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.

### See Also

`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[1]*log(y0)+(times<30)*p[2]*
(times-30)+(times>30)*p[3]*(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]