Yaliwu
Linear mixed models
package  function  estimation  inference (tests)  inference (confidence intervals)  random effects (G structure)  residuals (R structure)  ~other 

nlme  lme  ML, REML  Wald (summary), likelihood ratio test (anova), sequential and marginal conditional F tests (anova)  Wald intervals on fixed and RE parameters (intervals)  multiple (nested) random effects; diagonal, blocked structures (pdClasses); crossed possible, but slow 
spatial and temporal correlations (corStruct), continuous and discrete heteroscedasticity (varStruct) 

lme4  lmer^{1} ML, REML  ML, REML  F statistics (sans denominator df: summary), likelihood ratio test (anova), posthoc MCMC (mcmcsamp)^{2} 
posthoc MCMC mcmcsamp  nested and crossed RE, $$\Sigma$$ diagonal or block diagonal^{3}  none  
lme4a  lmer^{4}  as above  as above  as above + likelihood profiles, fast parametric bootstrapping bootMer  as above  none  
lmm  ecmeml.lmm  ML(ECME algorithm)  
lmm  fastml.lmm  ML(rapidly Converging algorithm)  
asreml  asreml  Sparse matrix, Average Information REML  Wald anova  Standard errors  Multiple crossed/nested/blocked/splines  (Blocked) AR1xAR1, Matern, Factor Analytic, Heteroskedastic  
statmod  mixedModel2^{5}  REML  
SAS  PROC MIXED  REML,ML, MIVQUE0, or Type1–Type3(method= option)  wald t and F test  multiple,complex (you can define the covariance structure by type option in random statement)  
SAS  PROC GLIMMIX  pseduo likelihood(default),Laplace,GHQ,REML,PQL 
Wald, LRT(COVTEST Statement) ,Type III test for fixed effects  Wald (default),LRT  Multiple,nested or crossed  
SAS  HPMIXED  REML  wald t, F test, type III test and chisq test  wald intervals on fixed effect and random effect (CL option)  multiple,complex  
HLM  HLM  REML,FML  Multilevel,nested and or crossed random effects  
MLWiN  ML,MCMC  Multilevel,nested/crossed random effects  
Stata?  xtmixed//xtreg(randomintercept model)  REML,ML  Wald,LR test (with ML)  Wald  multilevel,nested/crossed,4 types of covariance structure diagonalblocked structures,Heteroskedastic random effects 
Heteroskedastic (residuals()), _ independent/exchangeable/unstructured/banded/exponential 
GLMMs
package  function  estimation  inference (tests)  inference (confidence intervals)  families  random effects  other 

lme4  glmer  Laplace, AGHQ  Wald (summary), LRT (anova), simulation tests of simple random effects (RLRsim package) 
Wald (by hand)  Poisson, binomial  multiple: nested, crossed  
lme4a  glmer  Laplace, AGHQ  Wald (summary), LRT (anova)  Wald (by hand): eventually, likelihood profiles  Poisson, binomial  multiple: nested, crossed  
glmmML  glmmML  Laplace, AGHQ  Wald  Poisson, binomial [logit, cloglog]  single  
glmmAK  logpoissonRE  MCMC  Wald  Poisson  single (normal or Gspline)  
MCMCglmm  MCMCglmm  MCMC  'Bayesian pvalue'  credible intervals (coda::HPDinterval)  Gaussian, Poisson, categorical, multinomial, exponential, geometric, categorical, various zeroinflated/altered 
multiple, complex  
MASS  glmmPQL  PQL  Wald (summary)  Wald  binomial, Poisson, Gamma, … (see ?family) 
spatial/temporal correlation structures (?nlme::corClasses) 

gamlss.mx  glmmNP  GHQ/Expectationmaximization  many (see gamlss.family in the gamlss.dist package)  single ("twolevel")  
glmmBUGS  glmmBUGS  MCMC  Poisson, Binomial  spatial effects  
hglm  hglm or hglm2  hierarchical likelihood  Wald (summary)  see ?family  
HGLMMM  HGLMfit  hierarchical likelihood first order Laplace ? 
Wald (summary) LRT (HGLMLRTest()) 
Binomial(logit),poisson(log),Normal(Identity), Gamma(log, inverse) 
complex,multiple  profile(LapFix=TRUE)  
bernor  bnlogl  Monte Carlo sampling  Bernoulli (logit link)  
glmmADMB  glmm.admb  Laplace  Wald (summary), LRT (anova), MCMC  Poisson, negative binomial, Bernoulli (+ zeroinflation)  single (multiple under development)  profiles  
repeated  glmm  GHQ  Wald (summary)  Wald (by hand)  see ?family  single  
RINLA  inla  nested Laplace  Poisson,Binomial [logit,probit,cloglog] Negative Binomial … 
Spatial and temporal correlation models  
SAS PROC GLIMMIX  PROC GLIMMIX  pseduo likelihood(default),Laplace,GHQ,REML,PQL 
Wald, LRT(COVTEST Statement) Type III test for fixed effects 
Wald (default),LRT  Binomial,Poisson,Gamma(check the Dist option)  multiple,nested and crossed  profile or nonprofile 
SAS PROC NLMIXED  PROC NLMIXED  GHQ, Firstorder method…(Check "method=" option) Laplace (QPOINTS=1 option) 
Wald, LRT  Wald  Normal,Binomial,Poisson,Binary,Gamma Negative Binomial, General (custom defined), zeroinflated 
number of random effects < 5 limited to only 2 levels 
NLMMs and other extensions
package  function  estimation  inference (tests)  inference (confidence intervals)  families  random effects  other 

nlme  nlme  ML OR REML  Wald t (summary) Wald F (anova) 
use intervals()  no specific family required ?  nested  
lme4  nlmer  Laplace or PQL (method option) 
wald (summary)  wald (hand?)  no family required  nested or crossed 
Accessors
lme (nlme)  glmmPQL (MASS)  [g]lmer (lme4)  [g]lmer (lme4a)  MCMCglmm  glmm.admb  

summary  estimate, std err, t, df, p  estimate, std err, t, df, p  lmer: estimate, std err, t glmer: est, std err, Z, p (Wald/asymptotic) 
like lme4  post.mean, CI, eff.sample  estimate,std.error,z values, p  
coef  all coefficients (predicted values for each group) 
✓  ✓  ✓  ✓  ✓  ✓ 
fixef  fixed effect parameters ($\beta$)  ✓  ✓  ✓  ✓  ✓  
ranef  random effect estimates ($u$)  ✓  ✓  ✓  ✓  ✓  
logLik  (marginal) loglikelihood  ✓  ✓  ✓  ✓  ✓  
AIC  marginal AIC  ✓  ✓  ✓  ✓  ✓  
confint  confidence intervals  ✓  ✓  ✓  
intervals  confidence intervals  ✓  ✓  
plot  diagnostic plots  ✓  ✓ (not diagnostic plots)  ✓  
predict  predicted values, allowing new data 
✓  ✓  ✓  ✓  ✓  
simulate  simulated values from fitted model 
✓  ✓  ✓ (for lmer)  ✓  
fitted  fitted values  ✓  ✓  ✓  ✓  ✓  ✓ 
update  update model  ✓  ✓  ✓  ✓  ✓  
residuals  ✓  ✓  ✓  ✓  
VarCorr  variancecovariance matrices of random effects 
✓  ✓  ✓  ✓  ✓  
coefplot  plot of coefficients and confidence/credible intervals 
✓  ✓  ✓  ✓  
anova  ✓  ✓  ✓ (no pvalues)  ✓(compare two models)  
drop1  ✓ (no LRT)  ✓  ✓(no pvalues) 
page revision: 103, last edited: 10 Dec 2011 04:07