# Bin-Samples Strategic Knot Indices Breaks the predictor domain into a user-specified number of disjoint subregions, and randomly samples a user-specified number of observations from each (nonempty) subregion. ```r binsamp(x,xrng=NULL,nmbin=11,nsamp=1,alg=c("new","old")) ``` ## Arguments - `x`: Matrix of predictors $\mathbf{X}=\{x_{ij}\}_{n \times p}$ where $n$ is the number of observations, and $p$ is the number of predictors. - `xrng`: Optional matrix of predictor ranges: $\mathbf{R}=\{r_{kj}\}_{2 \times p}$ where $r_{1j}=\min_{i}x_{ij}$ and $r_{2j}=\max_{i}x_{ij}$. - `nmbin`: Vector $\mathbf{b}=(b_{1},\ldots,b_{p})'$, where $b_{j}\geq1$ is the number of marginal bins to use for the $j$-th predictor. If `length(nmbin) ## Note The number of returned knots will depend on the distribution of the covariate scores. The maximum number of possible bin-sampled knots is $s\prod_{j=1}^{p}b_{j}$, but fewer knots will be returned if one (or more) of the bins is empty (i.e., if there is no data in one or more bins). ## Warnings If $x_{ij}$ is nominal with $g$ levels, the function requires $b_{j}=g$ and $x_{ij}\in\{1,\ldots,g\}$ for $i\in\{1,\ldots,n\}$. ## Examples ```r ########## EXAMPLE 1 ########## # create 2-dimensional predictor (both continuous) set.seed(123) xmat <- cbind(runif(10^6),runif(10^6)) # Default use: # 10 marginal bins for each predictor # sample 1 observation from each subregion xind <- binsamp(xmat) # get the corresponding knots bknots <- xmat[xind,] # compare to randomly-sampled knots rknots <- xmat[sample(1:(10^6),100),] par(mfrow=c(1,2)) plot(bknots,main="bin-sampled") plot(rknots,main="randomly sampled") ########## EXAMPLE 2 ########## # create 2-dimensional predictor (continuous and nominal) set.seed(123) xmat <- cbind(runif(10^6),sample(1:3,10^6,replace=TRUE)) # use 10 marginal bins for x1 and 3 marginal bins for x2 # and sample one observation from each subregion xind <- binsamp(xmat,nmbin=c(10,3)) # get the corresponding knots bknots <- xmat[xind,] # compare to randomly-sampled knots rknots <- xmat[sample(1:(10^6),30),] par(mfrow=c(1,2)) plot(bknots,main="bin-sampled") plot(rknots,main="randomly sampled") ########## EXAMPLE 3 ########## # create 3-dimensional predictor (continuous, continuous, nominal) set.seed(123) xmat <- cbind(runif(10^6),runif(10^6),sample(1:2,10^6,replace=TRUE)) # use 10 marginal bins for x1 and x2, and 2 marginal bins for x3 # and sample one observation from each subregion xind <- binsamp(xmat,nmbin=c(10,10,2)) # get the corresponding knots bknots <- xmat[xind,] # compare to randomly-sampled knots rknots <- xmat[sample(1:(10^6),200),] par(mfrow=c(2,2)) plot(bknots[1:100,1:2],main="bin-sampled, x3=1") plot(bknots[101:200,1:2],main="bin-sampled, x3=2") plot(rknots[rknots[,3]==1,1:2],main="randomly sampled, x3=1") plot(rknots[rknots[,3]==2,1:2],main="randomly sampled, x3=2") ```

binsamp function