# Generalized partial linear model Fits a generalized partial linear model (kernel-based) using the (generalized) Speckman estimator or backfitting (in the generalized case combined with local scoring) for two additive component functions. ```r kgplm(x, t, y, h, family, link, b.start=NULL, m.start=NULL, grid = NULL, offset = 0, method = "speckman", sort = TRUE, weights = 1, weights.trim = 1, weights.conv = 1, max.iter = 25, eps.conv = 1e-8, kernel = "biweight", kernel.product = TRUE, verbose = FALSE) ``` ## Arguments - `x`: n x p matrix, data for linear part - `y`: n x 1 vector, responses - `t`: n x q matrix, data for nonparametric part - `h`: scalar or 1 x q, bandwidth(s) - `family`: text string, family of distributions (e.g. "gaussian" or "bernoulli", see details for `glm.ll`) - `link`: text string, link function (depending on family, see details for `glm.ll`) - `b.start`: p x 1 vector, start values for linear part - `m.start`: n x 1 vector, start values for nonparametric part - `grid`: m x q matrix, where to calculate the nonparametric function (default = t) - `offset`: offset - `method`: "speckman" or "backfit" - `sort`: logical, TRUE if data need to be sorted - `weights`: binomial weights - `weights.trim`: trimming weights for fitting the linear part - `weights.conv`: weights for convergence criterion - `max.iter`: maximal number of iterations - `eps.conv`: convergence criterion - `kernel`: text string, see `kernel.function` - `kernel.product`: (if p>1) product or spherical kernel - `verbose`: print additional convergence information ## Returns List with components: - **b**: p x 1 vector, linear coefficients - **b.cov**: p x p matrix, linear coefficients - **m**: n x 1 vector, nonparametric function estimate - **m.grid**: m x 1 vector, nonparametric function estimate on grid - **it**: number of iterations - **deviance**: deviance - **df.residual**: approximate degrees of freedom (residuals) - **aic**: Akaike's information criterion ## References Mueller, M. (2001). Estimation and testing in generalized partial linear models -- A comparative study. **Statistics and Computing**, 11:299--309. Hastie, T. and Tibshirani, R. (1990). **Generalized Additive Models**. London: Chapman and Hall. ## Author(s) Marlene Mueller ## See Also `kernel.function`, `kreg` ## Examples ```r ## data n <- 1000; b <- c(1,-1); rho <- 0.7 m <- function(t){ 1.5*sin(pi*t) } x1 <- runif(n,min=-1,max=1); u <- runif(n,min=-1,max=1) t <- runif(n,min=-1,max=1); x2 <- round(m(rho*t + (1-rho)*u)) x <- cbind(x1,x2) y <- x %*% b + m(t) + rnorm(n) ## partial linear model (PLM) gh <- kgplm(x,t,y,h=0.25,family="gaussian",link="identity") o <- order(t) plot(t[o],m(t[o]),type="l",col="green") lines(t[o],gh$m[o]); rug(t) ## partial linear probit model (GPLM) y <- (y>0) gh <- kgplm(x,t,y,h=0.25,family="bernoulli",link="probit") o <- order(t) plot(t[o],m(t[o]),type="l",col="green") lines(t[o],gh$m[o]); rug(t) ## data with two-dimensional m-function n <- 1000; b <- c(1,-1); rho <- 0.7 m <- function(t1,t2){ 1.5*sin(pi*t1)+t2 } x1 <- runif(n,min=-1,max=1); u <- runif(n,min=-1,max=1) t1 <- runif(n,min=-1,max=1); t2 <- runif(n,min=-1,max=1) x2 <- round( m( rho*t1 + (1-rho)*u , t2 ) ) x <- cbind(x1,x2); t <- cbind(t1,t2) y <- x %*% b + m(t1,t2) + rnorm(n) ## partial linear model (PLM) grid1 <- seq(min(t[,1]),max(t[,1]),length=20) grid2 <- seq(min(t[,2]),max(t[,2]),length=25) grid <- create.grid(list(grid1,grid2)) gh <- kgplm(x,t,y,h=0.5,grid=grid,family="gaussian",link="identity") o <- order(grid[,2],grid[,1]) est.m <- (matrix(gh$m.grid[o],length(grid1),length(grid2))) orig.m <- outer(grid1,grid2,m) par(mfrow=c(1,2)) persp(grid1,grid2,orig.m,main="Original Function", theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5) persp(grid1,grid2,est.m,main="Estimated Function", theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5) par(mfrow=c(1,1)) ```

kgplm function