# Response models currently implemented in depmix. Depmix contains a number of default response models. We provide a brief description of these here. ## BINOMresponse `BINOMresponse` is a binomial response model. It derives from the basic `GLMresponse` class. - **y:**: The dependent variable can be either a binary vector, a factor, or a 2-column matrix, with successes and misses. - **x:**: The design matrix. - **Parameters:**: A named list with a single element ``coefficients'', which contains the GLM coefficients. ## GAMMAresponse `GAMMAresponse` is a model for a Gamma distributed response. It extends the basic `GLMresponse` class directly. - **y:**: The dependent variable. - **x:**: The design matrix. - **Parameters:**: A named list with a single element ``coefficients'', which contains the GLM coefficients. ## MULTINOMresponse `MULTINOMresponse` is a model for a multinomial distributed response. It extends the basic `GLMresponse` class, although the functionality is somewhat different from other models that do so. - **y:**: The dependent variable. This is a binary matrix with N rows and Y columns, where Y is the total number of categories. - **x:**: The design matrix. - **Parameters:**: A named list with a single element ``coefficients'', which is an `ncol(x)` by `ncol(y)` matrix which contains the GLM coefficients. ## MVNresponse `MVNresponse` is a model for a multivariate normal distributed response. See `makeDepmix` for an example of how to use this and other non-glm like distributions. - **y:**: The dependent variable. This is a matrix. - **x:**: The design matrix. - **Parameters:**: A named list with a elements ``coefficients'', which contains the GLM coefficients, and ``Sigma'', which contains the covariance matrix. ## NORMresponse `NORMresponse` is a model for a normal (Gaussian) distributed response. It extends the basic `GLMresponse` class directly. - **y:**: The dependent variable. - **x:**: The design matrix. - **Parameters:**: A named list with elements ``coefficients'', which contains the GLM coefficients, and ``sd'', which contains the standard deviation. ## POISSONresponse `POISSONresponse` is a model for a Poisson distributed response. It extends the basic `GLMresponse` class directly. - **y:**: The dependent variable. - **x:**: The design matrix. - **Parameters:**: A named list with a single element ``coefficients'', which contains the GLM coefficients. ## Examples ```r # binomial response model x <- rnorm(1000) p <- plogis(x) ss <- rbinom(1000,1,p) mod <- GLMresponse(cbind(ss,1-ss)~x,family=binomial()) fit(mod) glm(cbind(ss,1-ss)~x, family=binomial) # gamma response model x=runif(1000,1,5) res <- rgamma(1000,x) ## note that gamma needs proper starting values which are not ## provided by depmixS4 (even with them, this may produce warnings) mod <- GLMresponse(res~x,family=Gamma(),pst=c(0.8,1/0.8)) fit(mod) glm(res~x,family=Gamma) # multinomial response model x <- sample(0:1,1000,rep=TRUE) mod <- GLMresponse(sample(1:3,1000,rep=TRUE)~x,family=multinomial(),pstart=c(0.33,0.33,0.33,0,0,1)) mod@y <- simulate(mod) fit(mod) colSums(mod@y[which(x==0),])/length(which(x==0)) colSums(mod@y[which(x==1),])/length(which(x==1)) # note that the response is treated as factor here, internal representation is in # dummy coded format: head(mod@y) # similar to the binomial model, data may also be entered in multi-column format # where the n for each row can be different dt <- data.frame(y1=c(0,1,1,2,4,5),y2=c(1,0,1,0,1,0),y3=c(4,4,3,2,1,1)) m2 <- mix(cbind(y1,y2,y3)~1,data=dt,ns=2,family=multinomial("identity")) fm2 <- fit(m2) summary(fm2) # multivariate normal response model mn <- c(1,2,3) sig <- matrix(c(1,.5,0,.5,1,0,0,0,2),3,3) y <- mvrnorm(1000,mn,sig) mod <- MVNresponse(y~1) fit(mod) colMeans(y) var(y) # normal (gaussian) response model y <- rnorm(1000) mod <- GLMresponse(y~1) fm <- fit(mod) cat("Test gaussian fit: ", all.equal(getpars(fm),c(mean(y),sd(y)),check.attributes=FALSE)) # poisson response model x <- abs(rnorm(1000,2)) res <- rpois(1000,x) mod <- GLMresponse(res~x,family=poisson()) fit(mod) glm(res~x, family=poisson) # this creates data with a single change point with Poisson distributed data set.seed(3) y1 <- rpois(50,1) y2 <- rpois(50,2) ydf <- data.frame(y=c(y1,y2)) # fit models with 1 to 3 states m1 <- depmix(y~1,ns=1,family=poisson(),data=ydf) fm1 <- fit(m1) m2 <- depmix(y~1,ns=2,family=poisson(),data=ydf) fm2 <- fit(m2) m3 <- depmix(y~1,ns=3,family=poisson(),data=ydf) fm3 <- fit(m3,em=em.control(maxit=500)) # plot the BICs to select the proper model plot(1:3,c(BIC(fm1),BIC(fm2),BIC(fm3)),ty="b") ``` ## Author(s) Maarten Speekenbrink & Ingmar Visser

responses function