Dear R Masters, I'm an anesthesiology resident trying to make his way through basic statistics. Recently I have been confronted with longitudinal data in a treatment vs. control analysis. My dataframe is in the form of:
subj | group | baseline | time | outcome (long) or subj | group | baseline | time1 |...| time6 | (wide) The measured variable is a continuous one. The null hypothesis in this analysis is that the Group factor does not significantly influence the outcome variable. A secondary null hypothesis is that the Group x Time interaction is not significant, either. Visual of the group means indicates the outcome measure decreases linearly (more or less) over time from baseline values. The time==1...time==6 intervals are equally-spaced and we have equal sample sizes for the groups. I've done a little reading around and found (at least) four possible approaches: A. Linear mixed model using lme4 with random intercept and slope with lmer() or lme() B. Repeated measures ANOVA using aov() with Error() stratification (found in Baron & Li, 2006), something along the lines of: aov(outcome ~ group * time + baseline + Error(subj+subj:time)) (from: http://cran.r-project.org/doc/contrib/Baron-rpsych.pdf, p. 41) C. "Repeated measures" MANOVA as follows (using data in wide format): response <- cbind(time1,time2,time3,time4,time5,time6) mlmfit <- lm(response ~ group) mlmfit1 <- lm(response ~ 1) mlmfit0 <- lm(response ~ 0) # Test time*group effect anova.mlm(mlmfit, mlmfit1, X=~1, test="Spherical") # Test overall group effect anova.mlm(mlmfit, mlmfit1, M=~1) # Test overall time effect anova.mlm(mlmfit1, mlmfit0, X=~1, test="Spherical") (taken from http://tolstoy.newcastle.edu.au/R/help/05/11/15744.html) Now, on with the questions: 1. This is really a curiosity. I find lmer() easier to use than lme(), but the former does not allow the user to model the correlation structure of the data. I figure lmer() is presently assuming no within-group correlation for the data, which I guess is unlikely in my example. Is there a way to compare directly (maybe in terms of log-likelihood?) similar models fitted in lme() and lmer()? 2. Baron & Li suggest a painful (at least for me) procedure to obtain Greenhouse-Geisser or Huyn-Feldt correction for the ANOVA analysis they propose. Is there a package or function which simplifies the procedure? 3. I must admit that I don't understand solution C. I can "hack" it to fit my model, and it seems to work, but I can't seem to grasp the overall concept, especially regarding the outer and/or inner projection matrices (M & X). Could anyone point me to a basic explanation of the procedure? 4. Provided the assumptions for ANOVA hold, or that deviations from them are not horrible, am I correct in saying that this procedure would be the most powerful one? How would you choose solution A over solution B (or viceversa)? My sincerest gratitude to anyone who will take the time to answer my questions! Best Regards, Marco ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
