Workshop in R and GLMs: #4

Diane Srivastava

University of British Columbia

srivast@zoology.ubc.ca

Exercise

1. Fit the binomial glm survival = size*treat

2. Fit the bionomial glm parasitism = size*treat

3. Predict what size has 50% parasitism in treatment “0”

Predicting size for p=0.5, treat=0

Output from logistic regression with logit link: predicted loge (p/1-p) = a+bx

So when p=0.5, solve log(1)=a+bx

Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.38462 0.16780 -14.211 <2e-16 ***size 0.76264 0.04638 16.442 <2e-16 ***treat 0.28754 0.23155 1.242 0.214 size:treat -0.09477 0.06357 -1.491 0.136

What is equation for treat 0? treat 1?

Rlecture.csv

0

10

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100

0 2 4 6 8

Size

Par

asit

ism

(%

)

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7

Size

Gro

wth

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7

Size

Sur

viva

l

3.12

Model simplification

1. Parsimonious/ Logical sequence (e.g. highest order interactions first)

2. Stepwise sequence

3. Bayesian comparison of candidate models (not covered)

0

2

4

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12

0 2 4 6

Plant size

Lo

git

par

asit

ism

0

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0 2 4 6

Plant size

Lo

git

par

asit

ism

ANCOVA: Difference between categories….

Constant, doesn’t depend on size

Depends on size

size*treat ns size*treat sig

Deletion testsHow to change your model quickly:model2<-update(model1,~.-size:treat)

How to do a deletion test:anova(reduced model, full model, test="Chi")

1. Test for interaction in logit parasitism ANCOVAIf not sig, remove and continue. If sig, STOP!

2. Test covariate If not sig, remove and continue. If sig, put back and continue

3. Test main effect

Code for “parasitism” analysis

> ds<-read.table(file.choose(), sep=",", header=TRUE); ds> attach(ds)> par<-cbind(parasitism, 100-parasitism); par> m1<-glm(par~size*treat, data=ds, family=binomial)> summary(m1)> m2<-update(m1, ~.-size:treat)> summary(m2)> anova(m2,m1, test="Chi")> m3<-update(m2, ~.-size)> anova(m3,m2, test="Chi")> m3<-update(m2, ~.-treat)> anova(m3,m2, test="Chi")

Context (often) matters!What is the p-value for treat in:

size+treat?

treat?

Stepwise regression:

step(model)

8 11109

Jump height (how high ball can be raised off the ground)

Feet off ground

Total SS = 11.11

7

7.5

8

8.5

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9.5

10

10.5

11

4.5 5.5 6.5 7.5 8.5

Height (ft)

Ju

mp

(ft

)

X variable parameter SS F1,13 p

Height +0.943 9.96 112 <0.0001of player

7

7.5

8

8.5

9

9.5

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11

105 125 145 165 185 205

Weight (lbs)

Ju

mp

(ft

)

X variable parameter SS p

Weight +0.040 7.92 32 <0.0001of player

F1,13

Why do you think weight is + correlated with jump height?

An idea

Perhaps if we took two people of identical height, the lighter one might actually jump higher? Excess weight may reduce ability to jump high…

7

7.5

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4 5 6 7 8

Height (lbs)

Ju

mp

(ft

)

lighterheavier

X variable parameter SS F p

Height +2.133 9.956 803 <0.0001Weight -0.059 1.008 81 <0.0001

Heavy people often tall (tall people often

heavy)

Tall people can jump higher

People light for their height can jump a bit more

Weight

HeightJump

+

+

-

Species.txt

Rothamsted Park Grass experiment started in 1856

Exercise (species.txt)diane<-read.table(file.choose(), header=T); diane;

attach(diane)

Univariate trends:

plot(Species~Biomass)

plot(Species~pH)

Combined trends:

plot(Species~Biomass, type="n");

points(Species[pH=="high"]~Biomass[pH=="high"]);

points(Species[pH=="mid"]~Biomass[pH=="mid"], pch=16);

points(Species[pH=="low"]~Biomass[pH=="low"], pch=0)

Exercise (species.txt)

1. With a normal distribution, fit pH*Biomass

• check model dignostics• test interaction for significance

2. With a poisson distribution, fit pH *Biomass

• check model dignostics• test interaction for significance

0 2 4 6 8 10

1020

3040

Biomass

Spe

cies

0 2 4 6 8 10

1.0

2.0

3.0

Biomass

log(

Spe

cies

)

0 2 4 6 8 10

1.0

2.0

3.0

Biomass

log(

Spe

cies

)

Moral of the story:

Make sure you KNOW what you are modelling!

Exercise (species.txt)

1. Fit glm: Species~pH, family=gaussian

2. Test if low and mid pH have the same effect

• this is a planned comparison

Further reading

Statistics: An Introduction using R

(M.J. Crawley, Wiley publishers)

Extending the linear model with R

(JJ Faraway, Chapman & Hall/CRC)

Code for “Species” analysis

> m1<-glm(Species~pH*Biomass, family=gaussian, data=diane)> summary(m1)> m2<-update(m1, ~.-pH:Biomass)> anova(m2,m1, test="Chi")> par(mfrow=c(2,2)); plot(m1)> m3<-glm(Species~pH*Biomass, family=poisson, data=diane)> m4<-update(m3, ~.-pH:Biomass)> anova(m4,m3, test="Chi")> par(mfrow=c(2,2)); plot(m3)>PH<-(pH!="high")+0> m5<-glm(Species~pH, family=gaussian, data=diane)> m6<-update(m5, ~.-pH+PH)> anova(m6,m5, test="Chi")