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

[Bert Gunter]

This is a **highly technical** statistical issue, not an R-Help topic.
I strongly suggest that you post to the R-sig-mixed-models list
instead.

Cheers,
Bert
Bert Gunter

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
   -- Clifford Stoll


On Tue, Jul 7, 2015 at 8:40 AM, John Sorkin <JSorkin at grecc.umaryland.edu> wrote:
> 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)
>
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