Dear all,
I collected data from subjects in a longitudinal study. However, I now want to compare groups of persons in a cross-sectional fashion. My problem is that some subjects appear twice in the same group, because they were tested twice (1-year gap), while others appear only once in the group. While I am sure that it's problematic to analyse a subject twice if they were tested at the same time, I am not sure whether or why it is justifiable to analyse the person twice within the same group when he or she was tested at two different times.
Thanks for your help,
Johannes
If you just include multiple observations without accounting for the dependencies between the measurements you underestimate the population variance and the estimation of the sampling distribution (and hence confidence intervalks an p-values) will be incorrect.
If you have good reasons to belive that observations from same individuals are essentially unrelated, you could argue that the potential error of ignoring dependency is not large and interpret with care. An argument could be that the ICC is low.
If the reason for the lack of second observations is that you did not yet collect the responses you could argue that these values are missing completely at random and view this as a longitudinal design with planned missingness and then use appropriate methods for longitudinal designs and define your tests as planned comparisons. The group with missing data would not be included in the contrasts, but the dependency of observations would be included in the estimation of the standard errors.
Agree with Andreas. Another possibility to analyse this data structure (nested data) would be multilevel modelling. You can account for the nested structure (Level 1 = retests, Level 2 = participants) and missings are not a problem for MLM. Furthermore, you can separate the within-subject variance from the between-subject variance.
Stefan, I would agree with you if there were at least two observations per person. Then a random intercept model would seem straightforeward to me. In the case of single observations I am not sure. For these cases the model would fit the observations perfectly (if I am not in error, I didn't try) and the single case observations would reduce the residual variance. Consequently, if my intuition is correct, the model would get better the more second observations are missing
Hey all,
maybe this article helps:
Hedeker & Gibbons(1997). Application of Random-Effects Pattern-Mixture Models for Missing Data in Longitudinal Studies.
or this one
Harvey Goldstein's (1999) "Multilevel statistical models" which includes a section adressing missing values, besides lots of good descriptions how to handle different data structures. He suggests that you enter a variable which 'predicts' the missings in a regression model... (which however is tailored to the assumption that the missings are not random)
Generally I think, you can make a somehow random effect ANOVA with an MLM. When you just use a constant as fixed effect, and enter the 2 factors (assuming a 2 (groups) x 2 (measurements) design) as single random effects as well as their interaction. E.g. in R:
DV ~ 1 + (1 | group) + (1 | measurment) + (1 | measurment:group)
then check whether the variances from the estimated random effects are different from zero (would equal to significance)... At least... I would bring this solution to the table, it usually produces the same results as an ANOVA, however without some of it's assumptions ...
Best,
René
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