Description Usage Arguments Details Value Note Author(s) References See Also Examples
These functions are all methods
for class dglm
or
summary.glm
objects.
1 2 
object 
an object of class 
dispersion 
the dispersion parameter for the fitting family.
By default it is obtained from 
correlation 
logical; if 
... 
further arguments to be passed to 
For more details, see summary.glm
.
If more than one of etastart
, start
and mustart
is specified, the first in the list will be used.
summary.dglm
returns an object of class
"summary.dglm"
, a list with components
call 
the component from 
terms 
the component from 
family 
the component from 
deviance 
the component from 
aic 

constrasts 
(where relevant) the contrasts used. NOT WORKING?? 
df.residual 
the component from 
null.deviance 
the component from 
df.null 
the residual degrees of freedom for the null model. 
iter 
the component from 
deviance.resid 
the deviance residuals: see 
coefficients 
the matrix of coefficients, standard errors, zvalues and pvalues. Aliased coefficients are omitted. 
aliased 
named logical vector showing if the original coefficients are aliased. 
dispersion 
either the supplied argument or the estimated dispersion
if the latter in 
df 
a 3vector of the rank of the model and the number of residual degrees of freedom, plus number of nonaliased coefficients. 
cov.unscaled 
the unscaled ( 
cov.scaled 
ditto, scaled by 
correlation 
(only if 
dispersion.summary 
the summary of the fitted dispersion model 
outer.iter 
the number of outer iteration of the alternating iterations 
m2loglik 
minus twice the loglikelihood of the fitted model 
The anova method is questionable when applied to an dglm
object with
method="reml"
(stick to method="ml"
).
Gordon Smyth, ported to R\ by Peter Dunn ([email protected])
Smyth, G. K. (1989). Generalized linear models with varying dispersion. J. R. Statist. Soc. B, 51, 47–60.
Smyth, G. K., and Verbyla, A. P. (1999). Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics, 10, 696709.
Verbyla, A. P., and Smyth, G. K. (1998). Double generalized linear models: approximate residual maximum likelihood and diagnostics. Research Report, Department of Statistics, University of Adelaide.
dglm.object
, dglm.control
,
anova.dglm
,
summary.glm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  # Continuing the example from glm, but this time try
# fitting a Gamma double generalized linear model also.
clotting < data.frame(
u = c(5,10,15,20,30,40,60,80,100),
lot1 = c(118,58,42,35,27,25,21,19,18),
lot2 = c(69,35,26,21,18,16,13,12,12))
# The same example as in glm: the dispersion is modelled as constant
out < dglm(lot1 ~ log(u), ~1, data=clotting, family=Gamma)
summary(out)
# Try a double glm
out2 < dglm(lot1 ~ log(u), ~u, data=clotting, family=Gamma)
summary(out2)
anova(out2)
# Summarize the mean model as for a glm
summary.glm(out2)
# Summarize the dispersion model as for a glm
summary(out2$dispersion.fit)

Loading required package: statmod
Call: dglm(formula = lot1 ~ log(u), dformula = ~1, family = Gamma,
data = clotting)
Mean Coefficients:
Estimate Std. Error t value Pr(>t)
(Intercept) 0.01655438 0.0009275491 17.84744 4.279230e07
log(u) 0.01534311 0.0004149596 36.97496 2.751191e09
(Dispersion Parameters for Gamma family estimated as below )
Scaled Null Deviance: 1890.363 on 8 degrees of freedom
Scaled Residual Deviance: 9.002787 on 7 degrees of freedom
Dispersion Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 6.288103 0.4712586 13.34321 1.297468e40
(Dispersion parameter for Digamma family taken to be 2 )
Scaled Null Deviance: 8.90448 on 8 degrees of freedom
Scaled Residual Deviance: 8.90448 on 8 degrees of freedom
Minus Twice the LogLikelihood: 31.98992
Number of Alternating Iterations: 4
Call: dglm(formula = lot1 ~ log(u), dformula = ~u, family = Gamma,
data = clotting)
Mean Coefficients:
Estimate Std. Error t value Pr(>t)
(Intercept) 0.01784797 0.0010062108 17.73780 4.464149e07
log(u) 0.01596262 0.0002301215 69.36604 3.402379e11
(Dispersion Parameters for Gamma family estimated as below )
Scaled Null Deviance: 2313.573 on 8 degrees of freedom
Scaled Residual Deviance: 9.003391 on 7 degrees of freedom
Dispersion Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 4.59256962 0.76357166 6.014589 1.803438e09
u 0.06966577 0.01502817 4.635680 3.557663e06
(Dispersion parameter for Digamma family taken to be 2 )
Scaled Null Deviance: 16.75853 on 8 degrees of freedom
Scaled Residual Deviance: 4.414477 on 7 degrees of freedom
Minus Twice the LogLikelihood: 22.17126
Number of Alternating Iterations: 5
Analysis of Deviance Table
Gamma double generalized linear model
Response: lot1
DF Seq.Chisq Seq.P Adj.Chisq Adj.P
Mean model 1 48.686 0.0000000 47.403 0.0000000
Dispersion model 1 9.819 0.0017275 9.819 0.0017275
Call:
dglm(formula = lot1 ~ log(u), dformula = ~u, family = Gamma,
data = clotting)
Deviance Residuals:
Min 1Q Median 3Q Max
0.076478 0.010122 0.001926 0.048233 0.093677
Coefficients:
Estimate Std. Error t value Pr(>t)
(Intercept) 0.0178480 0.0010062 17.74 4.46e07 ***
log(u) 0.0159626 0.0002301 69.37 3.40e11 ***

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for Gamma family taken to be 1.307633)
Null deviance: 2313.5733 on 8 degrees of freedom
Residual deviance: 9.0034 on 7 degrees of freedom
AIC: NA
Number of Fisher Scoring iterations: 5
Call:
dglm(formula = ~u, family = Digamma(link = "log"), data = clotting)
Deviance Residuals:
Min 1Q Median 3Q Max
2.18708 0.81757 0.07655 0.16104 1.16959
Coefficients:
Estimate Std. Error t value Pr(>t)
(Intercept) 4.59257 0.53790 8.538 6e05 ***
u 0.06967 0.01059 6.581 0.00031 ***

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for Digamma family taken to be 0.9925192)
Null deviance: 16.7585 on 7 degrees of freedom
Residual deviance: 4.4145 on 7 degrees of freedom
AIC: NA
Number of Fisher Scoring iterations: 5
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