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

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)

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