Example 5.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-163)

Exam5.1 is used to show polynomial multiple regression with binomial response
References

Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
Examples


##---Sequential Fit of the logit Model
Exam5.1.glm.1 <-
  glm(
      formula    =  F/N~ X
    , family     =  quasibinomial(link = "logit")
    , data       =  DataSet5.1
    , weights    =  NULL
 #  , subset
 #  , na.action
    , start      =  NULL
 #  , etastart
 #  , mustart
 #  , offset
 #  , control    =  list(...)
 #  , model      =  TRUE
    , method     =  "glm.fit"
 #  , x          =  FALSE
 #  , y          =  TRUE
    , contrasts  =  NULL
 #  , ...
  )
summary(Exam5.1.glm.1)
#> 
#> Call:
#> glm(formula = F/N ~ X, family = quasibinomial(link = "logit"), 
#>     data = DataSet5.1, weights = NULL, start = NULL, method = "glm.fit", 
#>     contrasts = NULL)
#> 
#> Deviance Residuals: 
#>      Min        1Q    Median        3Q       Max  
#> -0.76691  -0.22615  -0.02469   0.33388   0.69423  
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)  0.24519    0.33246   0.738    0.475
#> X            0.04325    0.04178   1.035    0.321
#> 
#> (Dispersion parameter for quasibinomial family taken to be 0.1700061)
#> 
#>     Null deviance: 2.2947  on 13  degrees of freedom
#> Residual deviance: 2.1078  on 12  degrees of freedom
#> AIC: NA
#> 
#> Number of Fisher Scoring iterations: 3
#> 

## confint.default()   produce Wald Confidence interval as SAS produces
##---Likelihood Ratio test for Model 1
(LRExam5.1.glm.1  <-
  anova(
      object =  Exam5.1.glm.1
    , test   = "Chisq")
)
#> Analysis of Deviance Table
#> 
#> Model: quasibinomial, link: logit
#> 
#> Response: F/N
#> 
#> Terms added sequentially (first to last)
#> 
#> 
#>      Df Deviance Resid. Df Resid. Dev Pr(>Chi)
#> NULL                    13     2.2947         
#> X     1  0.18694        12     2.1078   0.2944

library(aod)
WaldExam5.1.glm.1 <-
  wald.test(
      Sigma   = vcov(object=Exam5.1.glm.1)
    , b       = coef(object=Exam5.1.glm.1)
    , Terms   = 2
    , L       = NULL
    , H0      = NULL
    , df      = NULL
    , verbose = FALSE
  )

##---Sequential Fit of the logit Model quadratic terms involved
Exam5.1.glm.2 <-
  glm(
      formula    =  F/N~ X + I(X^2)
    , family     =  quasibinomial(link = "logit")
    , data       =  DataSet5.1
    , weights    =  NULL
 #  , subset
 #  , na.action
    , start      =  NULL
 #  , etastart
 #  , mustart
 #  , offset
 #  , control    =  list(...)
 #  , model      =  TRUE
    , method     =  "glm.fit"
 #  , x          =  FALSE
 #  , y          =  TRUE
    , contrasts  =  NULL
 #  , ...
  )
summary( Exam5.1.glm.2 )
#> 
#> Call:
#> glm(formula = F/N ~ X + I(X^2), family = quasibinomial(link = "logit"), 
#>     data = DataSet5.1, weights = NULL, start = NULL, method = "glm.fit", 
#>     contrasts = NULL)
#> 
#> Deviance Residuals: 
#>     Min       1Q   Median       3Q      Max  
#> -0.3909  -0.1442   0.1181   0.1454   0.2851  
#> 
#> Coefficients:
#>              Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -0.490760   0.259704  -1.890 0.085427 .  
#> X            0.511312   0.107904   4.739 0.000611 ***
#> I(X^2)      -0.029975   0.006617  -4.530 0.000858 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Dispersion parameter for quasibinomial family taken to be 0.06293754)
#> 
#>     Null deviance: 2.29474  on 13  degrees of freedom
#> Residual deviance: 0.69489  on 11  degrees of freedom
#> AIC: NA
#> 
#> Number of Fisher Scoring iterations: 4
#> 

##---Likelihood Ratio test for Model Exam5.1.glm.2
(LRExam5.1.glm.2   <-
  anova(
      object =  Exam5.1.glm.2
    , test   = "Chisq")
)
#> Analysis of Deviance Table
#> 
#> Model: quasibinomial, link: logit
#> 
#> Response: F/N
#> 
#> Terms added sequentially (first to last)
#> 
#> 
#>        Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
#> NULL                      13    2.29474              
#> X       1  0.18694        12    2.10780   0.08481 .  
#> I(X^2)  1  1.41292        11    0.69489 2.157e-06 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

WaldExam5.1.glm.2 <-
  wald.test(
      Sigma   = vcov(object=Exam5.1.glm.2)
    , b       = coef(object=Exam5.1.glm.2)
    , Terms   = 3
    , L       = NULL
    , H0      = NULL
    , df      = NULL
    , verbose = FALSE
  )

##---Sequential Fit of the logit Model 5th power terms involved
Exam5.1.glm.3 <-
  glm(
      formula    =  F/N~ X + I(X^2) + I(X^3) + I(X^4) + I(X^5)
    , family     =  quasibinomial(link = "logit")
    , data       =  DataSet5.1
    , weights    =  NULL
 #  , subset
 #  , na.action
    , start      =  NULL
 #  , etastart
 #  , mustart
 #  , offset
 #  , control    =  list(...)
 #  , model      =  TRUE
    , method     =  "glm.fit"
 #  , x          =  FALSE
 #  , y          =  TRUE
    , contrasts  =  NULL
 #  , ...
  )
summary(Exam5.1.glm.3)
#> 
#> Call:
#> glm(formula = F/N ~ X + I(X^2) + I(X^3) + I(X^4) + I(X^5), family = quasibinomial(link = "logit"), 
#>     data = DataSet5.1, weights = NULL, start = NULL, method = "glm.fit", 
#>     contrasts = NULL)
#> 
#> Deviance Residuals: 
#>      Min        1Q    Median        3Q       Max  
#> -0.36207  -0.15039   0.03148   0.16145   0.30127  
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.2986616  0.3875977  -0.771    0.463
#> X            0.2081471  0.7703070   0.270    0.794
#> I(X^2)       0.0603239  0.4225246   0.143    0.890
#> I(X^3)      -0.0120650  0.0821621  -0.147    0.887
#> I(X^4)       0.0008276  0.0064076   0.129    0.900
#> I(X^5)      -0.0000223  0.0001714  -0.130    0.900
#> 
#> (Dispersion parameter for quasibinomial family taken to be 0.07609603)
#> 
#>     Null deviance: 2.29474  on 13  degrees of freedom
#> Residual deviance: 0.62181  on  8  degrees of freedom
#> AIC: NA
#> 
#> Number of Fisher Scoring iterations: 4
#> 

## confint.default()   produce Wald Confidence interval as SAS produces
##---Likelihood Ratio test for Model 1
(LRExam5.1.glm.3   <-
  anova(
      object =  Exam5.1.glm.3
    , test   = "Chisq")
)
#> Analysis of Deviance Table
#> 
#> Model: quasibinomial, link: logit
#> 
#> Response: F/N
#> 
#> Terms added sequentially (first to last)
#> 
#> 
#>        Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
#> NULL                      13    2.29474             
#> X       1  0.18694        12    2.10780   0.1170    
#> I(X^2)  1  1.41292        11    0.69489 1.64e-05 ***
#> I(X^3)  1  0.07179        10    0.62310   0.3314    
#> I(X^4)  1  0.00000         9    0.62310   0.9952    
#> I(X^5)  1  0.00129         8    0.62181   0.8965    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

WaldExam5.1.glm.3 <-
  wald.test(
      Sigma   = vcov(object=Exam5.1.glm.3)
    , b       = coef(object=Exam5.1.glm.3)
    , Terms   = 6
    , L       = NULL
    , H0      = NULL
    , df      = NULL
    , verbose = FALSE
  )
Example 5.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-163)

References

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