Description Usage Arguments Value See Also Examples
Negative binomial (NB) regression for count data; 2 versions. NB(theta,xi) has pmf f(y;theta,xi)= [ Gamma(theta+y) xi^y] / [ Gamma(theta) y! (1+xi)^(theta+y) ]
1 2 3 4 5 6 7 8 9 |
param |
parameter of NB model, length is 2+number of covariates; the parameters are: b0=intercept, bvec= vector regression coefficients (length(bvec)=length(x)=ncol(xdat), and finally xi or theta. For NB1, mu(x)= exp(b[0]+bvec^T x), xi=(overdispersion index minus one) is fixed, and theta(x)=mu(x)/xi. For NB2, mu(x)= exp(b[0]+bvec^T x), theta=convolution parameter is fixed and xi(x)=mu(x)/theta. |
theta |
convolution parameter |
p |
probability parameter between 0 and 1 |
xdat |
matrix for nb1nllk and nb2nllk |
x |
vector for nb1pmfcdf, nb2pmfcdf, nb1cdf, nb2cdf, nb1pmf, nb2pmf |
y |
vector for nb1nllk and nb2nllk (with length(y)=nrow(xdat)); non-negative integer for the other functions |
ub |
upper bound integer for which pmf and cdf are computed |
negative log-likelihood for nb1nllk and nb2nllk; matrix with columns (0:ub,pmf,cdf) for nbpmfcdf, nb1pmfcdf and nb2pmfcdf, computed in an efficient way (parameters assumed to be such that most probability is on small counts); cdf for nb1cdf and nb2cdf; pmf for nb1pmf and nb2pmf.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | y= c(
2, 1, 1, 0,35, 9, 0, 1, 4, 0, 0, 1, 4, 0, 0, 8, 7, 2, 0, 7, 0, 0, 3, 4, 0,
4, 1, 3, 0, 6, 1, 0, 2, 8, 0,12, 0, 4, 2, 1, 3, 0, 9, 0, 0, 0, 2, 0, 8, 1,
2, 4, 2, 0, 0, 2, 1, 3, 2, 1, 3, 4, 4, 5, 0, 4, 0, 2, 0,28, 1,24, 1, 0,10,
3, 3, 0, 0, 7, 2, 4, 6, 4,13, 5, 8, 0, 1, 6, 0,24, 9, 0,10, 0, 0, 8, 5, 3,
16, 0, 4, 1, 1, 4,12, 4, 3, 5, 0, 2, 1, 5, 3, 0, 0, 6, 4, 2, 0, 2, 0,15, 3,
0, 2, 3, 4, 5, 0, 3, 0, 0, 6, 0, 0,15, 0, 0, 0, 1, 3, 0, 1, 0, 4, 2,10, 4,
1, 0, 0, 0, 5, 0, 0, 2, 0, 4, 0, 0, 2,25, 0, 0,13, 0, 0,21, 3, 0, 0, 0, 2,
2, 0, 4,13, 2, 9, 9, 2, 0, 1, 2, 2, 8, 6, 0, 4, 1, 2, 0, 0, 0, 0, 0, 0, 2,
2, 0, 3, 1, 1, 7, 3, 0, 2, 2, 1, 3, 2, 2, 1, 3, 3, 0, 0, 0, 2, 0, 0, 0, 0,
1, 2, 2, 0, 0, 9, 0, 0, 1, 1, 0, 2,10, 0,17, 2, 0,14, 0, 5, 9, 2, 0, 6, 3,
3, 1, 0,11, 4, 9, 0, 1, 0, 0,12, 4, 0, 1,21, 0, 3, 2, 0, 1, 0, 1, 3, 8,10,
19, 0, 2, 7, 1, 0, 2, 0, 4, 0, 6, 4, 7, 1, 0, 1, 3, 4, 0, 4)
hsat=c(
8, 7, 3,10, 6, 5, 8, 9, 9, 8,10, 8, 6, 7,10, 8, 5, 8, 8, 6, 8, 8, 8, 9,10,
7, 9,10, 8, 6, 6, 9, 7, 5,10, 4, 8, 4, 5, 5, 7, 6, 7,10, 9, 9, 5, 7, 4, 7,
6, 6, 7, 5,10, 9,10, 7, 8, 6, 5, 5, 0, 5, 7, 3, 8, 8, 7, 5, 5, 0, 7, 6, 3,
10, 7, 7,10, 5, 5, 4, 2, 7, 6, 2, 5,10, 7, 8, 5, 5, 5,10, 3, 9, 6, 8,10,10,
4, 7, 2, 8, 9, 0, 0, 5, 8, 3, 7, 6,10, 4, 5, 7, 6, 7, 3, 4,10, 4, 8, 8, 3,
9, 5,10, 9, 5,10,10, 8,10, 5,10, 6, 5, 9, 8,10, 7, 8, 9, 7, 8, 4, 8, 3, 5,
5, 7,10, 8, 1, 3, 3, 8,10, 3, 5, 5, 7, 5,10, 8, 5, 8, 5, 0, 6, 8, 2, 5, 6,
7,10, 5, 0, 5, 2, 0, 3,10, 7, 4, 6, 9, 2, 8, 5, 9, 7, 5,10, 8, 8, 7, 7, 7,
10,10, 2, 5, 7, 5, 9, 6, 7, 6, 9, 9, 6, 8,10, 7, 8, 8,10,10, 5,10, 5, 8,10,
8, 7,10, 9,10, 4, 6, 9, 5, 9, 9, 6, 8, 8, 2, 5, 8, 3, 7, 0, 8, 8,10, 5, 7,
6, 7,10, 5, 5, 1, 5, 6, 4,10, 5, 5, 5, 7, 2, 8, 5,10,10,10,10, 6, 6, 6, 6,
7, 8, 8,10,10, 8, 7, 8, 3, 8, 8, 8, 6, 3, 7,10,10, 2, 9, 2)
fit1=nlm(ieenllk,p=c(2.5,-.2,4),hessian=TRUE,print.level=1,upmf=nb1pmf,
xdat=hsat,ydat=y,LB=c(-1,-2,0),UB=c(10,10,10))
fit2=nlm(ieenllk,p=c(2.5,-.2,0.8),hessian=TRUE,print.level=1,upmf=nb2pmf,
xdat=hsat,ydat=y,LB=c(-1,-2,0),UB=c(10,10,10))
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