agridat_mixed_model_example.R
In agridat: Agricultural Datasets

## ----setup------------------------------------------------------------------------------
library(agridat)
data(crowder.seeds)
dat <- crowder.seeds

## ----plot-------------------------------------------------------------------------------
libs(lattice)
dotplot(germ/n~gen|extract, dat, main="crowder.seeds", xlab="gen")

## ----brms, eval=FALSE-------------------------------------------------------------------
# if(require(brms)){
#   m1.brms <- brms::brm( germ|trials(n)~ gen*extract,
#      data = dat,
#      family = binomial,
#      chains=3, iter=3000, warmup=1000)
#   summary(m1.brms)
#   # round(  summary(m1.brms)$fixed[,1:4] , 2)
#   #                        Estimate Est.Error l-95% CI u-95% CI
#   # Intercept                 -0.42      0.18    -0.77    -0.06
#   # genO75                    -0.14      0.22    -0.56     0.29
#   # extractcucumber            0.55      0.25     0.07     1.05
#   # genO75:extractcucumber     0.77      0.30     0.18     1.36
# }

## ----glm,eval=FALSE---------------------------------------------------------------------
# # ----- GLM.
# # family=binomial() fixes dispersion at 1
# # family=quasibinomial() estimates dispersion, had larger std errors
# m1.glm <- glm(cbind(germ,n-germ) ~ gen*extract,
#               data=dat,
#               #family="binomial",
#               family=quasibinomial()
#               )
# summary(m1.glm)
# ## round(summary(m1.glm)$coef,2)
# ##                        Estimate Std. Error t value Pr(>|t|)
# ## (Intercept)               -0.41       0.25   -1.64     0.12
# ## genO75                    -0.15       0.30   -0.48     0.64
# ## extractcucumber            0.54       0.34    1.58     0.13
# ## genO75:extractcucumber     0.78       0.42    1.86     0.08

## ----eval=FALSE-------------------------------------------------------------------------
#   # ----- Stan using pre-built models from rstanarm
#   libs(tidyverse, rstan, rstanarm,bayesplot)
#   set.seed(42)
#   m1.stan <- stan_glm( cbind(germ,n-germ) ~ gen*extract,
#                       data=dat,
#                       family = binomial(link="logit")  )
#   summary(m1.stan)
#   ## round(posterior_interval(m1.stan, prob=.90),3)
#   #                            5%    95%
#   # (Intercept)            -0.728 -0.115
#   # genO75                 -0.506  0.243
#   # extractcucumber         0.133  0.947
#   # genO75:extractcucumber  0.255  1.267
# 
#   libs(bayesplot)
#   mcmc_areas(m1.stan, prob = 0.9) +
#     ggtitle("Posterior distributions",
#             "with medians and 95 pct intervals")
# 

## ----asreml,eval=FALSE------------------------------------------------------------------
# if(require(asreml)){
#   m1.asreml <- asreml(germ ~ gen*extract,
#                       data=dat,
#                       random= ~ plate,
#                       family=asr_binomial(dispersion=1, total=n))
#   summary(m1.asreml)
#   ##
#   ##                          effect
#   ## (Intercept)               -0.47
#   ## gen_O73                    0.00
#   ## gen_O75                   -0.08
#   ## extract_bean               0.00
#   ## extract_cucumber           0.51
#   ## gen_O73:extract_bean       0.00
#   ## gen_O73:extract_cucumber   0.00
#   ## gen_O75:extract_bean       0.00
#   ## gen_O75:extract_cucumber   0.83
# 
# }

## ----glmmpql,eval=FALSE-----------------------------------------------------------------
# # --- GLMM.  Assumes Gaussian random effects
# libs(MASS)
# m1.glmm <- glmmPQL(cbind(germ, n-germ) ~ gen*extract,
#                    random= ~1|plate,
#                    family=binomial(), data=dat)
# summary(m1.glmm)
# ## round(summary(m1.glmm)$tTable,2)
# ##                        Value Std.Error DF t-value p-value
# ## (Intercept)            -0.44      0.25 17   -1.80    0.09
# ## genO75                 -0.10      0.31 17   -0.34    0.74
# ## extractcucumber         0.52      0.34 17    1.56    0.14
# ## genO75:extractcucumber  0.80      0.42 17    1.88    0.08
# 

## ----glmmtmb,eval=FALSE-----------------------------------------------------------------
# libs(glmmTMB)
# m1.glmmtmb <- glmmTMB(cbind(germ, n-germ) ~ gen*extract + (1|plate),
#                       data=dat,
#                       family=binomial)
# round(summary(m1.glmmtmb)$coefficients$cond , 2)
# ##                        Estimate Std. Error z value Pr(>|z|)
# ## (Intercept)               -0.45       0.22   -2.03     0.04
# ## genO75                    -0.10       0.28   -0.35     0.73
# ## extractcucumber            0.53       0.30    1.74     0.08
# ## genO75:extractcucumber     0.81       0.38    2.11     0.04

## ----hglm,eval=FALSE--------------------------------------------------------------------
# # ----- HGML package. Beta-binomial with beta-distributed random effects
# if(require(hglm)){
#   m1.hglm <- hglm(fixed= germ/n ~ I(gen=="O75")*extract, weights=n, data=dat,
#                   random=~1|plate, family=binomial(), rand.family=Beta(),
#                   fix.disp=1)
#   summary(m1.hglm)
#   # round(summary(m1.hglm)$FixCoefMat,2)
#   ##                                     Estimate Std. Error t-value Pr(>|t|)
#   ## (Intercept)                            -0.47       0.24   -1.92     0.08
#   ## I(gen == "O75")TRUE                    -0.08       0.31   -0.25     0.81
#   ## extractcucumber                         0.51       0.33    1.53     0.16
#   ## I(gen == "O75")TRUE:extractcucumber     0.83       0.43    1.92     0.08
# }

## ----inla,eval=FALSE--------------------------------------------------------------------
# if(require(INLA)){
#   #gen,extract are fixed. plate is a random effect
#   #Priors for hyper parameters. See: inla.doc("pc.prec")
#   hyper1 = list(theta = list(prior="pc.prec", param=c(1,0.01)))
#   m1.inla = inla(germ ~ gen*extract + f(plate, model="iid", hyper=hyper1),
#                  data=crowder.seeds,
#                  family="binomial", Ntrials=n,
#                  control.family=list(control.link=list(model="logit")))
#   round( summary(m1.inla)$fixed, 2)
#   ##                         mean   sd 0.025quant 0.5quant 0.975quant  mode kld
#   ## (Intercept)            -0.47 0.24      -0.96    -0.46       0.00 -0.46   0
#   ## genO75                 -0.08 0.31      -0.68    -0.09       0.54 -0.09   0
#   ## extractcucumber         0.53 0.33      -0.13     0.53       1.18  0.53   0
#   ## genO75:extractcucumber  0.82 0.43      -0.01     0.82       1.69  0.82   0
# }

## ----rjags,eval=FALSE-------------------------------------------------------------------
# 
# # JAGS/BUGS.  See https://mathstat.helsinki.fi/openbugs/Examples/Seeds.html
# # Germination rate depends on p, which is a logit of a linear predictor
# # based on genotype and extract, plus random deviation to intercept
# 
# # To match the output on the BUGS web page, use: dat$gen=="O73".
# # We use dat$gen=="O75" to compare with the parameterization above.
# 
# jdat =list(germ = dat$germ, n = dat$n,
# root = as.numeric(dat$extract=="cucumber"),
# gen = as.numeric(dat$gen=="O75"),
# nobs = nrow(dat))
# 
# jinit = list(int = 0, genO75 = 0, extcuke = 0, g75ecuke = 0, tau = 10)
# 
# # Use logical names (unlike BUGS documentation)
# mod.bug =
# "model {
#   for(i in 1:nobs) {
#     germ[i] ~ dbin(p[i], n[i])
#     b[i] ~ dnorm(0.0, tau)
#     logit(p[i]) <- int + genO75 * gen[i] + extcuke * root[i] +
#                    g75ecuke * gen[i] * root[i] + b[i]
#   }
#   int ~ dnorm(0.0, 1.0E-6)
#   genO75 ~ dnorm(0.0, 1.0E-6)
#   extcuke ~ dnorm(0.0, 1.0E-6)
#   g75ecuke ~ dnorm(0.0, 1.0E-6)
#   tau ~ dgamma(0.001, 0.001)
#   sigma <- 1 / sqrt(tau)
# }"
# 
# libs(rjags)
# oo <- textConnection(mod.bug)
# j1 <- jags.model(oo, data=jdat, inits=jinit, n.chains=1)
# close(oo)
# 
# c1 <- coda.samples(j1, c("int","genO75","g75ecuke","extcuke","sigma"),
#                    n.iter=20000)
# summary(c1) # Medians are very similar to estimates from hglm
# # libs(lucid)
# # print(vc(c1),3)
# ##             Mean    SD    2.5%  Median   97.5%
# ## extcuke   0.543  0.331 -0.118   0.542   1.2
# ## g75ecuke  0.807  0.436 -0.0586  0.802   1.7
# ## genO75   -0.0715 0.309 -0.665  -0.0806  0.581
# ## int      -0.479  0.241 -0.984  -0.473  -0.0299
# ## sigma     0.289  0.142  0.0505  0.279   0.596
# 
# # Plot observed data with HPD intervals for germination probability
# c2 <- coda.samples(j1, c("p"), n.iter=20000)
# hpd <- HPDinterval(c2)[[1]]
# med <- summary(c2, quantiles=.5)$quantiles
# fit <- data.frame(med, hpd)
# 
# libs(latticeExtra)
# obs <- dotplot(1:21 ~ germ/n, dat,
#                main="crowder.seeds", ylab="plate",
#                col=as.numeric(dat$gen), pch=substring(dat$extract,1))
# obs + segplot(1:21 ~ lower + upper, data=fit, centers=med)
# 

## ----R2jags,eval=FALSE------------------------------------------------------------------
# libs("agridat")
# libs("R2jags")
# dat <- crowder.seeds
# 
# # To match the output on the BUGS web page, use: dat$gen=="O73".
# # We use dat$gen=="O75" to compare with the parameterization above.
# jdat =list(germ = dat$germ, n = dat$n,
#            root = as.numeric(dat$extract=="cucumber"),
#            gen = as.numeric(dat$gen=="O75"),
#            nobs = nrow(dat))
# 
# jinit = list(list(int = 0, genO75 = 0, extcuke = 0, g75ecuke = 0, tau = 10))
# 
# mod.bug = function() {
#   for(i in 1:nobs) {
#     germ[i] ~ dbin(p[i], n[i])
#     b[i] ~ dnorm(0.0, tau)
#     logit(p[i]) <- int + genO75 * gen[i] + extcuke * root[i] +
#       g75ecuke * gen[i] * root[i] + b[i]
#   }
#   int ~ dnorm(0.0, 1.0E-6)
#   genO75 ~ dnorm(0.0, 1.0E-6)
#   extcuke ~ dnorm(0.0, 1.0E-6)
#   g75ecuke ~ dnorm(0.0, 1.0E-6)
#   tau ~ dgamma(0.001, 0.001)
#   sigma <- 1 / sqrt(tau)
# }
# 
# parms <- c("int","genO75","g75ecuke","extcuke","sigma")
# 
# j1 <- jags(data=jdat, inits=jinit, parms, model.file=mod.bug,
#            n.iter=20000, n.chains=1)
# print(j1)
# ##          mu.vect sd.vect   2.5%    25%     50%     75%   97.5%
# ## extcuke    0.519   0.325 -0.140  0.325   0.531   0.728   1.158
# ## g75ecuke   0.834   0.429 -0.019  0.552   0.821   1.101   1.710
# ## genO75    -0.096   0.305 -0.670 -0.295  -0.115   0.089   0.552
# ## int       -0.461   0.236 -0.965 -0.603  -0.455  -0.312   0.016
# ## sigma      0.255   0.148  0.033  0.140   0.240   0.352   0.572
# ## deviance 103.319   7.489 90.019 98.010 102.770 108.689 117.288
# 
# traceplot(as.mcmc(j1))
# densityplot(as.mcmc(j1))
# HPDinterval(as.mcmc(j1))
# 
# }