README.md

In SuneelChatla/cmp: Conway-Maxwell Poisson Regression and Additive models using IRLS algorithm

CMP Distribution

Conway-Maxwell-Poisson GLM and GAM

The package contains two routines to fit CMP generalized additive models. They only differ interms of the models for the dispersion parameter.

1. gam.cmp(): allows models for both lambda and nu parameters main inputs:

   • formula: could be a list of two formulas for both lambda and nu or just a single formula for lambda and in this case the parameter nu is treated as constant.
   • dataset
   • family=cmp

2. gam.perf1(): allows only a constant dispersion parameter.

   • formula: allows only a single formula for lambda model and nu will be treated as constant.
   • dataset
   • family=cmp or negbin or poisson

   For the remaining parameters, the default values are good enough to get the desired results.

If the formulas do not contain smooth terms (s()), then the model fitted is simply a generalized linear model.

For more details about the model formulations and estimation procedures, please refer to

Suneel Babu Chatla, Galit Shmueli, Efficient estimation of COM–Poisson regression and a generalized additive model, Computational Statistics & Data Analysis, Volume 121, 2018, Pages 71-88, ISSN 0167-9473, https://doi.org/10.1016/j.csda.2017.11.011. (http://www.sciencedirect.com/science/article/pii/S0167947317302608)

Example:

Data simulation example

set.seed(123)\ n=200\ sdata=data.frame(x0 = runif(n, 0, 1))\ sdata$x1 <- runif(n, 0, 1)\ sdata$x2 <- runif(n, 0, 1)\ sdata$x3 <- runif(n, 0, 1)

f0 <- function(x) sin(pi * x)\ f1 <- function(x) exp( x)\ f2 <- function(x) 0.02 * x^2 * ( (1 - x)) + (0.5 * x)^2 * (1 - x)^3\ f3 <- function(x) 2*x-(x^2)

sdata$f <- 2*f3(sdata$x3) +1*f1(sdata$x1) +1* f2(sdata$x2)\ lambda=exp(sdata$f)\ nu= exp(f0(sdata$x0))\ s=rep(0,n)\ y=.C("cmpsim_all",lambda=as.double(lambda),nu=as.double(nu),n=as.integer(n),y=as.double(s))$y\ sdata$y=y

Model formulations

m1 <- as.formula(y~s(x3)+s(x1)+s(x2))\ m21 <- as.formula(y~s(x0))\ m22 <- as.formula(y~x0)

### CMP GAM with additive models for both lambda and nu cmpgam <- gam.cmp(list(m1,m21),data = sdata,family = cmp)\ summary.gam.cmp(cmpgam)

### CMP GAM with additive model for lambda and linear model for nu cmpglm <- gam.cmp(list(m1,m22),data = sdata,family = cmp)\ summary.gam.cmp(cmpglm)

### CMP GAM with additive model for lambda and constant model for nu cmpglm1 <- gam.perf1(m1,data = sdata,family = cmp)\ summary.gam1(cmpglm1)

### Negative Binomial GAM nbgam <- gam.perf1(m1,data=sdata,family = negbin(c(1,10000)))\ summary.gam1(nbgam)

SuneelChatla/cmp documentation built on Aug. 15, 2022, 10:24 a.m.