mixedMem (version 1.1.2)

mixedMemModel: Constructor for a Mixed Membership Model Object

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, fixedObs = NULL, P = NULL, beta = NULL)

Arguments

Total

the number of individuals in the sample.

J

the number of variables observed on each individual.

Rj

a vector of length J specifying the number of repeated measurements for each variable.

Nijr

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

K

the number of sub-populations.

Vj

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

alpha

a vector of length K which is the parameter for Dirichlet membership distribution.

theta

an array with dimensions (J,K,max(Vj)) which governs the variable distributions. The parameter theta[j,k,] governs the distribution of variable J for a complete member of sub-population k. For instance, if variable j is a Bernoulli variable, theta[j,k,1] is the probability of success; if variable j is a multinomial variable, theta[j,k, 1:Vj[j]] is the probability for each of the Vj[j] categories; if variable j is a rank variable, theta[j,k, 1:Vj[j]] are the support parameters for each of the Vj[j] alternatives. Since the dimension of the relevant parameters can differ across variables, any unused elements of the array should be set to 0, while all other elements should be positive.

phi

an array with dimensions (Total,K) which specifies the variational parameters for the membership vectors, \(\lambda\). The default group membership initialization is uniform across all groups (phi[i,k] = 1/K for all k). The default initialization is highly recommended.

delta

an array with dimensions (Total,J,max(Rj), max(Nijr), K) which specifies the variational parameters for the context vectors Z. The default initialization is uniform across all sub-populations (delta[i, j, r, n, k] = 1/K for all k).

dist

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

obs

an array with dimensions (Total,J,max(Rj), max(Nijr)) corresponding to the observed data. For Bernoulli random variables, the data consist of 0/1's. For multinomial or rank data the data consist of integers 0,1,…,(Vj[j]-1).

fixedObs

an array with dimensions (1, J, max(Rj), max(Nijr)) corresonding to the observed responses for a fixed group in the extended GoM model from Erosheva et al (2007)

P

scalar between 0 and 1 corresponding to initial value for the proportion of individuals in the fixed group

beta

scalar between 0 and 1 corresponding to the initial value of beta, the conditional probability of being in the fixed group for an individual who's observed responses match the fixed group.

Value

returns an object of class mixedMemModel

Details

The function returns an object of mixedMemModel class. This object contains dimensions of the model, the observed data, and the model parameters. Once a mixedMemModel object is created, the specified model can be fit for the data using the mmVarFit function. If the inputs are inconsistent (ie if dimensions do not match, or if observations and distribution types are not compatible,mixedMemModel will throw an error. For additional details on usage, and model assumptions, see the corresponding vignette "Fitting Mixed Membership Models Using mixedMem".

Examples

# NOT RUN {
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 categories/alternatives for each variable. For the Bernoulli, Vj = 1
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]))

# Items selected for each observation. For Multinomial and Bernoulli, this is always 1
# For rank data, this will be the number of alternatives 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)
# }