# Constructor for a Mixed Membership Model Object Constructor for a `mixedMemModel` object which can be used for analysis in the `mixedMem` package. ```r 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. ## Returns 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 ```r 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) ```

mixedMemModel function