# Coordinate representation of a compositional cube and of a sample of compositional cubes cubeCoord computes a system of orthonormal coordinates of a compositional cube. Computation of either pivot coordinates or a coordinate system based on the given SBP is possible. Wrapper (cubeCoordWrapper): For each compositional cube in the sample cubeCoordWrapper computes a system of orthonormal coordinates and provide a simple descriptive analysis. Computation of either pivot coordinates or a coordinate system based on the given SBP is possible. ```r cubeCoord( x, row.factor = NULL, col.factor = NULL, slice.factor = NULL, value = NULL, SBPr = NULL, SBPc = NULL, SBPs = NULL, pivot = FALSE, print.res = FALSE ) cubeCoordWrapper( X, obs.ID = NULL, row.factor = NULL, col.factor = NULL, slice.factor = NULL, value = NULL, SBPr = NULL, SBPc = NULL, SBPs = NULL, pivot = FALSE, test = FALSE, n.boot = 1000 ) ``` ## Arguments - `x`: a data frame containing variables representing row, column and slice factors of the respective compositional cube and variable with the values of the composition. - `row.factor`: name of the variable representing the row factor. Needs to be stated with the quotation marks. - `col.factor`: name of the variable representing the column factor. Needs to be stated with the quotation marks. - `slice.factor`: name of the variable representing the slice factor. Needs to be stated with the quotation marks. - `value`: name of the variable representing the values of the composition. Needs to be stated with the quotation marks. - `SBPr`: an $I-1\times I$ array defining the sequential binary partition of the values of the row factor, where I is the number of the row factor levels. The values assigned in the given step to the + group are marked by 1, values from the - group by -1 and the rest by 0. If it is not provided, the pivot version of coordinates is constructed automatically. - `SBPc`: an $J-1\times J$ array defining the sequential binary partition of the values of the column factor, where J is the number of the column factor levels. The values assigned in the given step to the + group are marked by 1, values from the - group by -1 and the rest by 0. If it is not provided, the pivot version of coordinates is constructed automatically. - `SBPs`: an $K-1\times K$ array defining the sequential binary partition of the values of the slice factor, where K is the number of the slice factor levels. The values assigned in the given step to the + group are marked by 1, values from the - group by -1 and the rest by 0. If it is not provided, the pivot version of coordinates is constructed automatically. - `pivot`: logical, default is FALSE. If TRUE, or one of the SBPs is not defined, its pivot version is used. - `print.res`: logical, default is FALSE. If TRUE, the output is displayed in the Console. - `X`: a data frame containing variables representing row, column and slice factors of the respective compositional cubes, variable with the values of the composition and variable distinguishing the observations. - `obs.ID`: name of the variable distinguishing the observations. Needs to be stated with the quotation marks. - `test`: logical, default is FALSE. If TRUE, the bootstrap analysis of coordinates is provided. - `n.boot`: number of bootstrap samples. ## Returns - **Coordinates**: an array of orthonormal coordinates. - **Grap.rep**: graphical representation of the coordinates. Parts denoted by + form the groups in the numerator of the respective computational formula, parts - form the denominator and parts . are not involved in the given coordinate. - **Row.balances**: an array of row balances. - **Column.balances**: an array of column balances. - **Slice.balances**: an array of slice balances. - **Row.column.OR**: an array of row-column OR coordinates. - **Row.slice.OR**: an array of row-slice OR coordinates. - **Column.slice.OR**: an array of column-slice OR coordinates. - **Row.col.slice.OR**: an array of coordinates describing the mutual interaction between all three factors. - **Contrast.matrix**: contrast matrix. - **Log.ratios**: an array of pure log-ratios between groups of parts without the normalizing constant. - **Coda.cube**: cube form of the given composition. - **Bootstrap**: array of sample means, standard deviations and bootstrap confidence intervals. - **Cubes**: Cube form of the given compositions. ## Details cubeCoord This transformation moves the IJK-part compositional cubes from the simplex into a (IJK-1)-dimensional real space isometrically with respect to its three-factorial nature. Wrapper (cubeCoordWrapper): Each of n IJK-part compositional cubes from the sample is with respect to its three-factorial nature isometrically transformed from the simplex into a (IJK-1)-dimensional real space. Sample mean values and standard deviations are computed and using bootstrap an estimate of 95 % confidence interval is given. ## Examples ```r ################### ### Coordinate representation of a CoDa Cube ## Not run: ### example from Fa\v cevicov\'a (2019) data(employment2) CZE <- employment2[which(employment2$Country == 'CZE'), ] # pivot coordinates cubeCoord(CZE, "Sex", 'Contract', "Age", 'Value') # coordinates with given SBP r <- t(c(1,-1)) c <- t(c(1,-1)) s <- rbind(c(1,-1,-1), c(0,1,-1)) cubeCoord(CZE, "Sex", 'Contract', "Age", 'Value', r,c,s) ## End(Not run) ################### ### Analysis of a sample of CoDa Cubes ## Not run: ### example from Fa\v cevicov\'a (2019) data(employment2) ### Compositional tables approach, ### analysis of the relative structure. ### An example from Facevi\v cov\'a (2019) # pivot coordinates cubeCoordWrapper(employment2, 'Country', 'Sex', 'Contract', 'Age', 'Value', test=TRUE) # coordinates with given SBP (defined in the paper) r <- t(c(1,-1)) c <- t(c(1,-1)) s <- rbind(c(1,-1,-1), c(0,1,-1)) res <- cubeCoordWrapper(employment2, 'Country', 'Sex', 'Contract', "Age", 'Value', r,c,s, test=TRUE) ### Classical approach, ### generalized linear mixed effect model. library(lme4) employment2$y <- round(employment2$Value*1000) glmer(y~Sex*Age*Contract+(1|Country),data=employment2,family=poisson) ### other relations within cube (in the log-ratio form) ### e.g. ratio between women and man in the group FT, 15to24 ### and ratio between age groups 15to24 and 55plus # transformation matrix T <- rbind(c(1,rep(0,5), -1, rep(0,5)), c(rep(c(1/4,0,-1/4), 4))) T %*% t(res$Contrast.matrix) %*%res$Bootstrap[,1] ## End(Not run) ``` ## References Facevicova, K., Filzmoser, P. and K. Hron (2019) Compositional Cubes: Three-factorial Compositional Data. Under review. ## See Also `tabCoord` `tabCoordWrapper` ## Author(s) Kamila Facevicova

cubeCoord function