[R] Random intercept model with time-dependent covariates, results different from SAS
Keith Wong
keithw at med.usyd.edu.au
Sun Jul 4 11:21:32 CEST 2004
Thank you for the very prompt response. I only included a small part of the
output to make the message brief. I'm sorry it did not provide enough detail to
answer my question. I have appended the summary() and anova() outputs to the
two models I fitted in R.
Quoting Prof Brian Ripley <ripley at stats.ox.ac.uk>:
> Looking at the significance of a main effect (group) in the presence of an
> interaction (time:group) is hard to interpret, and in your case is I think
> not even interesting. (The `main effect' probably represents difference
> in intercept for the time effect, that is the group difference at the last
> time. But see the next para.) Note that the two systems are returning
> different denominator dfs.
I take your point that the main effect is probably not interesting in the
presence of an interaction. I was checking the results for consistency to see
if I was doing the right thing. I was not 100% sure that the SAS code was in
itself correct.
> At this point you have not told us enough. My guess is that you have
> complete balance with the same number of subjects in each group. In that
> case the `group' effect is in the between-subjects stratum (as defined for
> the use of Error in aov, which you could also do), and thus R's 11 df
> would be right (rather than 44, without W and Z). Without balance Type
> III tests get much harder to interpret and the `group' effect would appear
> in two strata and there is no simple F test in the classical theory. So
> further guessing, SAS may have failed to detect balance and so used the
> wrong test.
I had not appreciated the need for balance: in actual fact, one group has 5
subjects and the other 7. Will this be a problem? Would the R analysis still be
valid in that case?
> The time-dependent covariates muddy the issue more, and I looked mainly at
> the analyses without them. Again, a crucial fact is not here: do the
> covariates depend on the subjects as well?
Yes the covariates are measures of blood pressure and pulse, and they depend on
the subjects as well.
> The good news is that the results _are_ similar. You do have different
> time behaviour in the two groups. So stop worrying about tests of
> uninteresting hypotheses and concentrate of summarizing that difference.
>
> --
> Brian D. Ripley, ripley at stats.ox.ac.uk
> Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
> University of Oxford, Tel: +44 1865 272861 (self)
> 1 South Parks Road, +44 1865 272866 (PA)
> Oxford OX1 3TG, UK Fax: +44 1865 272595
Thank you. I was concerned that one or both methods were incorrect given the
results were inconsistent. Perhaps reassuringly, the parameter estimates for
the fixed effects in both SAS and R were the same.
Is the model specification OK for the model with just time, group and their
interaction?
Is the model specification with the 2 time dependent covariates appropriate?
Once again, I'm very grateful for the time you've taken to answer my questions.
Keith
[Output from the 2 models fitted in R follows]
> g1 = lme(Y ~ time + group + time:group, random = ~ 1 | id, data = datamod)
> anova(g1)
numDF denDF F-value p-value
(Intercept) 1 44 3.387117 0.0725
time 4 44 10.620547 <.0001
group 1 11 0.508092 0.4908
time:group 4 44 3.961726 0.0079
> summary(g1)
Linear mixed-effects model fit by REML
Data: datamod
AIC BIC logLik
372.4328 396.5208 -174.2164
Random effects:
Formula: ~1 | id
(Intercept) Residual
StdDev: 11.05975 3.228684
Fixed effects: Y ~ time + group + time:group
Value Std.Error DF t-value p-value
(Intercept) 8.250 4.073428 44 2.025321 0.0489
time1 -0.250 1.614342 44 -0.154862 0.8776
time2 -8.125 1.614342 44 -5.033011 0.0000
time3 -8.875 1.614342 44 -5.497596 0.0000
time4 -4.250 1.614342 44 -2.632652 0.0116
group1 2.126 6.568205 11 0.323681 0.7523
time1:group1 -2.734 2.603048 44 -1.050307 0.2993
time2:group1 5.583 2.603048 44 2.144793 0.0375
time3:group1 5.549 2.603048 44 2.131732 0.0387
time4:group1 3.634 2.603048 44 1.396056 0.1697
Correlation:
(Intr) time1 time2 time3 time4 group1 tm1:g1 tm2:g1 tm3:g1
time1 -0.198
time2 -0.198 0.500
time3 -0.198 0.500 0.500
time4 -0.198 0.500 0.500 0.500
group1 -0.620 0.123 0.123 0.123 0.123
time1:group1 0.123 -0.620 -0.310 -0.310 -0.310 -0.198
time2:group1 0.123 -0.310 -0.620 -0.310 -0.310 -0.198 0.500
time3:group1 0.123 -0.310 -0.310 -0.620 -0.310 -0.198 0.500 0.500
time4:group1 0.123 -0.310 -0.310 -0.310 -0.620 -0.198 0.500 0.500 0.500
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.63416413 -0.42033405 0.03577472 0.46164486 1.74068368
Number of Observations: 65
Number of Groups: 13
> g2 = lme(Y ~ time + group + time:group + W + Z, random = ~ 1 | id, data =
datamod)
> anova(g2)
numDF denDF F-value p-value
(Intercept) 1 42 5.54545 0.0233
time 4 42 16.41069 <.0001
group 1 11 0.83186 0.3813
W 1 42 0.07555 0.7848
Z 1 42 45.23577 <.0001
time:group 4 42 3.04313 0.0273
> summary(g2)
Linear mixed-effects model fit by REML
Data: datamod
AIC BIC logLik
355.2404 382.8245 -163.6202
Random effects:
Formula: ~1 | id
(Intercept) Residual
StdDev: 8.639157 2.597380
Fixed effects: Y ~ time + group + time:group + W + Z
Value Std.Error DF t-value p-value
(Intercept) 10.056433 9.583658 42 1.049331 0.3000
time1 0.209668 1.301306 42 0.161121 0.8728
time2 4.111435 2.556420 42 1.608278 0.1153
time3 0.423056 2.077066 42 0.203679 0.8396
time4 -3.976417 1.300572 42 -3.057437 0.0039
group1 4.677706 5.162006 11 0.906180 0.3843
W 0.377142 0.127146 42 2.966212 0.0050
Z -0.531895 0.093276 42 -5.702395 0.0000
time1:group1 -0.845857 2.126289 42 -0.397809 0.6928
time2:group1 -5.145361 2.962470 42 -1.736848 0.0897
time3:group1 -3.261241 2.597008 42 -1.255769 0.2161
time4:group1 4.153245 2.096587 42 1.980956 0.0542
Correlation:
(Intr) time1 time2 time3 time4 group1 W Z tm1:g1
tm2:g1
time1 -0.051
time2 0.199 0.308
time3 0.023 0.361 0.817
time4 -0.029 0.501 0.293 0.342
group1 -0.202 0.131 0.136 0.146 0.129
W -0.790 0.019 0.243 0.366 -0.015 0.044
Z -0.146 -0.063 -0.853 -0.779 -0.041 -0.086 -0.409
time1:group1 -0.028 -0.601 -0.043 -0.074 -0.302 -0.187 0.147 -0.144
time2:group1 -0.293 -0.262 -0.818 -0.642 -0.255 -0.198 -0.051 0.665 0.276
time3:group1 -0.016 -0.286 -0.626 -0.774 -0.273 -0.214 -0.277 0.590 0.308
0.668
time4:group1 0.065 -0.306 -0.116 -0.159 -0.616 -0.199 0.002 -0.046 0.497
0.318
tm3:g1
time1
time2
time3
time4
group1
W
Z
time1:group1
time2:group1
time3:group1
time4:group1 0.376
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.11181231 -0.43210237 0.04949838 0.32444580 2.77710590
Number of Observations: 65
Number of Groups: 13
>
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