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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