[R] Follow-up to Reply: Overdispersion with binomial distribution

[Michael Dewey]

At 15:24 23/02/2009, Jessica L Hite/hitejl/O/VCU wrote:

>THANKS so very much for your help (previous and future!). I have a two
>follow-up questions.
>
>1) You say that dispersion = 1 by definition ....dispersion changes from 1
>to 13.5 when I go from binomial to quasibinomial....does this suggest that
>I should use the binomial? i.e., is the dispersion factor more important
>that the
>
>2) Is there a cutoff for too much overdispersion - mine seems to be
>huge......Residual deviance: 1580.1  on 123  degrees of freedom
>I do have some outliers - but they are legitimate (i.e., not typos).....
>
>I included my data below....if it helps

In your model you have y and Pred1 but in your dataset you have Pred1 
and PercentSurvival so that is not the model you fitted. If you 
fitted PercentSurvival ~ Pred1 did you not get any warning?



>  summary(glm.D93)$dispersion ## 1 (by definition)
>
>Call:
>glm(formula = y ~ Pred1, family = "binomial")
>
>Deviance Residuals:
>    Min      1Q  Median      3Q     Max
>-9.940  -2.778  -0.710   2.130  10.479
>
>Coefficients:
>             Estimate Std. Error z value Pr(>|z|)
>(Intercept)  1.63942    0.07205  22.753  < 2e-16 ***
>Pred1F      -0.65228    0.11781  -5.537 3.08e-08 ***
>Pred1O      -3.03239    0.12782 -23.724  < 2e-16 ***
>Pred1SN     -3.60714    0.11057 -32.623  < 2e-16 ***
>Pred1W      -1.22131    0.10734 -11.378  < 2e-16 ***
>---
>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>(Dispersion parameter for binomial family taken to be 1)
>
>     Null deviance: 3506.7  on 127  degrees of freedom
>Residual deviance: 1580.1  on 123  degrees of freedom
>   (1 observation deleted due to missingness)
>AIC: 1863.1
>
>Number of Fisher Scoring iterations: 5
>
> > glm1<-glm(y~Pred1,"quasibinomial")
> > summary(glm1)
>
>Call:
>glm(formula = y ~ Pred1, family = "quasibinomial")
>
>Deviance Residuals:
>    Min      1Q  Median      3Q     Max
>-9.940  -2.778  -0.710   2.130  10.479
>
>Coefficients:
>             Estimate Std. Error t value Pr(>|t|)
>(Intercept)   1.6394     0.2646   6.197 7.96e-09 ***
>Pred1F       -0.6523     0.4326  -1.508  0.13415
>Pred1O       -3.0324     0.4693  -6.461 2.19e-09 ***
>Pred1SN      -3.6071     0.4060  -8.885 6.51e-15 ***
>Pred1W       -1.2213     0.3941  -3.099  0.00241 **
>---
>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>(Dispersion parameter for quasibinomial family taken to be 13.48239)
>
>     Null deviance: 3506.7  on 127  degrees of freedom
>Residual deviance: 1580.1  on 123  degrees of freedom
>   (1 observation deleted due to missingness)
>AIC: NA
>
>Number of Fisher Scoring iterations: 5
>
>
>DATA
>
>
>Pred1 PercentSurvival
>O     0.181818182
>O     0
>O     0
>O     0
>O     0
>F     0.766666667
>F     0.967741935
>F     0.8
>F     0.966666667
>F     0.833333333
>F     0.775
>F     0.641025641
>F     0.272727273
>F     0.606060606
>F     0.621621622
>F     0.574468085
>F     0.918918919
>F     0.854166667
>F     0.684210526
>A     0.438596491
>A     0.8
>A     0.125
>A     0.936507937
>A     0.911764706
>A     0.75
>A     0
>A     0.64
>A     0.740740741
>A     0.703703704
>A     0.962962963
>A     0.911111111
>A     0.97260274
>A     0.842105263
>A     0.795454545
>A     0.970588235
>A     0.755555556
>A     0.947368421
>A     1
>A     0.947368421
>A     0.785714286
>A     0.782178218
>A     1
>A     0.6
>A     0.875
>A     0.625
>A     0.666666667
>A     1
>A     1
>A     0.611111111
>A     0.916666667
>A     0.625
>A     0.97826087
>A     0.975
>A     0.933333333
>A     1
>A     1
>A     0.930232558
>A     0.810810811
>O     0
>O     0
>O     1
>O     0
>SN    0
>SN    0
>SN    0.696969697
>SN    0
>SN    0.533333333
>SN    0
>SN    0.027777778
>SN    0.6
>SN    0.052631579
>SN    0
>SN    0
>SN    0
>SN    0.619047619
>SN    0
>SN    0
>SN    0
>SN    0.08
>SN    0
>SN    0.090909091
>SN    0
>SN    0.5
>SN    0
>SN    0.78125
>SN    0
>SN    0
>SN    0
>SN    0
>SN    0.542857143
>SN    0
>SN    0
>SN    0
>SN    0
>SN    0.4
>SN    0
>SN    0
>SN    0.433333333
>O     0.655172414
>O     0.238095238
>O     0
>O     0.409090909
>O     0
>O     0
>O     0.090909091
>O     0.310344828
>O     0
>O     0
>O     0
>O     0.783783784
>W     0.928571429
>W     0
>W     0.651162791
>W     0.3125
>
>W     0.871794872
>W     0.511627907
>W     0.566666667
>W     0.756756757
>W     0
>W     0.666666667
>W     0.55
>W     0.826086957
>W     0.8
>W     0.682926829
>W     0.586206897
>W     1
>W     0.75
>W     0.5625
>
>         [[alternative HTML version deleted]]

Michael Dewey
http://www.aghmed.fsnet.co.uk