tests/formulatest.R

In bbolker/bbmle: Tools for General Maximum Likelihood Estimation

library(bbmle)
set.seed(1001)

## test 1
x <- 0:10
y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
d <- data.frame(x,y)
suppressWarnings(m1 <- mle2(y~dpois(lambda=ymax/(1+x/xhalf)),
           parameters=list(ymax~1,xhalf~1),
           start=list(ymax=1,xhalf=1),data=d))

suppressWarnings(p1 <- profile(m1))

suppressWarnings(m2 <- mle2(y~dpois(lambda=ymax/(1+x/xhalf)),
           start=list(ymax=1,xhalf=1),data=d))

## should be able to omit parameters (?) or
## have them taken from 
## test 2:

ReedfrogSizepred <-
structure(list(TBL = as.integer(c(9, 9, 9, 12, 12, 12, 21, 21, 
21, 25, 25, 25, 37, 37, 37)), Kill = as.integer(c(0, 2, 1, 3, 
4, 5, 0, 0, 0, 0, 1, 0, 0, 0, 0))), .Names = c("TBL", "Kill"), class = "data.frame", row.names = c("1", 
"2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", 
"14", "15"))

VBlogist <- function(x,sizep1,sizep2,sizep3) {
  exp(sizep1*(sizep3-x))/(1+exp(sizep2*sizep1*(sizep3-x)))
}
startp <- list(sizep1=0,sizep2=1,sizep3=12)
mle2(Kill~dbinom(prob=VBlogist(TBL,sizep1,sizep2,sizep3),size=10),
     start=startp,
     method="Nelder-Mead",
     data=ReedfrogSizepred)
             
## test 3:
f <- factor(rep(1:2,each=20))
xhalf <- c(5,10)
ymax <- 10
  x <- rep(0:19,2)
  y <- rpois(40,ymax/(1+x/xhalf[f]))
d <- data.frame(x,y)
##  plot(x,y,col=as.numeric(f))

  m3 <- mle2(y~dpois(lambda=ymax/(1+x/xhalf)),
             parameters=list(xhalf~f),
             start=list(ymax=1,xhalf=1),data=d)

  m4 <- mle2(y~dpois(lambda=ymax/(1+x/xhalf)),
             parameters=list(ymax~f,xhalf~f),
             start=list(ymax=1,xhalf=1),data=d)

  suppressWarnings(m5 <- mle2(y~dpois(lambda=ymax/(1+x/xhalf)),
             parameters=list(ymax~f),
             start=list(ymax=1,xhalf=1),data=d))

  anova(m2,m3,m4)
  anova(m2,m5,m4)
  AICtab(m2,m3,m4,m5)

GobySurvival <-
structure(list(exper = as.integer(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 
5, 5, 5)), year = as.integer(c(2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 
2000, 2000, 2000, 2000, 2000, 2000, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 
2001, 2001, 2001, 2001, 2001, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 2002, 
2002)), site = structure(as.integer(c(2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1)), .Label = c("backreef", "patchreef"), class = "factor"), 
    head = structure(as.integer(c(15, 15, 15, 15, 15, 15, 15, 
    15, 15, 15, 15, 4, 4, 4, 19, 19, 24, 24, 24, 24, 24, 24, 
    6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 10, 10, 10, 10, 10, 10, 
    10, 10, 10, 10, 10, 13, 13, 13, 13, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 2, 2, 2, 5, 5, 5, 5, 12, 12, 12, 12, 7, 7, 7, 11, 11, 
    11, 11, 11, 11, 11, 11, 11, 14, 14, 14, 23, 23, 23, 23, 23, 
    23, 23, 23, 23, 22, 22, 22, 8, 8, 8, 8, 8, 8, 8, 8, 8, 20, 
    20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 1, 17, 17, 17, 17, 17, 17, 17, 16, 16, 16, 16, 16, 
    16, 16, 16, 18, 18, 18, 26, 26, 26, 55, 55, 55, 57, 57, 41, 
    41, 41, 45, 45, 47, 47, 48, 48, 58, 58, 34, 34, 34, 34, 35, 
    35, 35, 35, 50, 50, 50, 32, 32, 32, 25, 25, 25, 25, 25, 33, 
    33, 33, 28, 28, 31, 31, 31, 36, 36, 36, 44, 44, 44, 44, 29, 
    29, 29, 27, 27, 27, 40, 40, 40, 46, 46, 46, 46, 46, 39, 39, 
    39, 39, 30, 30, 30, 30, 30, 51, 51, 51, 51, 51, 51, 56, 56, 
    56, 56, 56, 56, 52, 52, 52, 52, 52, 52, 55, 55, 55, 53, 53, 
    53, 57, 57, 57, 57, 57, 57, 35, 35, 35, 35, 35, 35, 33, 33, 
    33, 33, 33, 33, 29, 29, 29, 45, 45, 45, 45, 45, 45, 38, 38, 
    38, 38, 38, 38, 27, 27, 27, 27, 27, 27, 59, 59, 59, 59, 59, 
    59, 54, 54, 54, 54, 54, 54, 39, 39, 39, 39, 39, 39, 42, 42, 
    42, 41, 41, 41, 41, 41, 41, 49, 49, 49, 46, 46, 46, 46, 46, 
    46, 47, 47, 47, 47, 47, 47, 37, 37, 37, 43, 43, 43, 43, 43, 
    43, 40, 40, 40, 40, 40, 40, 48, 48, 48, 48, 48, 48, 51, 51, 
    51, 45, 45, 45, 41, 41, 41, 47, 47, 47, 37, 37, 37, 49, 49, 
    49, 34, 34, 34, 25, 25, 25)), .Label = c("p1", "p10", "p11", 
    "p12", "p13", "p14", "p15", "p16", "p17", "p18", "p19", "p2", 
    "p20", "p21", "p3", "p4", "p42", "p5", "p51", "p6", "p7", 
    "p70", "p8", "p9", "r10", "r11", "r13", "r14", "r15", "r17", 
    "r18", "r19", "r2", "r20", "r21", "r22", "r23", "r24", "r25", 
    "r26", "r27", "r28", "r29", "r3", "r30", "r33", "r34", "r35", 
    "r36", "r37", "r41", "r45", "r47", "r48", "r5", "r6", "r7", 
    "r8", "r9"), class = "factor"), density = as.integer(c(11, 
    11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 3, 3, 3, 2, 2, 6, 
    6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 11, 11, 11, 
    11, 11, 11, 11, 11, 11, 11, 11, 4, 4, 4, 4, 8, 8, 8, 8, 8, 
    8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 9, 
    9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 
    9, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 
    8, 8, 3, 3, 3, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 
    7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 
    4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 3, 3, 
    3, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 5, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 11, 11, 
    11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 6, 6, 6, 6, 6, 6, 
    3, 3, 3, 3, 3, 3, 11, 11, 11, 11, 11, 11, 6, 6, 6, 6, 6, 
    6, 11, 11, 11, 11, 11, 11, 3, 3, 3, 6, 6, 6, 6, 6, 6, 11, 
    11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
    11, 11, 6, 6, 6, 6, 6, 6, 11, 11, 11, 11, 11, 11, 3, 3, 3, 
    11, 11, 11, 11, 11, 11, 3, 3, 3, 6, 6, 6, 6, 6, 6, 11, 11, 
    11, 11, 11, 11, 3, 3, 3, 11, 11, 11, 11, 11, 11, 6, 6, 6, 
    6, 6, 6, 11, 11, 11, 11, 11, 11, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3)), qual = as.integer(c(1, 
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 
    2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
    2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 
    4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 
    5, 5, 5, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 
    9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
    10, 10, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 
    14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 
    2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 
    4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 
    6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 
    9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 12, 12, 12, 12, 18, 18, 
    18, 18, 18, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
    2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 
    5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 
    7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 
    9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 
    10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 16, 16, 16, 16, 
    16, 16, 2, 2, 2, 5, 5, 5, 8, 8, 8, 9, 9, 9, 10, 10, 10, 9, 
    9, 9, 4, 4, 4, 3, 3, 3)), d1 = as.integer(c(1, 1, 1, 1, 1, 
    1, 1, 1, 1, 1, 4, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 1, 8, 8, 4, 8, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 11, 11, 1, 1, 1, 4, 4, 11, 11, 11, 4, 8, 11, 11, 
    1, 1, 1, 11, 1, 1, 8, 11, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 
    11, 11, 1, 8, 11, 4, 8, 8, 8, 11, 11, 11, 11, 11, 1, 1, 8, 
    1, 1, 1, 1, 1, 1, 1, 4, 8, 1, 1, 1, 1, 1, 1, 4, 11, 1, 1, 
    1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 1, 1, 1, 1, 1, 1, 8, 1, 
    1, 1, 1, 1, 8, 11, 11, 1, 4, 11, 1, 1, 3, 1, 1, 1, 1, 1, 
    1, 1, 4, 2, 12, 2, 12, 3, 12, 2, 12, 1, 1, 1, 1, 1, 1, 1, 
    12, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 4, 1, 1, 12, 1, 1, 1, 1, 
    4, 1, 1, 12, 1, 1, 3, 8, 1, 2, 12, 1, 1, 1, 1, 1, 8, 1, 1, 
    3, 3, 12, 1, 1, 2, 12, 1, 2, 4, 8, 8, 1, 2, 3, 1, 1, 1, 1, 
    1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 
    8, 1, 2, 10, 1, 1, 12, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 4, 6, 
    3, 3, 4, 1, 4, 12, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 12, 3, 6, 
    10, 1, 1, 12, 1, 1, 8, 1, 2, 12, 1, 1, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 12, 2, 2, 12, 1, 12, 12, 4, 4, 4, 1, 1, 2, 1, 1, 
    1, 1, 1, 8, 1, 1, 2, 1, 1, 4, 1, 1, 12, 1, 1, 12, 1, 3, 12, 
    2, 4, 12, 2, 10, 12, 1, 1, 8, 1, 1, 8)), d2 = as.integer(c(4, 
    4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 70, 4, 4, 4, 4, 4, 4, 
    4, 4, 4, 4, 4, 4, 4, 4, 11, 11, 8, 11, 70, 4, 4, 4, 4, 4, 
    4, 4, 4, 4, 4, 4, 4, 4, 70, 70, 4, 4, 4, 8, 8, 70, 70, 70, 
    8, 11, 70, 70, 4, 4, 4, 70, 4, 4, 11, 70, 4, 4, 70, 4, 4, 
    4, 4, 4, 4, 4, 70, 70, 4, 11, 70, 8, 11, 11, 11, 70, 70, 
    70, 70, 70, 4, 4, 11, 4, 4, 4, 4, 4, 4, 4, 8, 11, 4, 4, 4, 
    4, 4, 4, 8, 70, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 70, 70, 
    4, 4, 4, 4, 4, 4, 11, 4, 4, 4, 4, 4, 11, 70, 70, 4, 8, 70, 
    2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 8, 3, 70, 3, 70, 4, 70, 3, 
    70, 2, 2, 2, 2, 2, 2, 2, 70, 2, 2, 2, 2, 2, 8, 2, 2, 2, 3, 
    8, 2, 2, 70, 2, 2, 2, 2, 8, 2, 2, 70, 2, 2, 4, 12, 2, 3, 
    70, 2, 2, 2, 2, 2, 12, 2, 2, 4, 4, 70, 2, 2, 3, 70, 2, 3, 
    8, 12, 12, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 4, 2, 
    2, 2, 2, 2, 2, 2, 2, 70, 2, 2, 10, 2, 3, 12, 2, 2, 70, 2, 
    2, 4, 2, 2, 2, 2, 3, 3, 2, 6, 8, 4, 4, 6, 2, 6, 70, 2, 2, 
    4, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8, 2, 2, 2, 
    2, 2, 2, 2, 2, 70, 2, 2, 70, 4, 8, 12, 2, 2, 70, 2, 2, 10, 
    2, 3, 70, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 70, 3, 3, 70, 
    2, 70, 70, 6, 6, 6, 2, 2, 3, 2, 2, 2, 2, 2, 10, 2, 2, 3, 
    2, 2, 6, 2, 2, 70, 2, 2, 70, 2, 4, 70, 3, 6, 70, 3, 12, 70, 
    2, 2, 10, 2, 2, 10))), .Names = c("exper", "year", "site", 
"head", "density", "qual", "d1", "d2"), class = "data.frame", row.names = c("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", "31", "32", "33", "34", "35", 
"36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", 
"47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", 
"58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", 
"69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79", 
"80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "90", 
"91", "92", "93", "94", "95", "96", "97", "98", "99", "100", 
"101", "102", "103", "104", "105", "106", "107", "108", "109", 
"110", "111", "112", "113", "114", "115", "116", "117", "118", 
"119", "120", "121", "122", "123", "124", "125", "126", "127", 
"128", "129", "130", "131", "132", "133", "134", "135", "136", 
"137", "138", "139", "140", "141", "142", "143", "144", "145", 
"146", "147", "148", "149", "150", "151", "152", "153", "154", 
"155", "156", "157", "158", "159", "160", "161", "162", "163", 
"164", "165", "166", "167", "168", "169", "170", "171", "172", 
"173", "174", "175", "176", "177", "178", "179", "180", "181", 
"182", "183", "184", "185", "186", "187", "188", "189", "190", 
"191", "192", "193", "194", "195", "196", "197", "198", "199", 
"200", "201", "202", "203", "204", "205", "206", "207", "208", 
"209", "210", "211", "212", "213", "214", "215", "216", "217", 
"218", "219", "220", "221", "222", "223", "224", "225", "226", 
"227", "228", "229", "230", "231", "232", "233", "234", "235", 
"236", "237", "238", "239", "240", "241", "242", "243", "244", 
"245", "246", "247", "248", "249", "250", "251", "252", "253", 
"254", "255", "256", "257", "258", "259", "260", "261", "262", 
"263", "264", "265", "266", "267", "268", "269", "270", "271", 
"272", "273", "274", "275", "276", "277", "278", "279", "280", 
"281", "282", "283", "284", "285", "286", "287", "288", "289", 
"290", "291", "292", "293", "294", "295", "296", "297", "298", 
"299", "300", "301", "302", "303", "304", "305", "306", "307", 
"308", "309", "310", "311", "312", "313", "314", "315", "316", 
"317", "318", "319", "320", "321", "322", "323", "324", "325", 
"326", "327", "328", "329", "330", "331", "332", "333", "334", 
"335", "336", "337", "338", "339", "340", "341", "342", "343", 
"344", "345", "346", "347", "348", "349", "350", "351", "352", 
"353", "354", "355", "356", "357", "358", "359", "360", "361", 
"362", "363", "364", "365", "366", "367", "368", "369"))

dicweib <- function(x,shape,scale,log=FALSE) {
  if (is.matrix(x)) {
    day1 <- x[,1]
    day2 <- x[,2]
  } else {
    day1 <- x[1]
    day2 <- x[2]
  }
  v <- log(pweibull(day2,shape,scale)-pweibull(day1,shape,scale))
  if (log) v else exp(v)
}

GS2 <- transform(GobySurvival,
                          day1 = d1-1,
                          day2 = ifelse(d2==70,Inf,d2-1),
                          fexper=factor(exper))
totmeansurv <- with(GS2,mean((d1+d2)/2))

mle2(cbind(day1,day2)~dicweib(exp(shape),exp(scale)),
     parameters=list(scale~fexper+qual*density),
     start=list(scale=log(totmeansurv),shape=0),data=GS2)

## GH 8
set.seed(1001)
lymax <- c(0,2)
lhalf <- 0
x <- sort(runif(200))
g <- factor(sample(c("a","b"),200,replace=TRUE))
y <- rnbinom(200,mu=exp(lymax[g])/(1+x/exp(lhalf)),size=2)
d2 <- data.frame(x,g,y)
fit3b <- mle2(y~dnbinom(mu=exp(lymax)/(1+x/exp(lhalf)),size=exp(logk)),
    parameters=list(lhalf~1,lymax~g),data=d2,
    start=list(lhalf=0,lymax=0,logk=0))
coef(fit3b)
stopifnot(all.equal(names(coef(fit3b)),
                    c("lhalf", "lymax.(Intercept)", "lymax.gb", "logk")))