I have RNA-seq data from four different cell fractions derived from two different developmental stages. There are 5 replicates for one stage and 6 replicates for the other.

I am currently attempting to mitigate an obvious batch effect due to the donor rather than the cell fraction (See the list of samples below). When I use an experimental design ~name I can see the donor effect in the PCA plot where samples from the same donor cluster closer together rather than samples from the same fraction.

I am having difficulty coming up with the experimental design to mitigate the issue because samples from stage A are not from the same donor as samples from stage B. I am interested in DE calls between different cell fractions within the same stage and between stages.

When I try to include the donor information ~name + donor in the design matrix I end up getting an error that the matrix is not full rank. I assume I need some kind of nested design matrix but I cannot wrap my head around it.

sample    name           donor       stage    fraction
A_4mm     Amm            A4          A        mm
A_4mp     Amp            A4          A        mp
A_4pm     Apm            A4          A        pm
A_4pp     App            A4          A        pp
A_5mm     Amm            A5          A        mm
A_5mp     Amp            A5          A        mp
A_5pm     Apm            A5          A        pm
A_5pp     App            A5          A        pp
A_7mm     Amm            A7          A        mm
A_7mp     Amp            A7          A        mp
A_7pm     Apm            A7          A        pm
A_7pp     App            A7          A        pp
A_1mm     Amm            A1          A        mm
A_1mp     Amp            A1          A        mp
A_1pm     Apm            A1          A        pm
A_1pp     App            A1          A        pp
A_2mm     Amm            A2          A        mm
A_2mp     Amp            A2          A        mp
A_2pm     Apm            A2          A        pm
A_2pp     App            A2          A        pp
A_3mm     Amm            A3          A        mm
A_3mp     Amp            A3          A        mp
A_3pm     Apm            A3          A        pm
A_3pp     App            A3          A        pp
B_1mm     Bmm            B1          B        mm
B_1mp     Bmp            B1          B        mp
B_1pm     Bpm            B1          B        pm
B_1pp     Bpp            B1          B        pp
B_2mm     Bmm            B2          B        mm
B_2mp     Bmp            B2          B        mp
B_2pm     Bpm            B2          B        pm
B_2pp     Bpp            B2          B        pp
B_3mm     Bmm            B3          B        mm
B_3mp     Bmp            B3          B        mp
B_3pm     Bpm            B3          B        pm
B_3pp     Bpp            B3          B        pp
B_5mm     Bmm            B5          B        mm
B_5mp     Bmp            B5          B        mp
B_5pm     Bpm            B5          B        pm
B_5pp     Bpp            B5          B        pp
B_6mm     Bmm            B6          B        mm
B_6mp     Bmp            B6          B        mp
B_6pm     Bpm            B6          B        pm
B_6pp     Bpp            B6          B        pp