# representative_point: Computes representative point based on the coordinates of... In RADanalysis: Normalization and Study of Rank Abundance Distributions

## Description

Computes representative point based on the coordinates of points which are in the same group.

## Usage

 ```1 2``` ```representative_point(input, ids = NULL, coord_names = c(1, 2), standard_error_mean = TRUE, plot = FALSE, ...) ```

## Arguments

 `input` A matrix which contains the coordinates of samples. Usually this is the result of ordination of normalized RADs using multi-dimensional scaling (`cmdscale`). In the input matrix each row contains vector of coordinates of one sample. `ids` Vector of row numbers of the desired group, from which a representative point is going to be represented `coord_names` A vector which contains the coordintes number that should be used to create representative point. Default is `c(1,2)`. `standard_error_mean` A logical. If `TRUE`, uses the standard error of the mean and plot it with representative points. It works only if `plot = TRUE`. `plot` A logical. If `TRUE`, shows the representative points on the previous plot. `...` other graphical parameters to use for plotting. This function uses internally the functions `points` and `arrows` to plot.

## Value

A list of following parameters:

\$mean: Contains the average of points. A vector with the length of coordinates used for computing the average. These coordinates are preset in `coord_names`.

\$sd: A vector with a length similar to `mean` which contains the standard deviation for each coordinate.

\$mean_standard_error: A vector with a length similar to `mean` which contain the standard deviation of the mean for each coordinate. This vector is the result of `sd / sqrt(n)`, when n is the number of members of the group (length of `sample_ids`).

If `plot = TRUE`, representative points would be added to the previous plot.

If `standard_error_mean = TRUE`, the standard error of the mean would be added to the representative points.

`RADnormalization` for normalize an abundance vector. This function return more details compared to `RADnormalization_matrix`, `RADnormalization_matrix` for normalize an entire otutable, `representative_RAD` for study the representative of group of norm rads.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```line_cols <- c("green","red","blue") sample_classes <- c(1,1,1,1,2,2,3,3,1,1,2,3,3,1,1,2,3,3) maxrank <- 400 data("gut_nrads") nrads <- gut_nrads nrads <- nrads\$norm_matrix #distance matrix using manhattan distance d <- dist(x = nrads,method = "manhattan") #ordination using classical multi-dimensional scaling mds <- cmdscale(d = d,k = 5,eig = TRUE) #plot the points plot(mds\$points,xlab = "First coordinate",ylab = "Second coordinate",pch = 19,cex =1, col = line_cols[sample_classes], main = "MDS plot with representative points \n of each group and error bars") #add the representative points wit erorr bar to the previous plot a <- representative_point(input = mds\$points,ids = which(sample_classes == 1), col = scales::alpha(line_cols,0.5), plot = TRUE,standard_error_mean = TRUE,pch = 19, cex = 4) a <- representative_point(input = mds\$points,ids = which(sample_classes == 2), col = scales::alpha(line_cols,0.5), plot = TRUE,standard_error_mean = TRUE,pch = 19, cex = 4) a <- representative_point(input = mds\$points,ids = which(sample_classes == 3), col = scales::alpha(line_cols,0.5), plot = TRUE,standard_error_mean = TRUE,pch = 19, cex = 4) legend("bottomleft",bty = "n",legend = c("pre Cp","under Cp","post Cp"), col = line_cols,pch = 19) ```