mixedMem (version 1.0.2)

mixedMemModel: Constructor for a Mixed Membership Model

Description

Constructor for a mixedMemModel object which can be used for analysis in the mixedMem package.

Usage

mixedMemModel(Total, J, Rj, Nijr, K, Vj, alpha, theta, phi = NULL,
  delta = NULL, dist, obs)

Arguments

Total

the number of individuals in the sample

J

the number of variables observed on each individual

Rj

vector of length J specifying the number of repeated measurements on each variable

Nijr

an array of dimension (Total, J, max(Rj)) indicating the number of ranking levels for each replication. For multinomial and bernoulli variables, Nijr[i,j,r] = 1. For rank variables, Nijr[i,j,r] indicates the number of candidates ranked.

K

the number of sub-populations

Vj

vector of length J specifying the number of possible candidates for each variable. For a bernoulli variable Vj[j] = 1.

alpha

vector of length K which is the hyperparameter for Dirichlet membership distribution

theta

array of dimension (J,K,max(Vj)) which governs the variable distributions. theta[j,k,] is the parameter for how sub-population k responds to the variable j. Initially, any element of theta corresponding to a valid candidate/category must be positive (ie

phi

array of dimension (Total,K) which specifies the variational parameters for the membership vectors, lambda. If left NULL, it is initialized to a uniformly across all groups. It is highly recommended to leave these NULL.

delta

array of dimension (Total,J,max(Rj), max(N), K) which specifies the variational parameters for the context vectors Z. If left blank, it is initialized to a uniformly across all sub-populations. It is highly recommended to leave these NULL.

dist

vector of length J specifying variable types. Options are "bernoulli", "multinomial" or "rank" corresponing to the distributions of the observed variables

obs

an array of dimension (Total,J,max(Rj), max(N)) corresponding to the observed data. For bernoulli random variables, this consists of 0/1's. For multinomial or rank data this consists of integers 0,1,...,(Vj[j]-1).

Value

• The mixedMemModel object

Details

The function returns an object of mixedMemModel class. This object holds dimensions of the model, the observed data, and the estimates of the model parameters. Once a mixedMemModel object is created, it can be fit using the mmVarFit function. For additional details on usage, and model assumptions, see the included vignette.

Examples

set.seed(123)
Total <- 50 # 50 Individuals
J <- 3 # 3 different variables
# distributions of each variable
dist <- c("multinomial", "bernoulli", "rank")
# 100 repeated measures of the multinomial, 5 repeated measures of the
# bernoulli, 1 repeated measure of the rank
Rj <- c(100, 5, 1)

K <- 4 # 4 sub-populations
alpha <- rep(.5, K) #hyperparameter for dirichlet distribution

# Number of choices for each variable. Note the Bernoulli must have 1 choice
Vj <- c(10, 1, 4)


theta <- array(0, dim = c(J, K, max(Vj)))
# Parameters governing multinomial
theta[1,,] <- gtools::rdirichlet(K, rep(.3, Vj[1]))
#parameters governing bernoulli
theta[2,,] <- cbind(rbeta(K, 1,1), matrix(0, nrow = K, ncol = Vj[1]-1))
theta[3,,] <- cbind(gtools::rdirichlet(K, rep(.3, Vj[3])),
 matrix(0, nrow = K, ncol = Vj[1]-Vj[3]))

# Candidates selected for each observation. For Multinomial and Bernoulli, this is always 1
# For rank data, this will be the number of candidates ranked
Nijr = array(0, dim = c(Total, J, max(Rj)))
Nijr[,1,c(1:Rj[1])] = 1 # N_ijr is 1 for multinomial variables
Nijr[,2,c(1:Rj[2])] = 1 # N_ijr is 1 for Bernoulli variables
Nijr[,3,c(1:Rj[3])] = sample.int(Vj[3], size = Total, replace = TRUE)

# generate random sample of observations
sampleMixedMem <- rmixedMem(Total, J, Rj, Nijr, K, Vj,
dist, theta, alpha)

## Initialize a mixedMemModel object
test_model <- mixedMemModel(Total = Total, J = J,Rj = Rj,
 Nijr= Nijr, K = K, Vj = Vj,dist = dist, obs = sampleMixedMem$obs,
  alpha = alpha, theta = theta)
# Look at Summary of the initialized model
summary(test_model)
# Plot the current values for theta
plot(test_model)