# glm:

Call:
glm(formula = y ~ x, family = binomial, data = data)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.1760  -0.6544  -0.3063   0.7146   2.1079  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -30.0715     5.7563  -5.224 1.75e-07 ***
x             2.9673     0.5697   5.208 1.90e-07 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 137.186  on 99  degrees of freedom
Residual deviance:  92.719  on 98  degrees of freedom
AIC: 96.719

Number of Fisher Scoring iterations: 5


# glm-quasi:

Call:
glm(formula = y ~ x, family = quasibinomial, data = data)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.1760  -0.6544  -0.3063   0.7146   2.1079  

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -30.0715     5.6353  -5.336 6.12e-07 ***
x             2.9673     0.5577   5.320 6.56e-07 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

(Dispersion parameter for quasibinomial family taken to be 0.9584242)

    Null deviance: 137.186  on 99  degrees of freedom
Residual deviance:  92.719  on 98  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5


# glmmPQL:
Linear mixed-effects model fit by maximum likelihood
 Data: data 
       AIC      BIC    logLik
  663.8606 674.2812 -327.9303

Random effects:
 Formula: ~1 | id
        (Intercept)     Residual
StdDev:    6.426077 1.099915e-57

Variance function:
 Structure: fixed weights
 Formula: ~invwt 
Fixed effects: y ~ x 
                Value Std.Error DF   t-value p-value
(Intercept) -88.78542 11.150328 98 -7.962584       0
x             8.77422  1.113142 98  7.882390       0
 Correlation: 
  (Intr)
x -0.998

Standardized Within-Group Residuals:
          Min            Q1           Med            Q3           Max 
-4.416298e+41 -1.194443e+41  0.000000e+00  1.258129e+41  3.978170e+41 

Number of Observations: 100
Number of Groups: 100 

# glmmML:

Call:  glmmML(formula = y ~ x, data = data, cluster = id, family = binomial) 


               coef se(coef)       z Pr(>|z|)
(Intercept) -68.969   146.76 -0.4699    0.638
x             6.801    14.47  0.4701    0.638

Standard deviation in mixing distribution:  3.447 
Std. Error:                                 9.31 

Residual deviance: 92.49 on 97 degrees of freedom 	AIC: 98.49 

# MCMClogit:

Iterations = 1:10000
Thinning interval = 1 
Number of chains = 1 
Sample size per chain = 10000 

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

               Mean     SD Naive SE Time-series SE
(Intercept) -31.214 5.9184 0.059184        0.10766
x             3.081 0.5848 0.005848        0.01064

2. Quantiles for each variable:

              2.5%     25%     50%     75%   97.5%
(Intercept) -43.87 -35.031 -30.842 -27.041 -20.642
x             2.02   2.674   3.047   3.454   4.328