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

[John Sorkin]

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) 

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