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Jointly testing several parameters of factor variable

For number (1) below you can either set up a set of contrasts such that when some of the contrasts are 0, the equality constraints of interest hold, then look at those specific contrasts (see functions 'contrasts' and 'C' for ways to specify the contrasts).  Or you can create variables recoded such that using one set of the variables is the full model and the other set is your constrained model, then just do a full/reduced model comparison between the 2 groups of variables.