nbkal {repeated} R Documentation

## Negative Binomial Models with Kalman Update

### Description

`nbkal` fits a negative binomial regression with Kalman update over time. The variance is proportional to the mean function, whereas, for `kalcount` with exponential intensity, it is a quadratic function of the mean.

Marginal and individual profiles can be plotted using `mprofile` and `iprofile` and residuals with `plot.residuals`.

### Usage

```nbkal(response, times, mu, preg, pdepend, kalman=TRUE,
print.level=0, ndigit=10, gradtol=0.00001, steptol=0.00001,
fscale=1, iterlim=100, typsiz=abs(p), stepmax=10*sqrt(p%*%p))
```

### Arguments

 `response` A list of two column matrices with counts and corresponding times for each individual, one matrix or dataframe of counts, or an object of class, response (created by `restovec`) or repeated (created by `rmna` or `lvna`). `times` When response is a matrix, a vector of possibly unequally spaced times when they are the same for all individuals or a matrix of times. Not necessary if equally spaced. Ignored if response has class, response or repeated. `mu` The mean function. `preg` The initial parameter estimates for the mean function. `pdepend` The estimates for the dependence parameters, either one or three. `kalman` If TRUE, fits the kalman update model, otherwise, a standard negative binomial distribution. `others` Arguments controlling `nlm`.

### Value

A list of classes `nbkal` and `recursive` is returned.

### Author(s)

P. Lambert and J.K. Lindsey

### References

Lambert, P. (1996) Applied Statistics 45, 31-38.

Lambert, P. (1996) Biometrics 52, 50-55.

`gar`, `gnlmm`, `gnlr`, `iprofile` `kalcount`, `mprofile`, `read.list`, `rmna`, `restovec`, `tcctomat`, `tvctomat`.

### Examples

```y <- matrix(rnbinom(20,5,0.5), ncol=5)
times <- matrix(rep(seq(10,50,by=10),4), ncol=5, byrow=TRUE)
y0 <- matrix(rep(rnbinom(5,5,0.5),4), ncol=5, byrow=TRUE)
mu <- function(p) p*log(y0)+(times<30)*p*
(times-30)+(times>30)*p*(times-30)
nbkal(y, preg=c(1.3,0.008,-0.05), times=times, pdep=1.2, mu=mu)
```

[Package repeated version 1.0 Index]