# Visually checking a fitted quantile model Given an additive quantile model, fitted using `qgam`, `cqcheck` provides some plots that allow to check what proportion of responses, `y`, falls below the fitted quantile. ```r cqcheck( obj, v, X = NULL, y = NULL, nbin = c(10, 10), bound = NULL, lev = 0.05, scatter = FALSE, ... ) ``` ## Arguments - `obj`: the output of a `qgam` call. - `v`: if a 1D plot is required, `v` should be either a single character or a numeric vector. In the first case `v` should be the names of one of the variables in the dataframe `X`. In the second case, the length of `v` should be equal to the number of rows of `X`. If a 2D plot is required, `v` should be either a vector of two characters or a matrix with two columns. - `X`: a dataframe containing the data used to obtain the conditional quantiles. By default it is NULL, in which case predictions are made using the model matrix in `obj$model`. - `y`: vector of responses. Its i-th entry corresponds to the i-th row of X. By default it is NULL, in which case it is internally set to `obj$y`. - `nbin`: a vector of integers of length one (1D case) or two (2D case) indicating the number of bins to be used in each direction. Used only if `bound==NULL`. - `bound`: in the 1D case it is a numeric vector whose increasing entries represent the bounds of each bin. In the 2D case a list of two vectors should be provided. `NULL` by default. - `lev`: the significance levels used in the plots, this determines the width of the confidence intervals. Default is 0.05. - `scatter`: if TRUE a scatterplot is added (using the `points` function). FALSE by default. - `...`: extra graphical parameters to be passed to `plot()`. ## Returns Simply produces a plot. ## Details Having fitted an additive model for, say, quantile `qu=0.4` one would expect that about 40 responses fall below the fitted quantile. This function allows to visually compare the empirical number of responses (`qu_hat`) falling below the fit with its theoretical value (`qu`). In particular, the responses are binned, which the bins being constructed along one or two variables (given be arguments `v`). Let (`qu_hat[i]`) be the proportion of responses below the fitted quantile in the ith bin. This should be approximately equal to `qu`, for every i. In the 1D case, when `v` is a single character or a numeric vector, `cqcheck` provides a plot where: the horizontal line is `qu`, the dots correspond to `qu_hat[i]` and the grey lines are confidence intervals for `qu`. The confidence intervals are based on `qbinom(lev/2, siz, qu)`, if the dots fall outside them, then `qu_hat[i]` might be deviating too much from `qu`. In the 2D case, when `v` is a vector of two characters or a matrix with two columns, we plot a grid of bins. The responses are divided between the bins as before, but now don't plot the confidence intervals. Instead we report the empirical proportions `qu_hat[i]` for the non-empty bin, and with colour the bins in red if `qu_hat[i].

cqcheck function