# Univariate P-spline smoothing Univariate P-spline smoothing with the smoothing parameter selected by leave-one-subject-out cross validation. ```r pspline(data, argvals.new = NULL, knots = 35, p = 3, m = 2, lambda = NULL, search.length = 100, lower = -20, upper = 20) ``` ## Arguments - `data`: a data frame with three arguments: (1) `argvals`: observation times; (2) `subj`: subject indices; (3) `y`: values of observations. Missing values not allowed. - `argvals.new`: a vector of observations times for prediction; if NULL, then the same as `data$argvals`. - `knots`: a vector of interior knots or the number of knots for B-spline basis functions to be used; defaults to 35. - `p`: the degrees of B-splines; defaults to 3. - `m`: the order of differencing penalty; defaults to 2. - `lambda`: the value of the smoothing parameter; defaults to NULL. - `search.length`: the number of equidistant (log scale) smoothing parameters to search; defaults to 100. - `lower, upper`: bounds for log smoothing parameter; defaults are -20 and 20. ## Details The function is an implementation of the P-spline smoothing in Eilers and Marx (1996). P-splines uses B-splines as basis functions and employs a differencing penalty on the coefficients. Leave-one-subject-out cross validation is used for selecting the smoothing parameter and a fast algorithm is implemented. ## Returns - **fitted.values**: Fitted mean values - **B**: B-spline design matrix - **theta**: Estimated coefficients - **s**: Eigenvalues - **knots**: Knots - **p**: The degrees of B-splines - **m**: The order of differencing penalty - **lambda**: The value of the smoothing parameter - **argvals.new**: A vector of observations times - **mu.new**: Fitted mean values at `argvals.new` ## References Paul Eilers and Brian Marx, Flexible smoothing with B-splines and penalties, Statist. Sci., 11, 89-121, 1996. Luo Xiao, Cai Li, William Checkley and Ciprian Crainiceanu, Fast covariance estimation for sparse functional data, Stat. Comput., tools:::Rd_expr_doi("10.1007/s11222-017-9744-8") . ## Author(s) Luo Xiao ## See Also `gam` in `mgcv`. ## Examples ```r ## Not run: ## cd4 data require(refund) data(cd4) n <- nrow(cd4) T <- ncol(cd4) id <- rep(1:n,each=T) t <- rep(-18:42,times=n) y <- as.vector(t(cd4)) sel <- which(is.na(y)) ## organize data data <- data.frame(y=log(y[-sel]), argvals = t[-sel], subj = id[-sel]) data <- data[data$y>4.5,] ## smooth fit <- pspline(data) ## plot plot(data$argvals,fit$mu.new,type="p") ## prediction pred <- predict(fit,quantile(data$argvals,c(0.2,0.6))) pred ## End(Not run) ```

pspline function