Description Usage Arguments Details Value Author(s) References Examples
Conditional Multinomial Maximum Likelihood Estimation for different sampling methodologies.
1 2 3 4 5 6 7 8 | cmulti(formula, data, type = c("rem", "mix", "dis"),
inits = NULL, method = "Nelder-Mead", ...)
cmulti.fit(Y, D, X=NULL, type=c("rem", "mix", "dis"),
inits=NULL, method="Nelder-Mead", ...)
cmulti2.fit(Y, D1, D2, X1=NULL, X2=NULL,
inits=NULL, method="Nelder-Mead", ...)
## S3 method for class 'cmulti'
fitted(object, ...)
|
formula |
formula, LHS takes 2 matrices in the form of |
data |
data. |
type |
character, one of |
Y |
this contains the cell counts.
|
D, D1, D2 |
design matrices, that describe the interval endpoints for the sampling
methodology, dimensions must match dimensions of |
X, X1, X2 |
design matrices, |
inits |
optional initial values. |
method |
method for |
object |
fitted model object. |
... |
additional options for |
Conditional Multinomial Maximum Likelihood Estimation for different sampling methodologies.
An object of class 'cmulti'.
Peter Solymos
Solymos, P., Matsuoka, S. M., Bayne, E. M., Lele, S. R., Fontaine, P., Cumming, S. G., Stralberg, D., Schmiegelow, F. K. A. & Song, S. J., 2013. Calibrating indices of avian density from non-standardized survey data: making the most of a messy situation. Methods in Ecology and Evolution, 4, 1047–1058.
Supporting info, including a tutorial for the above paper: http://dcr.r-forge.r-project.org/qpad/
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 | simfun1 <- function(n = 10, phi = 0.1, c=1, tau=0.8, type="rem") {
if (type=="dis") {
Dparts <- matrix(c(0.5, 1, NA,
0.5, 1, Inf,
1, Inf, NA), 3, 3, byrow=TRUE)
D <- Dparts[sample.int(3, n, replace=TRUE),]
CP <- 1-exp(-(D/tau)^2)
} else {
Dparts <- matrix(c(5, 10, NA,
3, 5, 10,
3, 5, NA), 3, 3, byrow=TRUE)
D <- Dparts[sample.int(3, n, replace=TRUE),]
CP <- 1-c*exp(-D*phi)
}
k <- ncol(D)
P <- CP - cbind(0, CP[, -k, drop=FALSE])
Psum <- rowSums(P, na.rm=TRUE)
PPsum <- P / Psum
Pok <- !is.na(PPsum)
N <- rpois(n, 10)
Y <- matrix(NA, ncol(PPsum), nrow(PPsum))
Ypre <- sapply(1:n, function(i) rmultinom(1, N, PPsum[i,Pok[i,]]))
Y[t(Pok)] <- unlist(Ypre)
Y <- t(Y)
list(Y=Y, D=D)
}
n <- 200
x <- rnorm(n)
X <- cbind(1, x)
## removal, constant
vv <- simfun1(n=n, phi=exp(-1.5))
m1 <- cmulti(vv$Y | vv$D ~ 1, type="rem")
coef(m1)
## mixture, constant
vv <- simfun1(n=n, phi=exp(-1.5), c=plogis(0.8))
m2 <- cmulti(vv$Y | vv$D ~ 1, type="mix")
coef(m2)
## dist, constant
vv <- simfun1(n=n, tau=exp(-0.2), type="dis")
m3 <- cmulti(vv$Y | vv$D ~ 1, type="dis")
coef(m3)
## removal, not constant
log.phi <- X %*% c(-2,-1)
vv <- simfun1(n=n, phi=exp(cbind(log.phi, log.phi, log.phi)))
m1 <- cmulti(vv$Y | vv$D ~ x, type="rem")
coef(m1)
## mixture, not constant
logit.c <- X %*% c(-2,1)
vv <- simfun1(n=n, phi=exp(-1.5), c=plogis(cbind(logit.c, logit.c, logit.c)))
m2 <- cmulti(vv$Y | vv$D ~ x, type="mix")
coef(m2)
## dist, not constant
log.tau <- X %*% c(-0.5,-0.2)
vv <- simfun1(n=n, tau=exp(cbind(log.tau, log.tau, log.tau)), type="dis")
m3 <- cmulti(vv$Y | vv$D ~ x, type="dis")
coef(m3)
summary(m3)
coef(m3)
vcov(m3)
AIC(m3)
confint(m3)
logLik(m3)
## fitted values
plot(exp(log.tau), fitted(m3))
## joint removal-distance estimation
## is not different from 2 orthogonal estimations
simfun12 <- function(n = 10, phi = 0.1, c=1, tau=0.8, type="rem") {
Flat <- function(x, DIM, dur=TRUE) {
x <- array(x, DIM)
if (!dur) {
x <- aperm(x,c(1,3,2))
}
dim(x) <- c(DIM[1], DIM[2]*DIM[3])
x
}
Dparts1 <- matrix(c(5, 10, NA,
3, 5, 10,
3, 5, NA), 3, 3, byrow=TRUE)
D1 <- Dparts1[sample.int(3, n, replace=TRUE),]
CP1 <- 1-c*exp(-D1*phi)
Dparts2 <- matrix(c(0.5, 1, NA,
0.5, 1, Inf,
1, Inf, NA), 3, 3, byrow=TRUE)
D2 <- Dparts2[sample.int(3, n, replace=TRUE),]
CP2 <- 1-exp(-(D2/tau)^2)
k1 <- ncol(D1)
k2 <- ncol(D2)
DIM <- c(n, k1, k2)
P1 <- CP1 - cbind(0, CP1[, -k1, drop=FALSE])
P2 <- CP2 - cbind(0, CP2[, -k2, drop=FALSE])
Psum1 <- rowSums(P1, na.rm=TRUE)
Psum2 <- rowSums(P2, na.rm=TRUE)
Pflat <- Flat(P1, DIM, dur=TRUE) * Flat(P2, DIM, dur=FALSE)
PsumFlat <- Psum1 * Psum2
PPsumFlat <- Pflat / PsumFlat
PokFlat <- !is.na(PPsumFlat)
N <- rpois(n, 10)
Yflat <- matrix(NA, ncol(PPsumFlat), nrow(PPsumFlat))
YpreFlat <- sapply(1:n, function(i) rmultinom(1, N, PPsumFlat[i,PokFlat[i,]]))
Yflat[t(PokFlat)] <- unlist(YpreFlat)
Yflat <- t(Yflat)
Y <- array(Yflat, DIM)
k1 <- dim(Y)[2]
k2 <- dim(Y)[3]
Y1 <- t(sapply(1:n, function(i) {
count <- rowSums(Y[i,,], na.rm=TRUE)
nas <- rowSums(is.na(Y[i,,]))
count[nas == k2] <- NA
count
}))
Y2 <- t(sapply(1:n, function(i) {
count <- colSums(Y[i,,], na.rm=TRUE)
nas <- colSums(is.na(Y[i,,]))
count[nas == k2] <- NA
count
}))
list(Y=Y, D1=D1, D2=D2, Y1=Y1, Y2=Y2)
}
## removal and distance, constant
vv <- simfun12(n=n, phi=exp(-1.5), tau=exp(-0.2))
res <- cmulti2.fit(vv$Y, vv$D1, vv$D2)
res1 <- cmulti.fit(vv$Y1, vv$D1, NULL, "rem")
res2 <- cmulti.fit(vv$Y2, vv$D2, NULL, "dis")
## points estimates are identical
cbind(res$coef, c(res1$coef, res2$coef))
## standard errors are identical
cbind(sqrt(diag(res$vcov)),
c(sqrt(diag(res1$vcov)),sqrt(diag(res2$vcov))))
## removal and distance, not constant
vv <- simfun12(n=n,
phi=exp(cbind(log.phi, log.phi, log.phi)),
tau=exp(cbind(log.tau, log.tau, log.tau)))
res <- cmulti2.fit(vv$Y, vv$D1, vv$D2, X1=X, X2=X)
res1 <- cmulti.fit(vv$Y1, vv$D1, X, "rem")
res2 <- cmulti.fit(vv$Y2, vv$D2, X, "dis")
## points estimates are identical
cbind(res$coef, c(res1$coef, res2$coef))
## standard errors are identical
cbind(sqrt(diag(res$vcov)),
c(sqrt(diag(res1$vcov)),sqrt(diag(res2$vcov))))
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