From: Keith Wong <keithw_at_med.usyd.edu.au>

Date: Sun 04 Jul 2004 - 19:21:32 EST

*> summary(g1)
*

Linear mixed-effects model fit by REML

Data: datamod

time4:group1 0.376

R-help@stat.math.ethz.ch mailing list

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Jul 04 19:26:32 2004

Date: Sun 04 Jul 2004 - 19:21:32 EST

Quoting Prof Brian Ripley <ripley@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@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

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 0.500time4: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 0.0897time3: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

*>
*

R-help@stat.math.ethz.ch mailing list

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Jul 04 19:26:32 2004

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