mixedMemModelVarInf: Constructor for a Mixed Membership Model object which can be...
In ysamwang/mixedMem: Tools for Discrete Multivariate Mixed Membership Models

Description Usage Arguments Details Value Examples

Constructor for a mixedMemModelVI object which can be used be fit using variational inference in the mixedMem package.

1 2	mixedMemModelVarInf(Total, J, Rj = rep(1, J), Nijr = array(1, dim = c(Total, J, max(Rj))), K, Vj, alpha, theta, phi = NULL, delta = NULL, dist, obs)

`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 responses 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] possible categories. 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, λ. 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).

The function returns an object of mixedMemModelVI class. This object contains dimensions of the model, the observed data, and the model parameters. Once a mixedMemModelVI 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, mixedMemModelVI will throw an error. For additional details on usage, and model assumptions, see the corresponding vignette "Fitting Mixed Membership Models Using mixedMem". Supported data types include Bernoulli, Multinomial, and Rank (Plackett-Luce). Note that the variational methods of mixeMem do not support the "Extended GoM" model which can be fit through the provided MCMC methods.

returns an object of class mixedMemModelVI

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)