Description Usage Arguments Details Value Author(s) See Also Examples
Predicted values and standard errors based on krls model object.
1 2 
object 
Fitted KRLS model, i.e. an object of class 
newdata 
A data frame or matrix with variables values at which to predict the outcome. Number and order of columns in 
se.fit 
logical flag if standard errors should be computed for pointwise predictions. 
... 
additional arguments affecting the predictions produced. 
Function produces predicted values, obtained by evaluating the fitted krls function with the newdata (ie. the test points). The prediction at a new test point x_i is based on
f(x_i)= sum_j=1^n c_j K_{x_j}(x_i)
where K is the kernel matrix and thus K_{x_j}
is a vector whose jth entry is K(x_j,x_i) (e.g. the distance between the test point x_i and the training point x_j). The training points are passed to the function with the krls fit in object
.
When data are missing in newdata
during prediction, the value of each k(x_i,x_j) is computed by using an adjusted Euclidean distance in the kernel definition. Assume x is Ddimensional but a given pair of observations x_i and x_j have only D' < D nonmissing dimensions in common. The adjusted Euclidean distance computes the sum of squared differences over the D' nonmissing dimensions, rescales this sum by D/D', and takes the square root. The result corresponds to an assumption that conditional on the observed data, the missing values would not have contributed new information predictive of the outcome.
fit 
M by 1 vector of fitted values for M test points. 
se.fit 
M by 1 vector of standard errors for the fitted values for M test points ( 
vcov.fit 
M by M variancecovariance matrix for the fitted values for M test points ( 
newdata 
M by D data matrix of of M test points with D predictors. 
newdataK 
M by N data matrix for pairwise Gauss Kernel distances between M test points and N training points from krls model fit in 
Jens Hainmueller (Stanford) and Chad Hazlett (MIT)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  # make up data
X < seq(3,3,.1)
Y < sin(X) + rnorm(length(X),.1)
# fit krls
krlsout < krls(y=Y,X=X)
# get insample prediction
predin < predict(krlsout,newdata=X,se.fit=TRUE)
# get outofsample prediction
X2 < runif(5)
predout < predict(krlsout,newdata=X2,se.fit=TRUE)
# plot true function and predictions
plot(y=sin(X),x=X,type="l",col="red",ylim=c(1.8,1.8),lwd=2,ylab="f(X)")
points(y=predin$fit,x=X,col="blue",pch=19)
arrows(y1=predin$fit+2*predin$se.fit,
y0=predin$fit2*predin$se.fit,
x1=X,x0=X,col="blue",length=0)
points(y=predout$fit,x=X2,col="green",pch=17)
arrows(y1=predout$fit+2*predout $se.fit,
y0=predout$fit2*predout $se.fit,
x1=X2,x0=X2,col="green",length=0)
legend("bottomright",
legend=c("true f(x)=sin(X)",
"KRLS fitted insample",
"KRLS fitted outofsample"),
lty=c(1,NA,NA),pch=c(NA,19,17),
lwd=c(2,NA,NA),
col=c("red","blue","green"),
cex=.8)

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