In charlotte-ngs/asmss2022: Applied Statistical Methods in Animal Science - Spring Semester 2022

Background

According to https://www.sciencedirect.com/science/article/pii/S1751731121001683#t0005 methane emission per cow and year ($E$) can be computed as

$$E = F * \alpha$$

where $F$ is the total dry matter intake per cow and year. Because this is a multiplicative model, we take logarithms to get a linear regression where

$$log(E) = log(F * \alpha) = log(\alpha) + log(F)$$

Hence using logarithms, we can use it as data for a linear regression

# methane in kgg per kg DM
alpha <- 20.72/1000
log(alpha)

# mean CH4 emmission in kg per year
n_mean_ch4 <- 120
n_sd_shrink_ch4 <- 10
n_sd_ch4 <- 31/n_sd_shrink_ch4

# DMI
n_mean_dmi <- n_mean_ch4 / alpha
n_mean_dmi

n_sd_dmi <- n_sd_ch4 / alpha
nd_sd_shrink_dmi <- 4
n_sd_dmi <- n_sd_dmi / nd_sd_shrink_dmi
n_sd_dmi

Data

set.seed(1532)
n_nr_rec_p2 <- 15
vec_log_ch4 <- rnorm(n_nr_rec_p2, mean = log(n_mean_ch4), sd = log(n_sd_ch4))
summary(vec_log_ch4)

vec_log_dmi <- rnorm(n_nr_rec_p2, mean = log(n_mean_dmi), sd = log(n_sd_dmi))
summary(vec_log_dmi)

Use a model for `lCH4``

n_ch4_dmi_beta <- 1.531
vec_log_ch4_fit <- n_ch4_dmi_beta * vec_log_dmi + log(alpha)/n_sd_shrink_ch4 + rnorm(n_nr_rec_p2, sd = n_sd_ch4)
mean(vec_log_ch4_fit)

tbl_ch4_dmi <- tibble::tibble(Animal = c(1:n_nr_rec_p2),
                              lDMI = round(vec_log_dmi, digits = 2), 
                              lCH4 = round(vec_log_ch4_fit, digits = 2))
tbl_ch4_dmi

Show a plot

library(ggplot2)
ggplot(data = tbl_ch4_dmi, aes(x = lDMI, y = lCH4)) + 
  geom_point() + 
  geom_smooth(method = "lm", se = FALSE, aes(color = "red"), show.legend = FALSE) 

Save Data to File

s_exam_data_p02 <- file.path(here::here(), "docs", "data", "asm_exam_p02.csv")
if (!file.exists(s_exam_data_p02))
  readr::write_csv(tbl_ch4_dmi, s_exam_data_p02)

charlotte-ngs/asmss2022 documentation built on June 7, 2022, 1:33 p.m.