as a numeric, but you said it represents 5 experimental conditions? Should it not be a factor then?
>
> Jake
>
>> Date: Tue, 7 Jul 2015 12:08:13 -0400
>> From: JSorkin at grecc.umaryland.edu
>> To: r-sig-mixed-models at r-project.org
>> Subject: [R-sig-ME] lme and lmer degrees of freedom (and hence p values) from don't agree . . . Why?????????
>>
>> I am posting this message to this list (after posting to R help) at the
>> suggestion of Bert Gunter.
>>
>> I am trying to fit data from 23 subjects using random effects
>> regression, and am comparing the results of lme and lmer. The point
>> estimates and the SEs are the same in both models, however the degrees
>> of freedom are widely different. lme reports 88 DF, lmer approximately
>> 22. Can someone help me understand why the DFs are not the same? I have
>> 23 subjects, each of whom is studied in up to five different
>> experimental conditions (i.e. Amp). For each condition multiple
>> measurements are made for each subject (i.e. X).
>> Thank you,
>> John
>>
>>
>>
>> # lme: Random intercept, random slope.
>> cat("********This analysis has 88 degrees of freedom\n")
>> fit0X.new <- groupedData(X~Amp|SS,data=data,order.groups=FALSE)
>> xx <- lme(fit0X.new,random=~1+Amp)
>> summary(xx)
>> cat("\n\n")
>>
>>
>> # lmer: Random intercept, random slope.
>> cat("*********This analysis has ~22 degrees of freedom\n")
>> fit0X <- lmer(X~Amp+(1+Amp|SS),data=data)
>> print(summary(fit0X))
>> fit0XSum<-summary(fit0X)$coefficients
>>
>>
>>
>> ********This analysis has 88 degrees of freedom
>> Linear mixed-effects model fit by REML
>>  Data: fit0X.new
>>        AIC      BIC    logLik
>>   331.7688 347.9717 -159.8844
>> Random effects:
>>  Formula: ~1 + Amp | SS
>>  Structure: General positive-definite, Log-Cholesky parametrization
>>             StdDev    Corr
>> (Intercept) 1.3515911 (Intr)
>> Amp         2.5619953 -0.366
>> Residual    0.6139429
>> Fixed effects: X ~ Amp
>>                Value Std.Error DF   t-value p-value
>> (Intercept) 1.718376 0.3609133 88  4.761188       0
>> Amp         6.890429 0.5978236 88 11.525856       0
>>  Correlation:
>>     (Intr)
>> Amp -0.526
>> Standardized Within-Group Residuals:
>>        Min         Q1        Med         Q3        Max
>> -2.2177007 -0.5770388 -0.1249565  0.5247444  4.1150164
>> Number of Observations: 112
>> Number of Groups: 23
>>
>> *********This analysis has ~22 degrees of freedom
>> Linear mixed model fit by REML t-tests use Satterthwaite approximations
>> to degrees of freedom [merModLmerTest]
>> Formula: X ~ Amp + (1 + Amp | SS)
>>    Data: data
>> REML criterion at convergence: 319.8
>> Scaled residuals:
>>     Min      1Q  Median      3Q     Max
>> -2.2177 -0.5770 -0.1250  0.5247  4.1150
>> Random effects:
>>  Groups   Name        Variance Std.Dev. Corr
>>  SS       (Intercept) 1.8268   1.3516
>>           Amp         6.5638   2.5620   -0.37
>>  Residual             0.3769   0.6139
>> Number of obs: 112, groups:  SS, 23
>> Fixed effects:
>>             Estimate Std. Error      df t value Pr(>|t|)
>> (Intercept)   1.7184     0.3609 21.1150   4.761 0.000104 ***
>> Amp           6.8904     0.5978 22.0460  11.526 8.37e-11 ***
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> Correlation of Fixed Effects:
>>     (Intr)
>> Amp -0.526
>>
>>
>>
>>
>>
>>
>> John David Sorkin M.D., Ph.D.
>> Professor of Medicine
>> Chief, Biostatistics and Informatics
>> University of Maryland School of Medicine Division of Gerontology and
>> Geriatric Medicine
>> Baltimore VA Medical Center
>> 10 North Greene Street
>> GRECC (BT/18/GR)
>> Baltimore, MD 21201-1524
>> (Phone) 410-605-7119
>> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>> John David Sorkin M.D., Ph.D.
>> Professor of Medicine
>> Chief, Biostatistics and Informatics
>> University of Maryland School of Medicine Division of Gerontology and
>> Geriatric Medicine
>> Baltimore VA Medical Center
>> 10 North Greene Street
>> GRECC (BT/18/GR)
>> Baltimore, MD 21201-1524
>> (Phone) 410-605-7119
>> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>>
>> Confidentiality Statement:
>> This email message, including any attachments, is for ...{{dropped:12}}
>
>
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