anovavglm: Analysis of Deviance for Vector Generalized Linear Model Fits

Description Usage Arguments Details Value Warning Note See Also Examples

Description

Compute an analysis of deviance table for one or more vector generalized linear model fits.

Usage

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## S3 method for class 'vglm'
anova(object, ..., type = c("II", "I", "III", 2, 1, 3),
     test = c("LRT", "none"), trydev = TRUE, silent = TRUE)

Arguments

object, ...

objects of class vglm, typically the result of a call to vglm, or a list of objects for the "vglmlist" method. Each model must have an intercept term. If "vglmlist" is used then type = 1 or type = "I" must be specified.

type

character or numeric; any one of the (effectively three) choices given. Note that anova.glm has 1 or "I" as its default; and that Anova.glm() in car has 2 or "II" as its default (and allows for type = "III"), so one can think of this function as a combination of anova.glm and Anova.glm() in car, but with the default of the latter. See Details below for more information.

test

a character string, (partially) matching one of "LRT" and "none". In the future it is hoped that "Rao" be also supported, to conduct score tests. The first value is the default.

trydev

logical; if TRUE then the deviance is used if possible. Note that only a few VGAM family functions have a deviance that is defined and implemented. Setting it FALSE means the log-likelihood will be used.

silent

logical; if TRUE then any warnings will be suppressed. These may arise by IRLS iterations not converging during the fitting of submodels. Setting it FALSE means that any warnings are given.

Details

anova.vglm is intended to be similar to anova.glm so specifying a single object and type = 1 gives a sequential analysis of deviance table for that fit. By analysis of deviance, it is meant loosely that if the deviance of the model is not defined or implemented, then twice the difference between the log-likelihoods of two nested models remains asymptotically chi-squared distributed with degrees of freedom equal to the difference in the number of parameters of the two models. Of course, the usual regularity conditions are assumed to hold. For Type I, the analysis of deviance table has the reductions in the residual deviance as each term of the formula is added in turn are given in as the rows of a table, plus the residual deviances themselves. Type I or sequential tests (as in anova.glm). are computationally the easiest of the three methods. For this, the order of the terms is important, and the each term is added sequentially from first to last.

The Anova() function in car allows for testing Type II and Type III (SAS jargon) hypothesis tests, although the definitions used are not precisely that of SAS. As car notes, Type I rarely test interesting hypotheses in unbalanced designs. Type III enter each term last, keeping all the other terms in the model. Type II tests, according to SAS, add the term after all other terms have been added to the model except terms that contain the effect being tested; an effect is contained in another effect if it can be derived by deleting variables from the latter effect. Type II tests are currently the default.

As in anova.glm, but not as Anova.glm() in car, if more than one object is specified, then the table has a row for the residual degrees of freedom and deviance for each model. For all but the first model, the change in degrees of freedom and deviance is also given. (This only makes statistical sense if the models are nested.) It is conventional to list the models from smallest to largest, but this is up to the user. It is necessary to have type = 1 with more than one objects are specified.

See anova.glm for more details and warnings. The VGAM package now implements full likelihood models only, therefore no dispersion parameters are estimated.

Value

An object of class "anova" inheriting from class "data.frame".

Warning

See anova.glm. Several VGAM family functions implement distributions which do not satisfying the usual regularity conditions needed for the LRT to work. No checking or warning is given for these.

As car says, be careful of Type III tests because they violate marginality. Type II tests (the default) do not have this problem.

Note

It is possible for this function to stop when type = 2 or 3, e.g., anova(vglm(cans ~ myfactor, poissonff, data = boxcar)) where myfactor is a factor.

The code was adapted directly from anova.glm and Anova.glm() in car by T. W. Yee. Hence the Type II and Type III tests do not correspond precisely with the SAS definition.

See Also

anova.glm, stat.anova, stats:::print.anova, Anova.glm() in car if car is installed, vglm, lrtest, add1.vglm, drop1.vglm, lrt.stat.vlm, score.stat.vlm, wald.stat.vlm, backPain2, update.

Examples

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# Example 1: a proportional odds model fitted to pneumo.
set.seed(1)
pneumo <- transform(pneumo, let = log(exposure.time), x3 = runif(8))
fit1 <- vglm(cbind(normal, mild, severe) ~ let     , propodds, pneumo)
fit2 <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo)
fit3 <- vglm(cbind(normal, mild, severe) ~ let + x3, cumulative, pneumo)
anova(fit1, fit2, fit3, type = 1)  # Remember to specify 'type'!!
anova(fit2)
anova(fit2, type = "I")
anova(fit2, type = "III")

# Example 2: a proportional odds model fitted to backPain2.
data("backPain2", package = "VGAM")
summary(backPain2)
fitlogit <- vglm(pain ~ x2 * x3 * x4, propodds, data = backPain2)
coef(fitlogit)
anova(fitlogit)
anova(fitlogit, type = "I")
anova(fitlogit, type = "III")

Example output

Loading required package: stats4
Loading required package: splines
Analysis of Deviance Table

Model 1: cbind(normal, mild, severe) ~ let
Model 2: cbind(normal, mild, severe) ~ let + x3
Model 3: cbind(normal, mild, severe) ~ let + x3
  Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1        13     5.0268                     
2        12     5.0192  1  0.00762   0.9304
3        10     4.4299  2  0.58934   0.7448
Analysis of Deviance Table (Type II tests)

Model: 'cumulative', 'VGAMordinal', 'VGAMcategorical'

Links: 'logitlink'

Response: cbind(normal, mild, severe)

    Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
let  1   65.908        13     70.927 4.724e-16 ***
x3   1    0.008        13      5.027    0.9304    
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1
Analysis of Deviance Table (Type I tests: terms added sequentially from
first to last)

Model: 'cumulative', 'VGAMordinal', 'VGAMcategorical'

Links: 'logitlink'

Response: cbind(normal, mild, severe)

     Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
NULL                    14    101.641             
let   1   96.614        13      5.027   <2e-16 ***
x3    1    0.008        12      5.019   0.9304    
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1
Analysis of Deviance Table (Type III tests: each term added last)

Model: 'cumulative', 'VGAMordinal', 'VGAMcategorical'

Links: 'logitlink'

Response: cbind(normal, mild, severe)

    Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
let  1   65.908        13     70.927 4.724e-16 ***
x3   1    0.008        13      5.027    0.9304    
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1
 x2     x3     x4                       pain   
 1:39   1:21   1:64   worse               : 5  
 2:62   2:52   2:37   same                :14  
        3:28          slight.improvement  :18  
                      moderate.improvement:20  
                      marked.improvement  :28  
                      complete.relief     :16  
(Intercept):1 (Intercept):2 (Intercept):3 (Intercept):4 (Intercept):5 
   5.62742642    4.03372036    3.02435251    2.00848426    0.17216407 
          x22           x32           x33           x42       x22:x32 
  -1.84984157   -1.47577010    0.05432835   -1.46663732    0.95375608 
      x22:x33       x22:x42       x32:x42       x33:x42   x22:x32:x42 
  -1.46519553    1.49258460    0.53828907   -0.46855766   -1.86609030 
  x22:x33:x42 
  -0.02565193 
Analysis of Deviance Table (Type II tests)

Model: 'cumulative', 'VGAMordinal', 'VGAMcategorical'

Links: 'logitlink'

Response: pain

         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
x2        1  13.2238       495     329.41 0.0002764 ***
x3        2   5.1993       497     321.48 0.0743001 .  
x4        1   7.5525       495     320.79 0.0059929 ** 
x2:x3     2   3.5567       493     315.99 0.1689175    
x2:x4     1   0.6212       492     313.06 0.4306016    
x3:x4     2   0.3554       493     312.79 0.8372021    
x2:x3:x4  2   1.2912       491     312.44 0.5243360    
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1
Analysis of Deviance Table (Type I tests: terms added sequentially from
first to last)

Model: 'cumulative', 'VGAMordinal', 'VGAMcategorical'

Links: 'logitlink'

Response: pain

         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
NULL                       500     343.06              
x2        1  15.9378       499     327.12 6.546e-05 ***
x3        2   4.5430       497     322.58   0.10315    
x4        1   6.1761       496     316.40   0.01295 *  
x2:x3     2   3.1601       494     313.24   0.20597    
x2:x4     1   0.4467       493     312.79   0.50390    
x3:x4     2   0.3554       491     312.44   0.83720    
x2:x3:x4  2   1.2912       489     311.15   0.52434    
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1
Analysis of Deviance Table (Type III tests: each term added last)

Model: 'cumulative', 'VGAMordinal', 'VGAMcategorical'

Links: 'logitlink'

Response: pain

         Df Deviance Resid. Df Resid. Dev Pr(>Chi)
x2        1   2.6030       490     313.75   0.1067
x3        2   3.7380       491     314.88   0.1543
x4        1   1.7479       490     312.89   0.1861
x2:x3     2   3.9591       491     315.11   0.1381
x2:x4     1   0.8115       490     311.96   0.3677
x3:x4     2   0.4165       491     311.56   0.8120
x2:x3:x4  2   1.2912       491     312.44   0.5243

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.