agridat (version 1.5)

senshu.rice: Response of rice to solar radiation and temperature

Description

Response of rice to solar radiation and temperature

Usage

data(senshu.rice)

source

Seshu, D. V. and Cady, F. B. 1984. Response of rice to solar radiation and temperature estimated from international yield trials. Crop Science, 24, 649-654.

Details

Minimum temperature is the average across 30 days post flowering.

References

Walter W. Piegorsch, A. John Bailer. (2005) Analyzing Environmental Data, Wiley.

Examples

dat <- senshu.rice

plot(yield~mint, dat)

# Model 1 of Senshu & Cady
m1 <- lm(yield ~ 1 + rad + mint + I(mint^2), dat)
coef(m1)

# Use Fieller to calculate conf int around optimum minimum temp
# See: Piegorsch & Bailer, p. 31. 
# Calculation derived from vegan:::fieller.MOStest
m2 <- lm(yield ~ 1 + mint + I(mint^2), dat)
b1 <- coef(m2)[2]
b2 <- coef(m2)[3]
vc <- vcov(m2)
sig11 <- vc[2,2]
sig12 <- vc[2,3]
sig22 <- vc[3,3]
u <- -b1/2/b2
tval <- qt(1-.05/2, nrow(dat)-3)
gam <- tval^2 * sig22 / b2^2
x <- u + gam * sig12 / (2 * sig22)
f <- tval / (-2*b2)
sq <- sqrt(sig11 + 4*u*sig12 + 4*u^2*sig22 - gam * (sig11 - sig12^2 / sig22) )
ci <- (x + c(1,-1)*f*sq) / (1-gam)
plot(yield ~ mint, dat, xlim=c(17, 32),
main="Quadratic fit and Fieller confidence interval")
lines(17:32, predict(m2, new=data.frame(mint=17:32)))
abline(v=ci, col="blue")