emBinRegMixedMAR.md
In glmfitmiss: Fitting GLMs with Missing Data in Both Responses and Covariates

emBinRegMixedMAR works correctly

Code
  print(f_fit$beta)
Output

  Call:
  stats::glm(formula = formula, family = family, data = data_all, 
      weights = y_weight, method = if (method == "brglmFit") brglm2::brglmFit else method)

  Deviance Residuals: 
       Min        1Q    Median        3Q       Max  
  -2.23872  -0.40348  -0.06374   0.22143   2.39043

  Coefficients:
              Estimate StdError LowerCI UpperCI Pr(>|z|)    
  (Intercept)   0.1255   0.6452 -1.1390   1.390   0.8458    
  city         -0.7950   0.1832 -1.1540  -0.436 1.42e-05 ***
  soc           1.0518   0.4144  0.2396   1.864   0.0111 *  
  cond          4.6805   0.8164  3.0804   6.280 9.85e-09 ***
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for binomial family taken to be 1)

      Null deviance: 191.73  on 215  degrees of freedom
  Residual deviance: 101.15  on 212  degrees of freedom
  AIC:  107.71

  Type of estimator: AS_mixed (mixed bias-reducing adjusted score equations)
  Number of Fisher Scoring iterations: 4
Code
  print(f_fit$alpha)
Output

  Call:
  stats::glm(formula = form_r, family = stats::binomial(link = "logit"), 
      data = data_all, weights = ry_weight, method = if (method == 
          "brglmFit") brglm2::brglmFit else method)

  Deviance Residuals: 
       Min        1Q    Median        3Q       Max  
  -2.06035  -0.05086  -0.00321   0.05664   1.75448

  Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
  (Intercept)  1.67929    2.04131   0.823   0.4107    
  Wheeze       9.66215    2.39452   4.035 5.46e-05 ***
  city        -0.44090    0.30581  -1.442   0.1494    
  soc         -1.28773    0.58982  -2.183   0.0290 *  
  cond         1.78801    1.05385   1.697   0.0898 .  
  age         -0.20562    0.05193  -3.959 7.51e-05 ***
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for binomial family taken to be 1)

      Null deviance: 169.571  on 215  degrees of freedom
  Residual deviance:  28.412  on 210  degrees of freedom
  AIC:  37.703

  Type of estimator: AS_mixed (mixed bias-reducing adjusted score equations)
  Number of Fisher Scoring iterations: 12

emBinRegMixedMAR with Firth works correctly

Code
  print(fit2$beta)
Output

  Call:
  stats::glm(formula = formula, family = family, data = data_all, 
      weights = y_weight, method = if (method == "brglmFit") brglm2::brglmFit else method)

  Deviance Residuals: 
       Min        1Q    Median        3Q       Max  
  -0.74599  -0.15889  -0.10043  -0.06214   1.09636

  Coefficients:
               Estimate  StdError   LowerCI UpperCI Pr(>|z|)  
  (Intercept)  -7.83023   4.78066 -17.20015   1.540   0.1014  
  Numnill       1.17722   0.68935  -0.17389   2.528   0.0877 .
  Numsleep      0.04619   0.88143  -1.68138   1.774   0.9582  
  Smoke         0.51548   1.46412  -2.35415   3.385   0.7248  
  Set           0.33725   0.93477  -1.49487   2.169   0.7183  
  Reftime       0.21356   0.18085  -0.14089   0.568   0.2376  
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for binomial family taken to be 1)

      Null deviance: 19.6931  on 163  degrees of freedom
  Residual deviance:  7.8656  on 158  degrees of freedom
  AIC:  18.725

  Type of estimator: AS_mixed (mixed bias-reducing adjusted score equations)
  Number of Fisher Scoring iterations: 15
Code
  print(fit2$alpha)
Output

  Call:
  stats::glm(formula = form_r, family = stats::binomial(link = "logit"), 
      data = data_all, weights = ry_weight, method = if (method == 
          "brglmFit") brglm2::brglmFit else method)

  Deviance Residuals: 
       Min        1Q    Median        3Q       Max  
  -0.77227  -0.17871  -0.09675  -0.06141   1.09799

  Coefficients:
              Estimate Std. Error z value Pr(>|z|)  
  (Intercept)  -9.9631     4.8392  -2.059   0.0395 *
  resp          1.5613     1.9015   0.821   0.4116  
  Numnill       0.5698     0.5534   1.030   0.3032  
  Numsleep      0.1179     0.6730   0.175   0.8610  
  Smoke         2.0225     1.3098   1.544   0.1226  
  Set           0.6934     0.7985   0.868   0.3852  
  Reftime       0.2296     0.1239   1.853   0.0639 .
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  (Dispersion parameter for binomial family taken to be 1)

      Null deviance: 21.656  on 163  degrees of freedom
  Residual deviance:  8.398  on 157  degrees of freedom
  AIC:  21.413

  Type of estimator: AS_mixed (mixed bias-reducing adjusted score equations)
  Number of Fisher Scoring iterations: 34