[R-sig-eco] Logistic regression with 2 categorical predictors

Tue Oct 21 16:53:42 CEST 2014

Hi Andrew,

Please keep the mailing list in cc.

The estimates in mc are the differences of the parameter estimates (betas) between both levels. E.g. 5.LR -1.LR = -1.168 or 5.LR = 1.LR - 1.168

summary(mc) should give you the significance of those differences. That should work. If it doesn't, please provide more info: at least your code and the error message. A small reproducible example is better.
confint(mc) gives the confidence intervals of the differences.

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

Van: Andrew Halford [mailto:andrew.halford at gmail.com]
Verzonden: dinsdag 21 oktober 2014 16:19
Aan: ONKELINX, Thierry
Onderwerp: Re: [R-sig-eco] Logistic regression with 2 categorical predictors

Hi Thierry,
Thanks for the response. I have run your code but it seems you cant call the summary function, you just have to call the object on its own i.e. mc. The results are I get are below but I am not sure how to interpret these, exactly what does the estimate represent? How do I measure significance here?

                   Estimate
2.LR - 1.LR == 0  1.252e-01
3.LR - 1.LR == 0 -5.390e-01
4.LR - 1.LR == 0  1.802e-02
5.LR - 1.LR == 0 -1.168e+00
6.LR - 1.LR == 0 -2.575e+01
1.SD - 1.LR == 0  7.411e-02
2.SD - 1.LR == 0 -2.408e-01
3.SD - 1.LR == 0  2.675e-01
etc etc

Andy

On 20 October 2014 23:04, ONKELINX, Thierry <Thierry.ONKELINX at inbo.be> wrote:
Dear Andrew,

anova() and summary() test different hypotheses. anova() tests is at least one level is different from the others. summary() tests if the coefficient is different from zero.

Multiple comparison of different interaction levels is probably the most relevant in this case. The easiest way is to make a new variable.

snapper2$inter <- with(snapper2, interaction(age, test))
model <- glm(cbind(prefer,avoid) ~ 0 + inter, data=snapper2, family=binomial)
library(multcomp)
mc <- glht(model, mcp(inter = "Tukey))
summary(mc)

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

-----Oorspronkelijk bericht-----
Van: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] Namens Andrew Halford
Verzonden: maandag 20 oktober 2014 16:06
Aan: r-sig-ecology at r-project.org
Onderwerp: [R-sig-eco] Logistic regression with 2 categorical predictors

Hi Listers,

I am trying to run a logistic regression to look at the effects of experiment type and age on the behavior of fish in a choice chamber experiment.

I am using the glm approach and would like some advice on how or whether to perform contrasts to work out what levels of Factor1 (Age) and Factor 2
(Test) are significantly different from each other. I have not been able to clarify from my reading what is the appropriate approach to take when dealing with a significant interaction term. I am also not sure as to how one interprets a model when all the coefficients are non-significant but the chi-square ANOVA shows a highly significant interaction term.

I have graphed up the data as dot plots and there is definitely evidence of changes in proportions in later ages.

I want to provide evidence for when and for which tests there was a 'significant' change in behavior.

> snapper2
   age test prefer avoid
1    1   LR     15    14
2    1   SD     15    13
3    1   SG     17    14
4    1   SW     14    14
5    2   LR     17    14
6    2   SD     16    19
7    2   SG     20    10
8    2   SW     15    21
9    3   LR     10    16
10   3   SD     14    10
11   3   SG     14     9
12   3   SW     13    15
13   4   LR     12    11
14   4   SD     14    11
15   4   SG     13    12
16   4   SW     11    14
17   5   LR      4    12
18   5   SD      8     8
19   5   SG      0    18
20   5   SW     10     6
21   6   LR      0     6
22   6   SD      3     4
23   6   SG      0     5
24   6   SW      5     3

 >
dotplot(age~prefer/avoid,data=snapper2,group=snapper2$test,cex=1.5,pch=19,ylab="age",auto.key=list(space="right",title="Tests"))

> out2 <- glm(cbind(prefer,avoid) ~ age*test, data=snapper2,
family=binomial)

> summary(out2)

Call:
glm(formula = cbind(prefer, avoid) ~ age * test, family = binomial,
    data = snapper2)

Deviance Residuals:
 [1]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Coefficients:
              Estimate Std. Error z value Pr(>|z|)
(Intercept)  6.899e-02  3.716e-01   0.186   0.8527
age2         1.252e-01  5.180e-01   0.242   0.8091
age3        -5.390e-01  5.483e-01  -0.983   0.3256
age4         1.802e-02  5.589e-01   0.032   0.9743
age5        -1.168e+00  6.866e-01  -1.701   0.0890 .
age6        -2.575e+01  9.348e+04   0.000   0.9998
testSD       7.411e-02  5.307e-01   0.140   0.8890
testSG       1.252e-01  5.180e-01   0.242   0.8091
testSW      -6.899e-02  5.301e-01  -0.130   0.8964
age2:testSD -4.401e-01  7.260e-01  -0.606   0.5444
age3:testSD  7.324e-01  7.846e-01   0.933   0.3506
age4:testSD  8.004e-02  7.863e-01   0.102   0.9189
age5:testSD  1.024e+00  9.301e-01   1.102   0.2707
age6:testSD  2.532e+01  9.348e+04   0.000   0.9998
age2:testSG  3.738e-01  7.407e-01   0.505   0.6138
age3:testSG  7.867e-01  7.832e-01   1.004   0.3152
age4:testSG -1.321e-01  7.764e-01  -0.170   0.8649
age5:testSG -2.568e+01  8.768e+04   0.000   0.9998
age6:testSG  2.121e-02  1.334e+05   0.000   1.0000
age2:testSW -4.616e-01  7.249e-01  -0.637   0.5242
age3:testSW  3.959e-01  7.662e-01   0.517   0.6054
age4:testSW -2.592e-01  7.858e-01  -0.330   0.7415
age5:testSW  1.678e+00  9.386e-01   1.788   0.0737 .
age6:testSW  2.626e+01  9.348e+04   0.000   0.9998
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 5.4908e+01  on 23  degrees of freedom Residual deviance: 2.6113e-10  on  0  degrees of freedom
AIC: 122.73

Number of Fisher Scoring iterations: 23

> anova(out2, test="Chisq")

Analysis of Deviance Table

Model: binomial, link: logit

Response: cbind(prefer, avoid)

Terms added sequentially (first to last)

         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)
NULL                        23     54.908
age       5   11.235        18     43.673 0.0469115 *
test      3    1.593        15     42.079 0.6608887
age:test 15   42.079         0      0.000 0.0002185 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

cheers

Andy
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The views expressed in this message and any annex are purely those of the writer and may not be regarded as stating an official position of INBO, as long as the message is not confirmed by a duly signed document.