# Perform an I-spline regression Evaluates the I-splines for all variables of a data frame of predictor variables, and perform a generalised linear regression with constraint on the parameters. ```r Reg.ispline( response, predictor, order.ispline = 2, kn.ispline = 1, family = stats::gaussian(), method.glm = "glm.fit.cons", cons = 1, cons.inter = 1, control = list(), Plot = TRUE, lty = NULL, lwd = 1 ) ``` ## Arguments - `response`: A vector of numeric values representing the response variable. - `predictor`: A data frame of numeric variables representing the predictors. - `order.ispline`: Order of the I-spline. - `kn.ispline`: Number of knots in the I-spline. - `family`: A description of the error distribution and link function to be used in the `glm` model (see `family` in package `stats` for details of family functions). - `method.glm`: Method used in fitting the generalised linear model. The default method "glm.fit.cons" is an adaptation of method `glm.fit2` from package `glm2` using a constrained least squares regression in the reweighted least squares. Another option is "glm.fit2", which calls `glm.fit2`; see help documentation for glm.fit2 in package `glm2`. - `cons`: type of constraint in the glm if `method.glm = "glm.fit.cons"`. Default is 1 for positive coefficients on the predictors. The other option is -1 for negative coefficients on the predictors. - `cons.inter`: type of constraint for the intercept. Default is 1 for positive intercept, suitable for Gaussian family. The other option is -1 for negative intercept, suitable for binomial family. - `control`: As for `glm`. - `Plot`: Boolean value indicating if the I-splines must be plotted. - `lty`: Line types to be used in the plotting. If nothing is provided, `lty` is a sequence of integers from 1 to the number of variables used for the computation of `msgdm`. - `lwd`: Line width. ## Returns `Reg.ispline` returns a list of the following elements: - **splines**: A data frame in which each columns contains the value resulting from the transformation of the predictors into individual I-splines. The number of columns of `splines` is the number of predictors times the number of splines (determined as the sum of `order.ispline` and `kn.ispline`). - **spline**: A data frame in which each columns contains the value resulting from the combinations of the individual I-splines. This combination is obtained by multiplying the coefficients of `model` and the values of the individual I-splines `splines`. - **model**: A `glm` model using `response` as the response variable, and `splines` as the predictors. ## Details `Reg.ispline` performs a non-linear regression using a combination of GLM and I-splines. It can, for example, be used to compare regression outputs when using MS-GDM with I-splines on environmental variables and biotic variables as in `Zetya.msgdm` to the same regression approach without environmental variables. ## Examples ```r utils::data(Marion.species) xy.marion <- Marion.species[1:2] data.spec.marion <- Marion.species[3:33] ##random other communities data.spec.marion2a <- data.spec.marion data.spec.marion2a[which(data.spec.marion2a==1,arr.ind=TRUE)] <- 0 for(i in 1:ncol(data.spec.marion2a)) data.spec.marion2a[sample(nrow(data.spec.marion2a),8),i] <- 1 data.spec.marion2b <- data.spec.marion data.spec.marion2b[which(data.spec.marion2b==1,arr.ind=TRUE)] <- 0 for(i in 1:ncol(data.spec.marion2b)) data.spec.marion2b[sample(nrow(data.spec.marion2b),8),i] <- 1 dat.spec.tot <- list(data.spec.marion,data.spec.marion2a,data.spec.marion2b) zeta.tot <- Zeta.order.mc.mult(data.spec=dat.spec.tot,order=3,sam=200) zeta.splines <- Ispline(zeta.tot$zeta.val[,2:3]) data.tot <- data.frame(zeta.val=zeta.tot$zeta.val[,1],zeta.splines$splines) dev.new() Reg.ispline(response = zeta.tot$zeta.val[,1], predictor = zeta.tot$zeta.val[,2:3], lwd=2, cons=1) ``` ## References Ramsay, J. O. (1988). Monotone regression splines in action. **Statistical Science**, 425-441. ## See Also `Zeta.msgdm`,`Ispline`

Reg.ispline function