bell_mccaffrey.md
In survey: Analysis of Complex Survey Samples

Bell-McAffrey standard errors run and are greater than linearized

Code
  summary(svyglm(api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey"))
Output

  Call:
  svyglm(formula = api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey")

  Survey design:
  dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)

  Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
  (Intercept)  99.85645   18.02030   5.541 0.000175 ***
  api99         0.90329    0.02734  33.039 2.33e-12 ***
  stypeH      -19.38726    5.43114  -3.570 0.004398 ** 
  stypeM      -18.15821    6.07011  -2.991 0.012267 *  
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for gaussian family taken to be 710.3237)

  Number of Fisher Scoring iterations: 2

Bell-McAffrey degrees of freedom go down

Code
  summary(svyglm(api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey",
  degf = TRUE))
Output

  Call:
  svyglm(formula = api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey", 
      degf = TRUE)

  Survey design:
  dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)

  Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
  (Intercept)  99.85645   18.02030   5.541  0.00218 ** 
  api99         0.90329    0.02734  33.039 2.39e-07 ***
  stypeH      -19.38726    5.43114  -3.570  0.01452 *  
  stypeM      -18.15821    6.07011  -2.991  0.02824 *  
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for gaussian family taken to be 710.3237)

  Number of Fisher Scoring iterations: 2

Code
  summary(svyglm(api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey-2",
  degf = TRUE))
Output

  Call:
  svyglm(formula = api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey-2", 
      degf = TRUE)

  Survey design:
  dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)

  Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
  (Intercept)  99.85645   18.02030   5.541  0.00989 ** 
  api99         0.90329    0.02734  33.039  3.8e-05 ***
  stypeH      -19.38726    5.43114  -3.570  0.03412 *  
  stypeM      -18.15821    6.07011  -2.991  0.05386 .  
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for gaussian family taken to be 710.3237)

  Number of Fisher Scoring iterations: 2

Bell-McAffrey degf work with confint.svyglm()

Code
  confint(svyglm(api00 ~ api99 + stype, design = dclus1, std.errors = "Bell-McAffrey",
  degf = TRUE))
Output
                    2.5 %      97.5 %
  (Intercept)  56.2792308 143.4336784
  api99         0.8387537   0.9678245
  stypeH      -33.1110597  -5.6634606
  stypeM      -31.8944852  -4.4219434
  attr(,"degf")
  (Intercept)       api99      stypeH      stypeM 
     6.308131    7.061340    5.304156    8.979698

Code
  confint(svyglm(as.factor(sch.wide) ~ api99 + stype, design = dclus1, family = "quasibinomial",
  std.errors = "Bell-McAffrey", degf = TRUE))
Output
                    2.5 %       97.5 %
  (Intercept) -0.50252632  6.077377146
  api99       -0.00549704  0.004222495
  stypeH      -3.04477253  0.830203522
  stypeM      -3.27515434 -0.014736530
  attr(,"degf")
  (Intercept)       api99      stypeH      stypeM 
     6.308131    7.061340    5.304156    8.979698