# GAM ordered categorical family Family for use with `gam` or `bam`, implementing regression for ordered categorical data. A linear predictor provides the expected value of a latent variable following a logistic distribution. The probability of this latent variable lying between certain cut-points provides the probability of the ordered categorical variable being of the corresponding category. The cut-points are estimated along side the model smoothing parameters (using the same criterion). The observed categories are coded 1, 2, 3, ... up to the number of categories. ```r ocat(theta=NULL,link="identity",R=NULL) ``` ## Arguments - `theta`: cut point parameter vector (dimension `R-2`). If supplied and all positive, then taken to be the cut point increments (first cut point is fixed at -1). If any are negative then absolute values are taken as starting values for cutpoint increments. - `link`: The link function: only `"identity"` allowed at present (possibly for ever). - `R`: the number of catergories. ## Returns An object of class `extended.family`. ## Details Such cumulative threshold models are only identifiable up to an intercept, or one of the cut points. Rather than remove the intercept, `ocat` simply sets the first cut point to -1. Use `predict.gam` with `type="response"` to get the predicted probabilities in each category. ## Author(s) Simon N. Wood simon.wood@r-project.org ## References Wood, S.N., N. Pya and B. Saefken (2016), Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association 111, 1548-1575 tools:::Rd_expr_doi("10.1080/01621459.2016.1180986") ## Examples ```r library(mgcv) ## Simulate some ordered categorical data... set.seed(3);n<-400 dat <- gamSim(1,n=n) dat$f <- dat$f - mean(dat$f) alpha <- c(-Inf,-1,0,5,Inf) R <- length(alpha)-1 y <- dat$f u <- runif(n) u <- dat$f + log(u/(1-u)) for (i in 1:R) { y[u > alpha[i]&u <= alpha[i+1]] <- i } dat$y <- y ## plot the data... par(mfrow=c(2,2)) with(dat,plot(x0,y));with(dat,plot(x1,y)) with(dat,plot(x2,y));with(dat,plot(x3,y)) ## fit ocat model to data... b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=ocat(R=R),data=dat) b plot(b,pages=1) gam.check(b) summary(b) b$family$getTheta(TRUE) ## the estimated cut points ## predict probabilities of being in each category predict(b,dat[1:2,],type="response",se=TRUE) ```

ocat function