# Prediction for a new observation using parameters estimated by the `GLSME` function The function takes parameters estimated by the `GLSME` function and predicts the response for a new observation of predictors. It also returns confidence intervals on the prediction. The function is still under development. ```r GLSME.predict(xo, glsme.estimate, vy, vx, alpha = 0.95) ``` ## Arguments - `xo`: The new observed predictors. In a intercept is in the model then a 1 has to be included for it. - `glsme.estimate`: The output of the `GLSME` function. Has to have format `"long"`. - `vy`: Residual variance, both biological and measurement error. - `vx`: Biological variance in predictor, NOT observation variance of predictor. If there is a predictor in the model then a 0 row and column have to included for it. - `alpha`: Level for confidence interval. ## Returns - **BiasCorr**: Prediction using the bias corrected estimate. * predictionPredicted value * MSEEstimate of mean square error. They are calculated by the formula $$ v_{y}+x_{o}^{T}(MSE[\beta | XO])x_{o}+ \beta'^{T} v_{x} \beta', $$ where $\beta'$ is the bias corrected estimate of $\beta$. * CI$1-\alpha$ level confidence intervals. They are calculated by the formula $$ \sqrt{1+1/n}*t_{\alpha}*(v_{y}+ \beta'^{T} v_{x} \beta'), $$ where $t_{\alpha}$ is the $1-\alpha/2$ level quantile of the t-distribution with n-k degrees of freedom, k is the number of regression parameters to estimate, $\beta'$ is the bias corrected estimate of $\beta$ and n is the sample size used in the estimation. - **BiasUncorr**: Prediction using the bias uncorrected estimate. * predictionPredicted value * MSEEstimate of mean square error. They are calculated by the formula $$ v_{y}+x_{o}^{T}(MSE[\beta | XO])x_{o}+ \beta'^{T} v_{x} \beta', $$ where $\beta'$ is the bias uncorrected estimate of $\beta$. * CI$1-\alpha$ level confidence intervals. They are calculated by the formula $$ \sqrt{1+1/n}*t_{\alpha}*(v_{y}+ \beta'^{T} v_{x} \beta'), $$ where $t_{\alpha}$ is the $1-\alpha/2$ level quantile of the t-distribution with n-k degrees of freedom, k is the number of regression parameters to estimate, $\beta'$ is the bias uncorrected estimate of $\beta$ and n is the sample size used in the estimation. ## References Hansen, T.F. and Bartoszek, K. (2012) Interpreting the evolutionary regression: the interplay between observational and biological errors in phylogenetic comparative studies. Systematic Biology 61(3):413-425. ## Author(s) Krzysztof Bartoszek ## Examples ```r set.seed(12345) n<-3 ## number of species apetree<-ape::rtree(n) ### Define Brownian motion parameters to be able to simulate data under the Brownian motion model. BMparameters<-list(vX0=matrix(0,nrow=2,ncol=1),Sxx=rbind(c(1,0),c(0.2,1))) ### Now simulate the data and remove the values corresponding to the internal nodes. xydata<-mvSLOUCH::simulBMProcPhylTree(apetree,X0=BMparameters$vX0,Sigma=BMparameters$Sxx) xydata<-xydata[(nrow(xydata)-n+1):nrow(xydata),] x<-xydata[,1] y<-xydata[,2] yerror<-diag((stats::rnorm(n,mean=0,sd=0.1))^2) #create error matrix y<-mvtnorm::rmvnorm(1,mean=y,sigma=yerror)[1,] xerror<-diag((stats::rnorm(n,mean=0,sd=0.1))^2) #create error matrix x<-mvtnorm::rmvnorm(1,mean=x,sigma=xerror)[1,] glsme.res<-GLSME(y=y, CenterPredictor=TRUE, D=cbind(rep(1, n), x), Vt=ape::vcv(apetree), Ve=yerror, Vd=list("F",ape::vcv(apetree)), Vu=list("F", xerror),OutputType="long") GLSME.predict(c(1,1), glsme.res, vy=1, vx=rbind(c(0,0),c(0,1))) ```

GLSME.predict function