Transcript PPT

Tobacco budworm Heliothis virescens
The tobacco budworm, Heliothis virescens (Fabricius), is a native
species and is found throughout the eastern and southwestern
United States, though it is also known from California. It
generally overwinters successfully only in southern states.
However, it occasionally survives cold climates in greenhouses
and other sheltered locations.
Tobacco budworm disperses northward annually, and
can be found in New England, New York, and southern
Canada during the late summer. It also occurs widely in
the Caribbean, and sporadically in Central and South
America.
Experiment: Reaction of the tobacco budworm Heliothis virescens to
doses of the pyrethroid trans-cypermethrin. Batches of 20 moth of each
sex were exposed for three days to the pyrethroid and the number in each
batch that were dead or knocked down was recorded.
M
0.8
Gender: represented by variable
y = M, F
M
F
0.6
M
F
F
0.4
M
0.2
F
Dose: represented by variable
x = 1,2,4,8,16,32
M
F
0.0
Proportion of knocked/dead
Proportion of knocked moths:
p(x,y)
1.0
Experiment data
M
F
1
2
5
Dose, mg
10
20
1.0
Model 1: logit [p(x,y)] = a + b x
M
F
0.6
M
F
F
0.4
M
F
0.2
Proportion of knocked/dead
0.8
M
M
0.0
F
M
F
1
2
5
Dose, mg
Effect of dose on survival rate
Effect is highly significant and explains most of the variation in the
data. Still, we see that the gender information can improve the
prediction.
10
20
1.0
Model 2: logit [p(x,y)] = a + g y
M
F
0.6
M
F
F
0.4
M
F
0.2
Proportion of knocked/dead
0.8
M
M
0.0
F
M
F
1
2
5
Dose, mg
Effect of moth gender on survival rate
Effect is significant but can’t explain the variation in data:
the residual deviance is almost the same as the null deviance.
Collinearity: Notice that significance of both parameters decreased.
This is because they both have the same effect (constant level) and
R cannot decide which one to choose.
10
20
1.0
Model 3: logit [p(x)] = a + b x + g y
M
F
0.6
M
F
F
0.4
M
F
0.2
Proportion of knocked/dead
0.8
M
M
0.0
F
M
F
1
2
5
Dose, mg
Individual effects of moth gender and dose on survival rate
The same dose-slope b for males and females,
different intercepts a + g and a.
Effects of both factors are significant and explain really well the data variation.
10
20
1.0
Model 4: logit [p(x)] = a + b1xI{y=M} + b2xI{y=F}
M
F
0.6
M
F
F
0.4
M
F
0.2
Proportion of knocked/dead
0.8
M
M
0.0
F
M
F
1
2
5
Dose, mg
Combined effect of gender-dose on survival rate
Different dose-slopes bi for males and females,
intercept a is the same.
All parameters are significant and explain really well the data variation.
10
20
1.0
Model 5: logit [p(x)] = a + bx + g y + b1xI{y=M}
M
F
0.6
M
F
F
0.4
M
F
0.2
Proportion of knocked/dead
0.8
M
M
0.0
F
M
F
1
2
5
Dose, mg
Effect of moth gender and dose on survival rate
Different dose-slopes (b + b1) and b for males and females,
different intercepts (a +g ) and a.
Effects of both factors are significant and explain really well the data
variation. The AIC suggests that this model is inferior to Model 4:
additional parameter is not worth the fit improvement.
10
20