R Under development (unstable) (2023-11-23 r85618 ucrt) -- "Unsuffered Consequences"
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> library(dglm)
> options(warnPartialMatchArgs=TRUE,warnPartialMatchAttr=TRUE,warnPartialMatchDollar=TRUE,width=120)
> 
> set.seed(0); u <- runif(100)
> 
> n <- 100
> y <- rnorm(n)
> x <- rnorm(n)
> z <- rnorm(n)
> 
> fit <- dglm(y~x,~z,method="ml")
Warning message:
In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> summary(fit)

Call: dglm(formula = y ~ x, dformula = ~z, method = "ml")

Mean Coefficients:
               Estimate Std. Error    t value  Pr(>|t|)
(Intercept) -0.07365451 0.08872031 -0.8301877 0.4084505
x           -0.09533765 0.08522001 -1.1187238 0.2659927
(Dispersion Parameters for gaussian family estimated as below )

    Scaled Null Deviance: 101.2771 on 99 degrees of freedom
Scaled Residual Deviance: 99.99999 on 98 degrees of freedom

Dispersion Coefficients:
               Estimate Std. Error    z value   Pr(>|z|)
(Intercept) -0.25841298  0.1416823 -1.8238907 0.06816859
z           -0.09276393  0.1520989 -0.6098922 0.54193325
(Dispersion parameter for Gamma family taken to be 2 )

    Scaled Null Deviance: 123.011 on 99 degrees of freedom
Scaled Residual Deviance: 122.6977 on 98 degrees of freedom

Minus Twice the Log-Likelihood: 257.4222 
Number of Alternating Iterations: 5 
Warning messages:
1: In x$coef : partial match of 'coef' to 'coefficients'
2: In xd$coef : partial match of 'coef' to 'coefficients'
> fit <- dglm(y~x,~z,method="reml")
Warning message:
In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> summary(fit)

Call: dglm(formula = y ~ x, dformula = ~z, method = "reml")

Mean Coefficients:
               Estimate Std. Error    t value  Pr(>|t|)
(Intercept) -0.07348603 0.08871715 -0.8283183 0.4095030
x           -0.09547360 0.08521748 -1.1203524 0.2653018
(Dispersion Parameters for gaussian family estimated as below )

    Scaled Null Deviance: 98.96709 on 99 degrees of freedom
Scaled Residual Deviance: 97.71554 on 98 degrees of freedom

Dispersion Coefficients:
               Estimate Std. Error    z value  Pr(>|z|)
(Intercept) -0.23523940  0.1445358 -1.6275509 0.1036202
z           -0.09388925  0.1554761 -0.6038821 0.5459221
(Dispersion parameter for Gamma family taken to be 2 )

    Scaled Null Deviance: 122.8569 on 99 degrees of freedom
Scaled Residual Deviance: 122.5692 on 98 degrees of freedom

Minus Twice the Log-Likelihood: 257.4488 
Number of Alternating Iterations: 5 
Warning messages:
1: In x$coef : partial match of 'coef' to 'coefficients'
2: In xd$coef : partial match of 'coef' to 'coefficients'
> anova(fit)
Analysis of Deviance Table

gaussian double generalized linear model

Response: y

                 DF Seq.Chisq   Seq.P Adj.Chisq   Adj.P
Mean model        1   0.96164 0.32677   1.16870 0.27967
Dispersion model  1   0.27429 0.60047   0.27429 0.60047
Warning messages:
1: In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
2: In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
3: In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> 
> y2 <- y^2
> fit <- dglm(y2~x,~z,family=Gamma(link="log"),method="ml")
Warning message:
In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> summary(fit)

Call: dglm(formula = y2 ~ x, dformula = ~z, family = Gamma(link = "log"), 
    method = "ml")

Mean Coefficients:
               Estimate Std. Error    t value   Pr(>|t|)
(Intercept) -0.23510547  0.1264333 -1.8595213 0.06595317
x           -0.07787201  0.1236347 -0.6298555 0.53025489
(Dispersion Parameters for Gamma family estimated as below )

    Scaled Null Deviance: 128.4689 on 99 degrees of freedom
Scaled Residual Deviance: 128.0307 on 98 degrees of freedom

Dispersion Coefficients:
              Estimate Std. Error   z value     Pr(>|z|)
(Intercept) 0.74222087  0.1164414 6.3742033 1.839165e-10
z           0.01570531  0.1249692 0.1256735 8.999904e-01
(Dispersion parameter for Digamma family taken to be 2 )

    Scaled Null Deviance: 158.2718 on 99 degrees of freedom
Scaled Residual Deviance: 161.8657 on 98 degrees of freedom

Minus Twice the Log-Likelihood: 100.1187 
Number of Alternating Iterations: 9 
Warning messages:
1: In x$coef : partial match of 'coef' to 'coefficients'
2: In xd$coef : partial match of 'coef' to 'coefficients'
> fit <- dglm(y2~x,~z,family=Gamma(link="log"),method="reml")
Warning message:
In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> summary(fit)

Call: dglm(formula = y2 ~ x, dformula = ~z, family = Gamma(link = "log"), 
    method = "reml")

Mean Coefficients:
               Estimate Std. Error    t value   Pr(>|t|)
(Intercept) -0.23496753  0.1264214 -1.8586062 0.06608415
x           -0.07774942  0.1236169 -0.6289545 0.53084220
(Dispersion Parameters for Gamma family estimated as below )

    Scaled Null Deviance: 127.1236 on 99 degrees of freedom
Scaled Residual Deviance: 126.6909 on 98 degrees of freedom

Dispersion Coefficients:
              Estimate Std. Error   z value     Pr(>|z|)
(Intercept) 0.75259599  0.1179156 6.3824985 1.742217e-10
z           0.01827825  0.1266276 0.1443465 8.852269e-01
(Dispersion parameter for Digamma family taken to be 2 )

    Scaled Null Deviance: 158.262 on 99 degrees of freedom
Scaled Residual Deviance: 161.5447 on 98 degrees of freedom

Minus Twice the Log-Likelihood: 100.1277 
Number of Alternating Iterations: 8 
Warning messages:
1: In x$coef : partial match of 'coef' to 'coefficients'
2: In xd$coef : partial match of 'coef' to 'coefficients'
> 
> # 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
> # However, dglm uses  ml  not  reml,  so the results are slightly different:
> out <- dglm(lot1 ~ log(u), ~1, data=clotting, family=Gamma)
Warning message:
In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> summary(out)

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 4.279230e-07
log(u)       0.01534311 0.0004149596  36.97496 2.751191e-09
(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 1.297468e-40
(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 Log-Likelihood: 31.98992 
Number of Alternating Iterations: 4 
Warning messages:
1: In x$coef : partial match of 'coef' to 'coefficients'
2: In xd$coef : partial match of 'coef' to 'coefficients'
> 
> # Try a double glm 
> out2 <- dglm(lot1 ~ log(u), ~u, data=clotting, family=Gamma)
Warning message:
In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> 
> summary(out2)

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 4.464149e-07
log(u)       0.01596262 0.0002301215  69.36604 3.402379e-11
(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 1.803438e-09
u           -0.06966577 0.01502817 -4.635680 3.557663e-06
(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 Log-Likelihood: 22.17126 
Number of Alternating Iterations: 5 
Warning messages:
1: In x$coef : partial match of 'coef' to 'coefficients'
2: In xd$coef : partial match of 'coef' to 'coefficients'
> anova(out2)
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
Warning messages:
1: In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
2: In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
3: In dfamily$dev.resid : partial match of 'dev.resid' to 'dev.resids'
> 
> # Summarize the mean model as for a glm
> summary.glm(out2)

Call:
dglm(formula = lot1 ~ log(u), dformula = ~u, family = Gamma, 
    data = clotting)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.0178480  0.0010062  -17.74 4.46e-07 ***
log(u)       0.0159626  0.0002301   69.37 3.40e-11 ***
---
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

>     
> # Summarize the dispersion model as for a glm
> summary(out2$dispersion.fit)

Call:
dglm(formula = ~u, family = Digamma(link = "log"), data = clotting)

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -4.59257    0.53790  -8.538    6e-05 ***
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

> 
> proc.time()
   user  system elapsed 
   0.28    0.09    0.35