Suppose that I am looking at data from an N = 32, within-subjects study.
There are three IVs - CL, PL, CPL - with two ordinal levels each (0 and 1). Every subject undergoes each of the 8 configurations of IVs exactly once.
During each configuration of (CL, PL, CPL), two dependent variables, A and Z, are measured four times each. A is a four-level nominal categorical variable with possible values 0, 1, 2, and 3, whereas Z is a continuous bounded variable. A and Z are always measured at the same time, hence there is one measurement of Z corresponding to each measurement of A. This yields, at the conclusion of data collection, 32 measurements of A and 32 measurements of Z for each of the 32 subjects.
Suppose that after collecting the data, it is observed that the fourth level of A is particular rare across the subjects. That is, for many of the subjects, when examining the measurements of A across a particular configuration of the two of the IVs, or even just a particular level of one IV, there are no measurements of the fourth level to be found.
For example, for a particular subject, across all (CL, PL, CPL) such that CL = 0 and PL = 0, the observed measurements of A in no particular order are: [0, 2, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 2, 0, 1, 1], omitting the fourth level, 3. For another subject, across all (CL, PL, CPL) such that CL = 1, 3 is not be found among the 16 measurements of A.
Such scarcity is present across most of the subjects, and across many of the configurations for a given subject.
Taking into account the extensive scarcity of values among the measurements of A and the fact that A is a four-level categorical variable that is measured rather than fixed, what would be the most appropriate way to answer the following questions about data?
(1). Whether CL, PL, CPL individually and/or interactively (including CL, PL, CPL, CLxPL, CLxCPL, PLxCPL) exert a significant effect on the measurements of (four-level categorical) A.
(2). Whether CL, PL, CPL individually and/or interactively exert a significant effect on the measurements of (continuous, bounded) Z. [Would a repeated measures ANOVA be appropriate?]
(3). Whether the measurements of A are significantly predictive of, or correlated with (which is more statistically valid?) the measurements of Z.
(4). Whether, and the extent to which if so, the measurements of A mediate the effects of CL, PL, CPL (individually and/or interactively) on the measurements of Z, taking into account the results of (1).
(5). Whether CL, PL, CPL individually and/or interactively exert a significant effect on the extent to which (3) is true.
(6). I am also aware that in order to answer these questions, I must restructure the data to treat A as a sort of predictor variable, but am not sure how to deal with the missing data and the fact that there are sometimes two or three measurements of a given value of A within a particular configuration of conditions. In the latter case, would I go about averaging the values of Z across those two or three measurements?
Please let me know if there is anything I've explained unclearly or if any other edits should be made. Thank you for your help and efforts!
