"weird" results from multilevel analysis I am examining the effect of a group variable (with five levels) along with other predictors on achievement growth using SPSS Mixed Model. The descriptive statistics showed a consistent pattern on achievement for these five groups across all waves of data collection. That is, the average score of group C > Group E> Group B > Group D > Group A. However, the results of my analysis showed that the estimate of Group C on intercept (which was set on the last time point) was significantly lower than Group E and even lower than Group B. Is that possible?
I can understand if the difference between Group C and E becomes insignificant because of other predictors in the model. However, is it possible that the addition of other predictors changes the relative standing of the groups in the model? 
I have rechecked and redone the analysis several times to make sure that the "weird" result was not due to my errors on recoding variables or imputing missing values. Should I be concerned about this results? Or can I say that the result was reasonable since the other predictors I added to the model may "explain away" the group difference? 
Any comment or advice is appreciated. Thanks!!!
 A: The intercept is rarely of interest.
One way the results you describe could happen is if the groups are, on average, different on the covariates. For example, you say the mean of group C was lower then E, but E was lower on the intercept. I don't have SPSS but here is R code that does this for a simplified case with one IV:
set.seed(12646)
group <- c(rep('c', 50), rep('e', 50))
meanval <- c(rnorm(50, 2, 1), rnorm(50, 0, 1))
iv <- c(rnorm(50, 10, 1), rnorm(50, 25, 1))
mean(meanval[group == 'c'])
mean(meanval[group == 'e'])  **#C IS HIGHER**
dv <- meanval + 10*iv + rnorm(100)
model <- lm(dv~iv + factor(group))
summary(model) **#E HAS HIGHER INTERCEPT**

with multiple IVs, the differences could be more subtle, but the principle is the same.
A: The addition of other predictors to the model can lead to a situation in which the adjusted ordering of C and E is the reverse of the unadjusted ordering.  Consider a situation in which C and E are runners in a footrace.  C finished the footrace far ahead of E.  But then you realize that before you declare that C is the fastest runner, you must take into account the fact that E was carrying a refrigerator on his back, while C was merely carrying a toaster.  In terms of speed adjusted for cargo weight, perhaps C's performance is superior to E's.
Stephen Brand
StatisticsDoc
