mixalg function

Fitting Finite Mixture Models

This hybrid mixture algorithm combines the VEM algorithm for flexible support size and the EM algorithm for a fixed number of components. The solution of the VEM algorithm provides starting values for the EM algorithm. By the NPMLE theorem the EM algorithm thus starts very close to the global maximum and proper convergence of the EM algorithm to a global maximum is ensured.

The algorithm proceeds as follows

Step 1: Define an approximating grid lambda[1], ..., lambda[L]

Step 2: Use the VEM algorithm to maximize L(P) in the simplex $\Omega$ and identify grid points with positive support. Here positive support is defined as p[j] >= epsilon (often epsilon = 10^-2).

This gives an initial estimate of k.

Step 3: Use these k points and corresponding mixing weights p[j] as starting values for the EM algorithm

Step 4: Collapse identical components if | lambda[j]- lambda[i] | < delta (often delta=0.05) for i != j

Step 5: Obtain the final number of components k

This sequential algorithm leads to an initial estimate of the NPMLE and a proper solution for the subsequent EM algorithm. Crucial points are the definitions of $\delta$ and $\epsilon$. Depending on these settings different solutions could result from this algorithm.

mixalg(obs, weights=NULL, family="gaussian", data=NULL, pop.at.risk=NULL, 
       var.lnOR=NULL, limit=0.01, acc=10^(-7), numiter=5000, startk=50)

Arguments

• obs: observed / dependent variable. Vector or colname of data. Must be specified!
• weights: weights of the data. Vector or colname of data. Default is NULL.
• family: the underlying type density function as a character ("gaussian", "poisson" or "binomial")!
• data: an optional data frame. obs, weights, pop.at.risk and var.lnOR can be specified as column name of the data frame.
• pop.at.risk: population at risk: These data could be used to determine a mixture model for Poisson data. Vector or colname of data. Default isNULL.
• var.lnOR: variances of the data: These variances might be given when working with meta analyses! Vector or colname of data. Default is NULL.
• limit: parameter to control the limit of union several components. Default is 0.01.
• acc: convergence criterion. VEM and EM loops stop when deltaLL<acc. Default is 10^(-7).
• numiter: parameter to control the maximal number of iterations in the VEM and EM loops. Default is 5000.
• startk: starting/maximal number of components. This number will be used to compute the grid in the VEM. Default is 50.

Returns

The function returns a CAMAN.object, describing a finite mixture model. The main information about the mixture model is printed by just typing the