gamma.shape.glm.RdFind the maximum likelihood estimate of the shape parameter of
the gamma distribution after fitting a Gamma generalized
linear model.
gamma.shape(object, ...)
# S3 method for class 'glm'
gamma.shape(object, it.lim = 10,
eps.max = .Machine$double.eps^0.25, verbose = FALSE, ...)Fitted model object from a Gamma family or quasi family with
variance = "mu^2".
Upper limit on the number of iterations.
Maximum discrepancy between approximations for the iteration process to continue.
If TRUE, causes successive iterations to be printed out. The
initial estimate is taken from the deviance.
further arguments passed to or from other methods.
List of two components
the maximum likelihood estimate
the approximate standard error, the square-root of the reciprocal of the observed information.
A glm fit for a Gamma family correctly calculates the maximum likelihood estimate of the mean parameters but provides only a crude estimate of the dispersion parameter. This function takes the results of the glm fit and solves the maximum likelihood equation for the reciprocal of the dispersion parameter, which is usually called the shape (or exponent) parameter.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
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))
clot1 <- glm(lot1 ~ log(u), data = clotting, family = Gamma)
gamma.shape(clot1)
#>
#> Alpha: 538.1315
#> SE: 253.5991
gm <- glm(Days + 0.1 ~ Age*Eth*Sex*Lrn,
quasi(link=log, variance="mu^2"), quine,
start = c(3, rep(0,31)))
gamma.shape(gm, verbose = TRUE)
#> Initial estimate: 1.060344
#> Iter. 1 Alpha: 1.238408
#> Iter. 2 Alpha: 1.276997
#> Iter. 3 Alpha: 1.278343
#> Iter. 4 Alpha: 1.278345
#>
#> Alpha: 1.2783449
#> SE: 0.1345175
summary(gm, dispersion = gamma.dispersion(gm)) # better summary
#>
#> Call:
#> glm(formula = Days + 0.1 ~ Age * Eth * Sex * Lrn, family = quasi(link = log,
#> variance = "mu^2"), data = quine, start = c(3, rep(0, 31)))
#>
#> Coefficients: (4 not defined because of singularities)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 3.06105 0.44223 6.922 4.46e-12 ***
#> AgeF1 -0.61870 0.59331 -1.043 0.297041
#> AgeF2 -2.31911 0.98885 -2.345 0.019014 *
#> AgeF3 -0.37623 0.53149 -0.708 0.479020
#> EthN -0.13789 0.62540 -0.220 0.825496
#> SexM -0.48844 0.59331 -0.823 0.410369
#> LrnSL -1.92965 0.98885 -1.951 0.051009 .
#> AgeF1:EthN 0.10249 0.82338 0.124 0.900942
#> AgeF2:EthN -0.50874 1.39845 -0.364 0.716017
#> AgeF3:EthN 0.06314 0.74584 0.085 0.932534
#> AgeF1:SexM 0.40695 0.94847 0.429 0.667884
#> AgeF2:SexM 3.06173 1.11626 2.743 0.006091 **
#> AgeF3:SexM 1.10841 0.74208 1.494 0.135267
#> EthN:SexM -0.74217 0.82338 -0.901 0.367394
#> AgeF1:LrnSL 2.60967 1.10114 2.370 0.017789 *
#> AgeF2:LrnSL 4.78434 1.36304 3.510 0.000448 ***
#> AgeF3:LrnSL NA NA NA NA
#> EthN:LrnSL 2.22936 1.39845 1.594 0.110899
#> SexM:LrnSL 1.56531 1.18112 1.325 0.185077
#> AgeF1:EthN:SexM -0.30235 1.32176 -0.229 0.819065
#> AgeF2:EthN:SexM 0.29742 1.57035 0.189 0.849780
#> AgeF3:EthN:SexM 0.82215 1.03277 0.796 0.425995
#> AgeF1:EthN:LrnSL -3.50803 1.54655 -2.268 0.023311 *
#> AgeF2:EthN:LrnSL -3.33529 1.92481 -1.733 0.083133 .
#> AgeF3:EthN:LrnSL NA NA NA NA
#> AgeF1:SexM:LrnSL -2.39791 1.51050 -1.587 0.112400
#> AgeF2:SexM:LrnSL -4.12161 1.60698 -2.565 0.010323 *
#> AgeF3:SexM:LrnSL NA NA NA NA
#> EthN:SexM:LrnSL -0.15305 1.66253 -0.092 0.926653
#> AgeF1:EthN:SexM:LrnSL 2.13480 2.08685 1.023 0.306317
#> AgeF2:EthN:SexM:LrnSL 2.11886 2.27882 0.930 0.352473
#> AgeF3:EthN:SexM:LrnSL NA NA NA NA
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for quasi family taken to be 0.7822615)
#>
#> Null deviance: 190.40 on 145 degrees of freedom
#> Residual deviance: 128.36 on 118 degrees of freedom
#> AIC: NA
#>
#> Number of Fisher Scoring iterations: 7
#>