# PRIM for multivariate data PRIM for multivariate data. ```r prim.box(x, y, box.init=NULL, peel.alpha=0.05, paste.alpha=0.01, mass.min=0.05, threshold, pasting=TRUE, verbose=FALSE, threshold.type=0, y.fun=mean) prim.hdr(prim, threshold, threshold.type, y.fun=mean) prim.combine(prim1, prim2, y.fun=mean) ``` ## Arguments - `x`: matrix of data values - `y`: vector of response values - `y.fun`: function applied to response y. Default is mean. - `box.init`: initial covering box - `peel.alpha`: peeling quantile tuning parameter - `paste.alpha`: pasting quantile tuning parameter - `mass.min`: minimum mass tuning parameter - `threshold`: threshold tuning parameter(s) - `threshold.type`: threshold direction indicator: 1 = ">= threshold", -1 = "<= threshold", 0 = ">= threshold[1] & <= threshold[2]" - `pasting`: flag for pasting - `verbose`: flag for printing output during execution - `prim,prim1,prim2`: objects of type `prim` ## Details The data are c("$(X_1, Y_1), \\ldots,\n$", "$ (X_n, Y_n)$") where $X_i$ is d-dimensional and $Y_i$ is a scalar response. PRIM finds modal (and/or anti-modal) regions in the conditional expectation $m(x) = E(Y | x).$ In general, $Y_i$ can be real-valued. See `vignette("prim")`. Here, we focus on the special case for binary $Y_i$. Let $Y_i$ = 1 when $X_i ~ F+$; and $Y_i$ = -1 when $X_i ~ F-$ where $F+$ and $F-$ are different distribution functions. In this set-up, PRIM finds the regions where $F+$ and $F-$ are most different. The tuning parameters `peel.alpha` and `paste.alpha` control the `patience' of PRIM. Smaller values involve more patience. Larger values less patience. The peeling steps remove data from a box till either the box mean is smaller than `threshold` or the box mass is less than `mass.min`. Pasting is optional, and is used to correct any possible over-peeling. The default values for `peel.alpha`, `paste.alpha` and `mass.min` are taken from Friedman & Fisher (1999). The type of PRIM estimate is controlled `threshold` and `threshold.type`: - **`threshold.type=1`**: search for {$m(x) >=$ `threshold`}. - **`threshold.type=-1`**: search for {$m(x) <=$ `threshold`}. - **`threshold.type=0`**: search for both {$m(x) >=$ `threshold[1]`} and {$m(x) <=$ `threshold[2]`}. There are two ways of using PRIM. One is `prim.box` with pre-specified threshold(s). This is appropriate when the threshold(s) are known to produce good estimates. On the other hand, if the user doesn't provide threshold values then `prim.box` computes box sequences which cover the data range. These can then be pruned at a later stage. `prim.hdr` allows the user to specify many different threshold values in an efficient manner, without having to recomputing the entire PRIM box sequence. `prim.combine` can be used to join the regions computed from `prim.hdr`. See the examples below. ## Returns -- `prim.box` produces a PRIM estimate, an object of type `prim`, which is a list with 8 fields: - **x**: list of data matrices - **y**: list of response variable vectors - **y.mean**: list of vectors of box mean for y - **box**: list of matrices of box limits (first row = minima, second row = maxima) - **mass**: vector of box masses (proportion of points inside a box) - **num.class**: total number of PRIM boxes - **num.hdr.class**: total number of PRIM boxes which form the HDR - **ind**: threshold direction indicator: 1 = ">= threshold", -1 = "<=threshold" The above lists have `num.class` fields, one for each box. -- `prim.hdr` takes a `prim` object and prunes it using different threshold values. Returns another `prim` object. This is much faster for experimenting with different threshold values than calling `prim.box` each time. -- `prim.combine` combines two `prim` objects into a single prim object. Usually used in conjunction with `prim.hdr`. See examples below. ## Examples ```r data(quasiflow) qf <- quasiflow[1:1000,1:2] qf.label <- quasiflow[1:1000,4] ## using only one command thr <- c(0.25, -0.3) qf.prim1 <- prim.box(x=qf, y=qf.label, threshold=thr, threshold.type=0) ## alternative - requires more commands but allows more control ## in intermediate stages qf.primp <- prim.box(x=qf, y=qf.label, threshold.type=1) ## default threshold too low, try higher one qf.primp.hdr <- prim.hdr(prim=qf.primp, threshold=0.25, threshold.type=1) qf.primn <- prim.box(x=qf, y=qf.label, threshold=-0.3, threshold.type=-1) qf.prim2 <- prim.combine(qf.primp.hdr, qf.primn) plot(qf.prim1, alpha=0.2) ## orange=x1>x2, blue x2

prim.box function