# Chapter 6 Building and using models

This chapter explains how to build and manipulate model objects starting from BUGS code.

## 6.1 Creating model objects

NIMBLE provides two functions for creating model objects: nimbleModel and readBUGSmodel. The first, nimbleModel, is more general and was illustrated in Chapter 2. The second, readBUGSmodel provides compatibility with BUGS file formats for models, variables, data, and initial values for MCMC.

In addition one can create new model objects from existing model objects.

### 6.1.1 Using nimbleModel to create a model

nimbleModel processes BUGS code to determine all the nodes, variables, and their relationships in a model. Any constants must be provided at this step. Data and initial values can optionally be provided. BUGS code passed to nimbleModel must go through nimbleCode.

We look again at the pump example from the introduction:

pumpCode <- nimbleCode({
for (i in 1:N){
theta[i] ~ dgamma(alpha,beta);
lambda[i] <- theta[i]*t[i];
x[i] ~ dpois(lambda[i])
}
alpha ~ dexp(1.0);
beta ~ dgamma(0.1,1.0);
})

pumpConsts <- list(N = 10,
t = c(94.3, 15.7, 62.9, 126, 5.24,
31.4, 1.05, 1.05, 2.1, 10.5))

pumpData <- list(x = c(5, 1, 5, 14, 3, 19, 1, 1, 4, 22))

pumpInits <- list(alpha = 1, beta = 1,

setData does two things: it sets the values of the data nodes, and it flags those nodes as containing data. nimbleFunction programmers can then use that information to control whether an algorithm should over-write data or not. For example, NIMBLE’s simulate functions by default do not overwrite data values but can be told to do so. Values of data variables can be replaced, and the indication of which nodes should be treated as data can be reset by using the resetData method, e.g. pump$resetData(). #### 6.1.1.3 Missing data values Sometimes one needs a model variable to have a mix of data and non-data, often due to missing data values. In NIMBLE, when data values are provided, any nodes with NA values will not be labeled as data. A node following a multivariate distribution must be either entirely observed or entirely missing. Here’s an example of running an MCMC on the pump model, with two of the observations taken to be missing. Some of the steps in this example are documented more below. NIMBLE’s default MCMC configuration will treat the missing values as unknowns to be sampled, as can be seen in the MCMC output here. pumpMiss <- pump$newModel()
pumpMiss$resetData() pumpDataNew <- pumpData pumpDataNew$x[c(1, 3)] <- NA
pumpMiss$setData(pumpDataNew) pumpMissConf <- configureMCMC(pumpMiss) pumpMissConf$addMonitors('x', 'alpha', 'beta', 'theta')
## thin = 1: alpha, beta, x, theta
pumpMissMCMC <- buildMCMC(pumpMissConf)
Cobj <- compileNimble(pumpMiss, pumpMissMCMC)

niter <- 10
set.seed(0)
Cobj$pumpMissMCMC$run(niter)
## NULL
samples <- as.matrix(Cobj$pumpMissMCMC$mvSamples)

samples[1:5, 13:17]
##      x[1] x[2] x[3] x[4] x[5]
## [1,]   17    1    2   14    3
## [2,]   11    1    4   14    3
## [3,]   14    1    9   14    3
## [4,]   11    1   24   14    3
## [5,]    9    1   29   14    3

Missing values may also occur in explanatory/predictor variables. Values for such variables should be passed in via the data argument to nimbleModel, with NA for the missing values. In some contexts, one would want to specify distributions for such explanatory variables, for example so that an MCMC would impute the missing values.

#### 6.1.1.4 Defining alternative models with the same code

Avoiding code duplication is a basic principle of good programming. In NIMBLE, one can use definition-time if-then-else statements to create different models from the same code. As a simple example, say we have a linear regression model and want to consider including or omitting x[2] as an explanatory variable:

regressionCode <- nimbleCode({
intercept ~ dnorm(0, sd = 1000)
slope1 ~ dnorm(0, sd = 1000)
if(includeX2) {
slope2 ~ dnorm(0, sd = 1000)
for(i in 1:N)
predictedY[i] <- intercept + slope1 * x1[i] + slope2 * x2[i]
} else {
for(i in 1:N) predictedY[i] <- intercept + slope1 * x1[i]
}
sigmaY ~ dunif(0, 100)
for(i in 1:N) Y[i] ~ dnorm(predictedY[i], sigmaY)
})

includeX2 <- FALSE
modelWithoutX2 <- nimbleModel(regressionCode, constants = list(N = 30),
check=FALSE)
modelWithoutX2$getVarNames() ## [1] "intercept" "slope1" ## [3] "predictedY" "sigmaY" ## [5] "lifted_d1_over_sqrt_oPsigmaY_cP" "Y" ## [7] "x1" includeX2 <- TRUE modelWithX2 <- nimbleModel(regressionCode, constants = list(N = 30), check = FALSE) modelWithX2$getVarNames()
## [1] "intercept"                       "slope1"
## [3] "slope2"                          "predictedY"
## [5] "sigmaY"                          "lifted_d1_over_sqrt_oPsigmaY_cP"
## [7] "Y"                               "x1"
## [9] "x2"

Whereas the constants are a property of the model definition – since they may help determine the model structure itself – data nodes can be different in different copies of the model generated from the same model definition. The setData and setInits described above can be used for each copy of the model.

#### 6.1.1.5 Providing dimensions via nimbleModel

nimbleModel can usually determine the dimensions of every variable from the declarations in the BUGS code. However, it is possible to use a multivariate object only with empty indices (e.g. x[,]), in which case the dimensions must be provided as an argument to nimbleModel.

Here’s an example with multivariate nodes. The first provides indices, so no dimensions argument is needed, while the second omits the indices and provides a dimensions argument instead.

code <- nimbleCode({
y[1:K] ~ dmulti(p[1:K], n)
p[1:K] ~ ddirch(alpha[1:K])
log(alpha[1:K]) ~ dmnorm(alpha0[1:K], R[1:K, 1:K])
})

K <- 5
model <- nimbleModel(code, constants = list(n = 3, K = K,
alpha0 = rep(0, K), R = diag(K)),
check = FALSE)

codeAlt <- nimbleCode({
y[] ~ dmulti(p[], n)
p[] ~ ddirch(alpha[])
log(alpha[]) ~ dmnorm(alpha0[], R[ , ])
})

model <- nimbleModel(codeAlt, constants = list(n = 3, K = K, alpha0 = rep(0, K),
R = diag(K)),
dimensions = list(y = K, p = K, alpha = K),
check = FALSE)

In that example, since alpha0 and R are provided as constants, we don’t need to specify their dimensions.

### 6.1.2 Creating a model from standard BUGS and JAGS input files

Users with BUGS and JAGS experience may have files set up in standard formats for use in BUGS and JAGS. readBUGSmodel can read in the model, data/constant values and initial values in those formats. It can also take information directly from R objects somewhat more flexibly than nimbleModel, specifically allowing inputs set up similarly to those for BUGS and JAGS. In either case, after processing the inputs, it calls nimbleModel. Note that unlike BUGS and JAGS, only a single set of initial values can be specified in creating a model. Please see help(readBUGSmodel) for argument details.

As an example of using readBUGSmodel, let’s create a model for the pump example from BUGS.

pumpDir <- system.file('classic-bugs', 'vol1', 'pump', package = 'nimble')
pumpModel <- readBUGSmodel('pump.bug', data = 'pump-data.R',
inits = 'pump-init.R', dir = pumpDir)
## Detected x as data within 'constants'.

Note that readBUGSmodel allows one to include var and data blocks in the model file as in some of the BUGS examples (such as inhaler). The data block pre-computes constant and data values. Also note that if data and inits are provided as files, the files should contain R code that creates objects analogous to what would populate the list if a list were provided instead. Please see the JAGS manual examples or the classic_bugs directory in the NIMBLE package for example syntax. NIMBLE by and large does not need the information given in a var block but occasionally this is used to determine dimensionality, such as in the case of syntax like xbar <- mean(x[]) where x is a variable that appears only on the right-hand side of BUGS expressions.

Note that NIMBLE does not handle formatting such as in some of the original BUGS examples in which data was indicated with syntax such as data x in 'x.txt'.

### 6.1.3 Making multiple instances from the same model definition

Sometimes it is useful to have more than one copy of the same model. For example, an algorithm (i.e., nimbleFunction) such as an MCMC will be bound to a particular model before it is run. A user could build multiple algorithms to use the same model instance, or they may want each algorithm to have its own instance of the model.

There are two ways to create new instances of a model, shown in this example:

simpleCode <- nimbleCode({
for(i in 1:N) x[i] ~ dnorm(0, 1)
})

# Return the model definition only, not a built model
simpleModelDefinition <- nimbleModel(simpleCode, constants = list(N = 10),
returnDef = TRUE, check = FALSE)
# Make one instance of the model
simpleModelCopy1 <- simpleModelDefinition$newModel(check = FALSE) # Make another instance from the same definition simpleModelCopy2 <- simpleModelDefinition$newModel(check = FALSE)
# Ask simpleModelCopy2 for another copy of itself
simpleModelCopy3 <- simpleModelCopy2$newModel(check = FALSE) Each copy of the model can have different nodes flagged as data and different values in any nodes. They cannot have different values of N because that is a constant; it must be a constant because it helps define the model. ## 6.2 NIMBLE models are objects you can query and manipulate NIMBLE models are objects that can be modified and manipulated from R. In this section we introduce some basic ways to use a model object. Chapter 13 covers more topics for writing algorithms that use models. ### 6.2.1 What are variables and nodes? This section discusses some basic concepts and terminology to be able to speak about NIMBLE models clearly. Suppose we have created a model from the following BUGS code. mc <- nimbleCode({ a ~ dnorm(0, 0.001) for(i in 1:5) { y[i] ~ dnorm(a, sd = 0.1) for(j in 1:3) z[i,j] ~ dnorm(y[i], tau) } tau ~ dunif(0, 20) y.squared[1:5] <- y[1:5]^2 }) model <- nimbleModel(mc, data = list(z = matrix(rnorm(15), nrow = 5))) In NIMBLE terminology: • The variables of this model are a, y, z, and y.squared. • The nodes of this model are a, y[1] $$,\ldots,$$ y[5], z[1,1] $$,\ldots,$$ z[5, 3], and y.squared[1:5]. In graph terminology, nodes are vertices in the model graph. • The node functions of this model are a ~ dnorm(0, 0.001), y[i] ~ dnorm(a, 0.1), z[i,j] ~ dnorm(y[i], sd = 0.1), and y.squared[1:5] <- y[1:5]^2. Each node’s calculations are handled by a node function. Sometimes the distinction between nodes and node functions is important, but when it is not important we may refer to both simply as nodes. • The scalar elements of this model include all the scalar nodes as well as the scalar elements y.squared[1] $$,\ldots,$$ y.squared[5] of the multivariate node y.squared[1:5]. ### 6.2.2 Determining the nodes and variables in a model One can determine the variables in a model using getVarNames and the nodes in a model using getNodeNames. Optional arguments to getNodeNames allow you to select only certain types of nodes, as discussed in Section 13.1.1 and in the R help for getNodeNames. model$getVarNames()
## [1] "a"                            "y"
## [3] "lifted_d1_over_sqrt_oPtau_cP" "z"
## [5] "tau"                          "y.squared"
model$getNodeNames() ## [1] "a" "tau" ## [3] "y[1]" "y[2]" ## [5] "y[3]" "y[4]" ## [7] "y[5]" "lifted_d1_over_sqrt_oPtau_cP" ## [9] "y.squared[1:5]" "z[1, 1]" ## [11] "z[1, 2]" "z[1, 3]" ## [13] "z[2, 1]" "z[2, 2]" ## [15] "z[2, 3]" "z[3, 1]" ## [17] "z[3, 2]" "z[3, 3]" ## [19] "z[4, 1]" "z[4, 2]" ## [21] "z[4, 3]" "z[5, 1]" ## [23] "z[5, 2]" "z[5, 3]" Note that some of the nodes may be ‘lifted’ nodes introduced by NIMBLE (Section 13.1.2). In this case lifted_d1_over_sqrt_oPtau_cP (this is a node for the standard deviation of the z nodes using NIMBLE’s canonical parameterization of the normal distribution) is the only lifted node in the model. To determine the dependencies of one or more nodes in the model, you can use getDependencies as discussed in Section 13.1.3. ### 6.2.3 Accessing nodes Model variables can be accessed and set just as in R using $ and [[ ]]. For example

model$a <- 5 model$a
## [1] 5
model[["a"]]
## [1] 5
model$y[2:4] <- rnorm(3) model$y
## [1]         NA -0.9261095 -0.1771040  0.4020118         NA
model[["y"]][c(1, 5)] <- rnorm(2)
model$y ## [1] -0.7317482 -0.9261095 -0.1771040 0.4020118 0.8303732 model$z[1,]
## [1] -0.3340008  1.2079084  0.5210227

While nodes that are part of a variable can be accessed as above, each node also has its own name that can be used to access it directly. For example, y[2] has the name ‘y[2]’ and can be accessed by that name as follows:

model[["y[2]"]]
## [1] -0.9261095
model[["y[2]"]] <- -5
model$y ## [1] -0.7317482 -5.0000000 -0.1771040 0.4020118 0.8303732 model[["z[2, 3]"]] ## [1] -0.1587546 model[["z[2:4, 1:2]"]][1, 2] ## [1] -1.231323 model$z[2, 2]
## [1] -1.231323

Notice that node names can include index blocks, such as model[["z[2:4, 1:2]"]], and these are not strictly required to correspond to actual nodes. Such blocks can be subsequently sub-indexed in the regular R manner, such as model[["z[2:4, 1:2]"]][1, 2].

### 6.2.4 How nodes are named

Every node has a name that is a character string including its indices, with a space after every comma. For example, X[1, 2, 3] has the name ‘X[1, 2, 3]’. Nodes following multivariate distributions have names that include their index blocks. For example, a multivariate node for X[6:10, 3] has the name ‘X[6:10, 3]’.

The definitive source for node names in a model is getNodeNames, described previously.

In the event you need to ensure that a name is formatted correctly, you can use the expandNodeNames method. For example, to get the spaces correctly inserted into ‘X[1,1:5]’:

multiVarCode <- nimbleCode({
X[1, 1:5] ~ dmnorm(mu[], cov[,])
X[6:10, 3] ~ dmnorm(mu[], cov[,])
})

multiVarModel <- nimbleModel(multiVarCode, dimensions =
list(mu = 5, cov = c(5,5)), calculate = FALSE)

multiVarModel$expandNodeNames("X[1,1:5]") ## [1] "X[1, 1:5]" Alternatively, for those inclined to R’s less commonly used features, a nice trick is to use its parse and deparse functions. deparse(parse(text = "X[1,1:5]", keep.source = FALSE)[[1]]) ## [1] "X[1, 1:5]" The keep.source = FALSE makes parse more efficient. ### 6.2.5 Why use node names? Syntax like model[["z[2, 3]"]] may seem strange at first, because the natural habit of an R user would be model[["z"]][2,3]. To see its utility, consider the example of writing the nimbleFunction given in Section 2.8. By giving every scalar node a name, even if it is part of a multivariate variable, one can write functions in R or NIMBLE that access any single node by a name, regardless of the dimensionality of the variable in which it is embedded. This is particularly useful for NIMBLE, which resolves how to access a particular node during the compilation process. ### 6.2.6 Checking if a node holds data Finally, you can query whether a node is flagged as data using the isData method applied to one or more nodes or nodes within variables: model$isData('z[1]')
## [1] TRUE
model$isData(c('z[1]', 'z[2]', 'a')) ## [1] TRUE TRUE FALSE model$isData('z')
##  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [15] TRUE
model\$isData('z[1:3, 1]')
## [1] TRUE TRUE TRUE