Created
July 26, 2021 00:00
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exploring the properties of truncated distributions with 'simple' data
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library(readxl) | |
my_sum <- function(f) { | |
C <- contr.sum(length(levels(f))) | |
colnames(C) <- paste0(".sum_",levels(f)[-length(levels(f))]) | |
return(C) | |
} | |
dd <- read_excel("Truncated.compois.problem.xlsx") | |
dd$pop <- as.factor(dd$pop) | |
contrasts(dd$pop) <- my_sum(dd$pop) | |
dd$morph <- as.factor(dd$morph) | |
contrasts(dd$morph) <- my_sum(dd$morph) | |
## options(contrasts = c("contr.sum","contr.poly")) | |
library(glmmTMB) | |
trunc_compois <- glmmTMB(mates ~ pop*morph, | |
family='truncated_compois', data=dd) | |
summary(trunc_compois) | |
pois <- update(trunc_compois, family = poisson) | |
## diagnose this: simpler | |
trunc_pois <- update(trunc_compois, family = truncated_poisson) | |
with(dd, table(mates,pop, morph)) | |
dd_ELS <- subset(dd, pop == "ELS") | |
trunc_pois_2 <- update(trunc_pois, | |
formula = . ~ morph, | |
data = dd_ELS) | |
summary(trunc_pois_2) | |
with(dd_ELS, table(morph, mates)) | |
dd_ELS_L <- subset(dd_ELS, morph == "L") | |
dd_ELS_S <- subset(dd_ELS, morph == "S") | |
trunc_pois_3 <- update(trunc_pois_2, | |
formula = ~ 1, | |
data = dd_ELS_L) | |
## false convergence warning | |
summary(trunc_pois_3) | |
with(dd_ELS_L, table(mates)) | |
## compare with bbmle | |
library(bbmle) | |
dtruncatedpois <- function(x, lambda, log) { | |
res <- dpois(x, lambda, log = log) | |
res[x==0] <- -Inf | |
res <- res - ppois(0, lambda, lower.tail = FALSE, log.p = TRUE) | |
if (log) res else exp(res) | |
} | |
m1 <- mle2(mates ~ dtruncatedpois(exp(log_lambda)), | |
start = list(log_lambda = 0), | |
data = dd_ELS_L) | |
nllfun <- function(log_lambda) { | |
-sum(dtruncatedpois(dd$mates, exp(log_lambda), log = TRUE)) | |
} | |
pvec <- seq(-30, 0, length=101) | |
lvec <- sapply(pvec, nllfun) | |
plot(pvec, lvec) | |
## truncated poisson of x ==1 | |
tpl <- function(lambda) (log(lambda) - lambda - log(1-exp(-lambda))) | |
tpl2 <- function(lambda) (log(lambda) - lambda - | |
ppois(0, lambda, lower.tail = FALSE, log.p = TRUE)) | |
## for lambda << 1, 1-exp(-lambda) → lambda | |
## negative log likelihood → lambda | |
tpl(2) | |
dtruncatedpois(1, 2, TRUE) | |
D(expression(log(lambda) - lambda - log(1-exp(-lambda))), "lambda") | |
## 1/lambda - 1 - 1/(exp(lambda) - 1) | |
## == 0 | |
curve(-1*tpl(x), from = 1e-9, 1, log = "xy") | |
curve(-1*tpl2(x), from = 1e-12, 1, log = "xy") |
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