update_classes_wb function

Weight-based update of latent classes

This function updates the latent classes based on their class weights.

update_classes_wb(Cmax, epsmin, epsmax, distmin, s, b, Omega)

Arguments

• Cmax: The maximum number of classes.
• epsmin: The threshold weight (between 0 and 1) for removing a class.
• epsmax: The threshold weight (between 0 and 1) for splitting a class.
• distmin: The (non-negative) threshold difference in class means for joining two classes.
• s: The vector of class weights of length C. Set to NA if P_r = 0. For identifiability, the vector must be non-ascending.
• b: The matrix of class means as columns of dimension P_r x C. Set to NA if P_r = 0.
• Omega: The matrix of class covariance matrices as columns of dimension P_r*P_r x C. Set to NA if P_r = 0.

Returns

A list of updated values for s, b, and Omega.

Details

The updating scheme bases on the following rules:

• We remove class $c$, if $s_c\<\epsilon_{min}$, i.e. if the class weight $s_c$ drops below some threshold $\epsilon_{min}$. This case indicates that class $c$ has a negligible impact on the mixing distribution.
• We split class $c$ into two classes $c_1$ and $c_2$, if $s_c\>\epsilon_{max}$. This case indicates that class $c$ has a high influence on the mixing distribution whose approximation can potentially be improved by increasing the resolution in directions of high variance. Therefore, the class means $b_{c_1}$ and $b_{c_2}$ of the new classes $c_1$ and $c_2$ are shifted in opposite directions from the class mean $b_c$ of the old class $c$ in the direction of the highest variance.
• We join two classes $c_1$ and $c_2$ to one class $c$, if $||b_{c_1} - b_{c_2}||\<\epsilon_{distmin}$, i.e. if the euclidean distance between the class means $b_{c_1}$ and $b_{c_2}$ drops below some threshold $\epsilon_{distmin}$. This case indicates location redundancy which should be repealed. The parameters of $c$ are assigned by adding the values of $s$ from $c_1$ and $c_2$ and averaging the values for $b$ and $\Omega$. The rules are executed in the above order, but only one rule per iteration and only if Cmax is not exceeded.

Examples

### parameter settings
s <- c(0.8,0.2)
b <- matrix(c(1,1,1,-1), ncol=2)
Omega <- matrix(c(0.5,0.3,0.3,0.5,1,-0.1,-0.1,0.8), ncol=2)

### Remove class 2
RprobitB:::update_classes_wb(Cmax = 10, epsmin = 0.3, epsmax = 0.9, distmin = 1,
                             s = s, b = b, Omega = Omega)

### Split class 1
RprobitB:::update_classes_wb(Cmax = 10, epsmin = 0.1, epsmax = 0.7, distmin = 1,
                             s = s, b = b, Omega = Omega)

### Join classes
RprobitB:::update_classes_wb(Cmax = 10, epsmin = 0.1, epsmax = 0.9, distmin = 3,
                             s = s, b = b, Omega = Omega)