galamm-lmm.md
In galamm: Generalized Additive Latent and Mixed Models

LMM with simple factor works

Code
  print(VarCorr(mod), digits = 2)
Output
   Groups     Name     Std.Dev. Variance
   sid:school abil.sid 0.24     0.055   
   school     abil.sid 0.21     0.046   
   Residual            0.37     0.137

Code
  round(confint(mod, parm = "beta"), 2)
Output
                   2.5 % 97.5 %
  as.factor(item)1  0.52   0.77
  as.factor(item)2  0.48   0.72
  as.factor(item)3  0.42   0.67

Code
  round(confint(mod, parm = "lambda"), 2)
Output
          2.5 % 97.5 %
  lambda1  0.63   1.48
  lambda2  0.56   1.49

Code
  round(confint(mod, parm = "theta"), 2)
Output
         2.5 % 97.5 %
  theta1  0.26   1.00
  theta2  0.29   0.86

Code
  print(summary(mod2), digits = 2)
Output
  GALAMM fit by maximum marginal likelihood.
  Formula: y ~ 0 + as.factor(item) + (0 + abil.sid | school/sid)
     Data: IRTsub
  Control: galamm_control(reduced_hessian = TRUE)

       AIC      BIC   logLik deviance df.resid 
     403.1    432.8   -193.6    387.1      292

  Scaled residuals: 
     Min     1Q Median     3Q    Max 
   -1.75  -0.78   0.29   0.60   1.82

  Lambda:
          abil.sid   SE
  lambda1      1.0    .
  lambda2      1.1 0.19
  lambda3      1.0 0.22

  Random effects:
   Groups     Name     Variance Std.Dev.
   sid:school abil.sid 0.055    0.24    
   school     abil.sid 0.046    0.21    
   Residual            0.137    0.37    
  Number of obs: 300, groups:  sid:school, 237; school, 26

  Fixed effects:
                   Estimate Std. Error t value Pr(>|t|)
  as.factor(item)1     0.65      0.063    10.3  1.2e-24
  as.factor(item)2     0.60      0.062     9.6  6.2e-22
  as.factor(item)3     0.55      0.063     8.6  5.9e-18

LMM with simple factor works with Nelder-Mead

Code
  print(VarCorr(mod), digits = 2)
Output
   Groups     Name     Std.Dev. Variance
   sid:school abil.sid 0.24     0.055   
   school     abil.sid 0.21     0.046   
   Residual            0.37     0.137

Code
  round(confint(mod, parm = "beta"), 2)
Output
                   2.5 % 97.5 %
  as.factor(item)1  0.52   0.77
  as.factor(item)2  0.48   0.72
  as.factor(item)3  0.42   0.67

Code
  round(confint(mod, parm = "lambda"), 2)
Output
          2.5 % 97.5 %
  lambda1  0.63   1.48
  lambda2  0.56   1.49

Code
  round(confint(mod, parm = "theta"), 2)
Output
         2.5 % 97.5 %
  theta1  0.26   1.00
  theta2  0.29   0.86

Code
  print(summary(mod2), digits = 2)
Output
  GALAMM fit by maximum marginal likelihood.
  Formula: y ~ 0 + as.factor(item) + (0 + abil.sid | school/sid)
     Data: IRTsub
  Control: galamm_control(reduced_hessian = TRUE)

       AIC      BIC   logLik deviance df.resid 
     403.1    432.8   -193.6    387.1      292

  Scaled residuals: 
     Min     1Q Median     3Q    Max 
   -1.75  -0.78   0.29   0.60   1.82

  Lambda:
          abil.sid   SE
  lambda1      1.0    .
  lambda2      1.1 0.19
  lambda3      1.0 0.22

  Random effects:
   Groups     Name     Variance Std.Dev.
   sid:school abil.sid 0.055    0.23    
   school     abil.sid 0.046    0.21    
   Residual            0.137    0.37    
  Number of obs: 300, groups:  sid:school, 237; school, 26

  Fixed effects:
                   Estimate Std. Error t value Pr(>|t|)
  as.factor(item)1     0.65      0.063    10.3  1.2e-24
  as.factor(item)2     0.60      0.062     9.6  6.2e-22
  as.factor(item)3     0.55      0.063     8.6  5.9e-18