# Varimax Rotation for Tucker3 and Tucker2 Performs varimax rotation of the core and component matrix rotations to simple structure. ```r varimcoco(A, B, C, H, wa_rel, wb_rel, wc_rel, rot1, rot2, rot3, nanal) ``` ## Arguments - `A`: Columnwise orthomornal component matrix for the `A`-mode - `B`: Columnwise orthomornal component matrix for the `B`-mode - `C`: Columnwise orthomornal component matrix for the `C`-mode - `H`: Matricized core array (frontal slices) - `wa_rel`: relative weight (>=0) for the simplicity of `A` - `wb_rel`: relative weight (>=0) for the simplicity of `B` - `wc_rel`: relative weight (>=0) for the simplicity of `C` - `rot1`: binary indicator (1 if the `A`-mode is rotated, 0 otherwise, default 1) - `rot2`: binary indicator (1 if the `B`-mode is rotated, 0 otherwise, default 1) - `rot3`: binary indicator (1 if the `C`-mode is rotated, 0 otherwise, default 1) - `nanal`: Number of random starts, default 5 ## Returns A list including the following components: - **AS**: Rotated component matrix for the `A`-mode - **BT**: Rotated component matrix for the `B`-mode - **CU**: Rotated component matrix for the `C`-mode - **K**: Rotated matricized core array (frontal slices) - **S**: Rotation matrix for the `A`-mode - **T**: Rotation matrix for the `B`-mode - **U**: Rotation matrix for the `C`-mode - **f**: Best solution for three-way orthomax function value - **f1**: Varimax value of `H` - **f2a**: Varimax value of `AS` - **f2b**: Varimax value of `BT` - **f2c**: Varimax value of `CU` - **func**: Function values upon convergence for all the runs of the orthomax algorithm ## Note The simplicity values `f1`, `f2a`, `f2b`, `f2c` are based on natural weigths and therefore comparable across matrices. When multiplied by the relative weights, they give the contribution to the overall simplicity value (they are `I^2/p`, `J^2/q` or `K^2/r`, respectively, times the sum of the variances of squared values). ## References H.A.L. Kiers (1998). Joint orthomax rotation of the core and component matrices resulting from three-mode principal components analysis. **Journal of Classification 15:245--263**. ## Author(s) Maria Antonietta Del Ferraro mariaantonietta.delferraro@yahoo.it Henk A.L. Kiers h.a.l.kiers@rug.nl Paolo Giordani paolo.giordani@uniroma1.it ## See Also `orthmax2`, `varim` ## Examples ```r data(Bus) # T3 solution BusT3 <- T3funcrep(Bus, 7, 5, 37, 2, 2, 2, 0, 1e-6) # Simplicity of A (with weight = 2.5), B (with weight = 2) and C (with weight = 1.5) T3vmABC <- varimcoco(BusT3$A, BusT3$B, BusT3$C, BusT3$H, 2.5, 2, 1.5) # Simplicity of only A (with weight = 2.5) and B (with weight = 2) # rot3=0; the value of wc_rel (= 0) does not play an active role T3vmAB <- varimcoco(BusT3$A, BusT3$B, BusT3$C, BusT3$H, 2.5, 2, 0, 1, 1, 0) # simplicity repeatedly with different relative weights for A, B and C T3vm <- list() weight.a <- c(1, 3, 6) weight.b <- c(0, 2, 5) weight.c <- c(1, 4) i <- 1 for (wa_rel in weight.a){ for (wb_rel in weight.b){ for (wc_rel in weight.c){ T3vm[[i]] <- varimcoco(BusT3$A, BusT3$B, BusT3$C, BusT3$H, wa_rel, wb_rel, wc_rel) i <- i+1 } } } ```

varimcoco function