# Convert a smooth to a form suitable for estimating as random effect A generic function for converting `mgcv` smooth objects to forms suitable for estimation as random effects by e.g. `lme`. Exported mostly for use by other package developers. ```r smooth2random(object,vnames,type=1) ``` ## Arguments - `object`: an `mgcv` smooth object. - `vnames`: a vector of names to avoid as dummy variable names in the random effects form. - `type`: `1` for `lme`, otherwise `lmer`. ## Details There is a duality between smooths and random effects which means that smooths can be estimated using mixed modelling software. This function converts standard `mgcv` smooth objects to forms suitable for estimation by `lme`, for example. A service routine for `gamm` exported for use by package developers. See examples for creating prediction matrices for new data, corresponding to the random and fixed effect matrices returned when `type=2`. ## Returns A list. - **rand**: a list of random effects, including grouping factors, and a fixed effects matrix. Grouping factors, model matrix and model matrix name attached as attributes, to each element. Alternatively, for `type=2` a list of random effect model matrices, each corresponding to an i.i.d. Gaussian random effect with a single variance component. - **trans.D**: A vector, trans.D, that transforms coefs, in order [rand1, rand2,... fix] back to original parameterization. If null, then taken as vector of ones. `b.original = trans.U %*% (trans.D*b.fit)`. - **trans.U**: A matrix, trans.U, that transforms coefs, in order [rand1, rand2,... fix] back to original parameterization. If null, then not needed. If null then taken as identity. - **Xf**: A matrix for the fixed effects, if any. - **fixed**: `TRUE/FALSE`, indicating if term was unpenalized or not. If unpenalized then other stuff may not be returned (it's not a random effect). - **rind**: an index vector such that if br is the vector of random coefficients for the term, br[rind] is the coefs in order for this term. - **pen.ind**: index of which penalty penalizes each coefficient: 0 for unpenalized. ## References Wood S.N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). Chapman and Hall/CRC Press. ## Author(s) Simon N. Wood simon.wood@r-project.org . ## See Also `gamm` ## Examples ```r ## Simple type 1 'lme' style... library(mgcv) x <- runif(30) sm <- smoothCon(s(x),data.frame(x=x))[[1]] smooth2random(sm,"") ## Now type 2 'lme4' style... z <- runif(30) dat <- data.frame(x=x,z=z) sm <- smoothCon(t2(x,z),dat)[[1]] re <- smooth2random(sm,"",2) str(re) ## For prediction after fitting we might transform parameters back to ## original parameterization using 'rind', 'trans.D' and 'trans.U', ## and call PredictMat(sm,newdata) to get the prediction matrix to ## multiply these transformed parameters by. ## Alternatively we could obtain fixed and random effect Prediction ## matrices corresponding to the results from smooth2random, which ## can be used with the fit parameters without transforming them. ## The following shows how... s2rPred <- function(sm,re,data) { ## Function to aid prediction from smooths represented as type==2 ## random effects. re must be the result of smooth2random(sm,...,type=2). X <- PredictMat(sm,data) ## get prediction matrix for new data ## transform to r.e. parameterization if (!is.null(re$trans.U)) X <- X%*%re$trans.U X <- t(t(X)*re$trans.D) ## re-order columns according to random effect re-ordering... X[,re$rind] <- X[,re$pen.ind!=0] ## re-order penalization index in same way pen.ind <- re$pen.ind; pen.ind[re$rind] <- pen.ind[pen.ind>0] ## start return object... r <- list(rand=list(),Xf=X[,which(re$pen.ind==0),drop=FALSE]) for (i in 1:length(re$rand)) { ## loop over random effect matrices r$rand[[i]] <- X[,which(pen.ind==i),drop=FALSE] attr(r$rand[[i]],"s.label") <- attr(re$rand[[i]],"s.label") } names(r$rand) <- names(re$rand) r } ## s2rPred ## use function to obtain prediction random and fixed effect matrices ## for first 10 elements of 'dat'. Then confirm that these match the ## first 10 rows of the original model matrices, as they should... r <- s2rPred(sm,re,dat[1:10,]) range(r$Xf-re$Xf[1:10,]) range(r$rand[[1]]-re$rand[[1]][1:10,]) ```

smooth2random function